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PART II.: SPECIAL ANALYSIS. - Herbert Spencer, The Principles of Psychology 
The Principles of Psychology (London: Longman, Brown, Green and Longmans, 1855).
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COMPOUND QUANTITATIVE REASONING.
§ 16. An analysis conducted in a truly systematic manner, must commence with the most complex phenomena of the series to be analysed: must seek to resolve these into the phenomena that stand next in order of complexity: must proceed after like fashion with the less complex phenomena thus disclosed: and so, by successive decompositions, must descend step by step to the simpler and more general phenomena; reaching at last the simplest and most general. As applied to Psychology this mode of procedure, though perhaps, if patiently pursued, the best in its results, is beset with difficulties. The most ordinary operations of consciousness are sufficiently perplexing to those whose thinking powers have not been well disciplined; and its highly involved operations, if dealt with at the outset, may naturally be expected to tax the powers even of the habitual student. Disadvantageous, however, in this respect, as such an arrangement of the subject may be, both to reader and writer, it is so much better fitted than any other for the adequate presentation of the general law which it is the object of this Special Analysis to disclose, that I do not hesitate to adopt it. A little patience only is asked during the perusal of the next few chapters; which will be comparatively abstract and uninteresting. What he finds in them that is not very comprehensible, the reader must pass over until subsequent chapters give the key to it. Should some of the matters discussed seem to him unimportant, perhaps he will suspend his judgment until their bearing upon the doctrine at large becomes visible. And if, as is very possible, he should not perceive the reason for interpreting certain mental phenomena after a particular fashion—for insisting upon a special mode of regarding them and defining them—he is requested to take the analyses upon trust; in the belief that he will presently see them to be the true ones, and eventually see them to be the only possible ones. Thus much premised, let us pass to our immediate topic—Compound Quantitative Reasoning.
§ 17. Of ratiocinative acts exhibiting a high degree of complexity, the following will fitly serve as an example. Suppose an engineer who has constructed a bridge—say an iron tubular bridge—of given span, and who finds that it is just strong enough to bear the strain it is subject to (a strain resulting mainly from its own weight)—suppose such an engineer is required to construct another bridge of like nature, but of double the span. Possibly it will be supposed that for this new bridge he might simply magnify the previous design in all its particulars—simply make the tube double the depth, double the width, and double the thickness, as well as double the length. But, duly acquainted as he is with mechanical principles, he sees that a bridge so proportioned would not support tself—he infers that the depth, or the thickness of the metal, or both, must be more than double. Now by what acts of thought does he reach this conclusion? He knows, in the first place, that the bulks of similar masses of matter are to each other as the cubes of the linear dimensions; and that consequently, when the masses are not only similar in form, but of the same material, the weights also, are as the cubes of the linear dimensions. He knows, too, that in similar masses of matter which are subject to compression or tension, or, as in this case, to the transverse strain, the power of resistance varies as the squares of the linear dimensions. Hence he sees that if another bridge be built proportioned in all respects, exactly like the first, but of double the size, the weight of it—that is, the gravitative force, or force tending to make it bend and break—will have increased as the cubes of the dimensions; while the cohesive force—that is, the sustaining force, or force by which the breaking is resisted—will have increased only as the squares of the dimensions: and that, therefore, the bridge will give way. Or, to present the reasoning in a more formal manner, he sees that the—
whilst at the same time he sees that the—
Whence he infers that as the destroying force has increased in a much greater ratio than the sustaining force, the larger tube cannot sustain itself; seeing that the smaller one has no excess of strength.
But now, leaving out of sight the various acts by which the premisses are reached and by which the final inference is drawn, let us consider the nature of the particular mental process implied by the cognition that the ratio between the sustaining forces in the two tubes, must differ from the ratio between the destroying forces: for this process it is which here concerns us as an example of the most complex ratiocination. There is, be it observed, no direct comparison between these two ratios. How then is it known that they are unlike? It is known by the intermediation of two other ratios, to which they are severally equal.
The ratio between the two sustaining forces equals the ratio 12: 22. The ratio between the two destroying forces equals the ratio 13: 23. And as it is seen that the ratio 12: 22 is unequal to the ratio 13: 23; it is by implication seen, that the ratio between the sustaining forces is unequal to the ratio between the destroying forces. What now is the nature of this implication? or rather—What is the mental act by which this implication is perceived? It is manifestly not decomposable into steps. Though involving many elements, it is a single intuition: and if expressed in an abstract form, amounts to the axiom—Ratios which are severally equal to certain other ratios that are unequal to each other, are themselves unequal: or, reducing it to a still more abstract form—Relations which are severally equal to certain other relations that are unequal to each other, are themselves unequal.
I do not propose here to enter upon an analysis of this highly complex intuition; but simply present it as an example of the more intricate acts of thought which occur in Compound Quantitative Reasoning—an example to which the reader may presently recur if he pleases. A nearly allied but somewhat simpler intuition will better serve to initiate our analysis.
§ 18. This intuition is embodied in an axiom which has not, so far as I am aware, been specifically stated; though it is taken for granted in Proposition XI. of the fifth book of Euclid; in which, as we shall presently see, the wider of two assumptions is assigned in proof of the narrower. This proposition, which is to the effect that “Ratios which are equal to the same ratio are equal to one another,” it will be needful to quote in full.∗ It is as follows:—
Take of A, C, E, any equimultiples whatever G, H, K; and of B, D, F, any equimultiples whatever L, M, N.† Therefore since A is to B as C to D, and G, H, are taken equimultiples of A, C, and L, M, of B, D; if G be greater than L, H is greater than M; and if equal, equal; and if less, less. Again, because C is to D as E to F, and H, K, are equimultiples of C, E; and M, N, of D, F; if H be greater than M, K is greater than N; and if equal, equal; and if less, less. But if G be greater than L, it has been shown that H is greater than M; and if equal, equal; and if less, less: therefore, if G be greater than L, K is greater than N; and if equal, equal; and if less, less. And G, K are any equimultiple whatever of A, E; and L, N, any whatever of B, F; therefore as A is to B so is E to F.”
Let us now, for the sake of simplicity, neglect all such parts of this demonstration as consist in taking equimultiples and drawing the immediate inferences; and inquire by what process is established that final relation amongst these equimultiples which serves as the premiss for the desired conclusion. And to make the matter the clearer, let us here separate these equimultiples from the original magnitudes; and consider by itself the argument concerning them.
From the hypothesis and the construction, it is proved that if G be greater than L, H is greater than M; and if equal, equal; and if less, less: and, similarly, that if H be greater than M, K is greater than N; and if equal, equal; and if less, less. Whence it is inferred (and here comes the petitio principii) that if G be greater than L, K is greater than N; and if equal, equal; and if less, less. That this is an assumption, under a less definite form, of the very thing to be proved, will readily be seen on simplifying the verbiage. For what, in general language, is the fact established when it is shown that if G be greater than L, H is greater than M; and if equal, equal; and if less, less? The fact established is, that whatever relation subsists between G and L, the same relation subsists between H and M: whether it be a relation of superiority, of equality, or of inferiority: in other words, that so far as they are defined, the relations G to L and H to M are equal. So, too, with the relations H to M and K to N, which are proved to be equal in respect to the characteristics predicated of them. And then, when it has been shown that the relation G to L equals the relation H to M; and that the relation K to N also equals it; it is said that therefore the relation G to L equals the relation K to N. Which therefore, involves the assumption that relations which are equal to the same relation, are equal to each other—an assumption differing only in its higher generality from the proposition that “Ratios which are equal to the same ratio, are equal to each other,”—an assumption which itself needs proof, if the proposition to be established by it needs proof.
The only rejoinder which it seems possible to make to this criticism is, that in asserting that if G be greater than L, H is greater than M; and if equal, equal; and if less, less; it is not asserted that the relation G to L equals the relation H to M: for that, without negativing the assertion, G may be supposed to exceed L in a greater proportion than H exceeds M; and that, in this case, the relations will not be equal. One reply is, that the possibility of this supposition arises from the extreme vagueness of the definition of proportional magnitudes; and that it needs only to seize the true meaning of that definition, to see that no such assumption is permissible. Not to dwell upon this, however, it is a sufficient answer to the objection, that though the relations G to L, and H to M, are left to some extent indeterminate, and cannot therefore be called equal in an absolute sense, yet, so far as they are determinate, they are equal; and that if it be allowable to assume of indeterminate relations, that in the respects in which they are equal to the same, they are equal to each other, it must be allowable to assume as much of determinate relations. This will be clearly perceived on considering the matter under any one of its concrete aspects. Suppose it to have been shown that if G be greater than L, H is greater than M; and that if H be greater than M, K is greater than N; then it is said that if G be greater than L, K is greater than N. What now are here the premisses and inference? It is argued that the first relation being like the second in a certain particular (the superiority of its first magnitude); and the third relation being also like the second in this particular; the first relation must be like the third in this particular. If now it be allowable to assume that two relations which are severally like a third in any particular, are like each other in that particular; it is allowable to assume as much when they are like in all particulars, or are equal. The one truth is not more self-evident than the other. The act of thought is the same in each case; and is valid either in both or in neither. Evidently, then, the reasoning involves a disguised petitio principii.
Thus the general truth that relations which are equal to the same relation are equal to each other—a truth of which the foregoing proposition concerning ratios is simply one of the more concrete forms—must be regarded as an axiom. Like its prototype—things that are equal to the same thing are equal to each other—it is incapable of proof. Seeing how closely, indeed, the two are connected both in nature and origin, perhaps some will contend that the one is but a particular form of the other, and should be included under it—that a relation is simply one species of thing; and that what is true of all things is, by implication, true of relations. Much as may be said in support of this position, it is, however, necessary, as will presently be seen, to specifically enunciate this general law in respect to relations, even if it be held derivative. At the same time the criticism serves to bring into yet clearer view the axiomatic nature of the law. For whether it be or be not true that a relation must be regarded as a thing, it is unquestionably true that in any intellectual process serving to establish the general fact—Relations that are equal to the same relation are equal to each other—the concepts dealt with are the relations, and not the objects between which the relations subsist; that the equality of these relations can be perceived only by making them the objects of thought, and not by thinking of the related objects; and that hence the axiom, being established by the comparison of three concepts, is established by just the same species of mental act as though it referred to substantive things instead of relations.
The truth—Relations that are equal to the same relation are equal to each other—which we thus find is known by an intuition,∗ and can only so be known, underlies many important geometrical truths. An examination of the first proposition in the sixth book of Euclid, and of the deductions made from it in succeeding propositions, will show that there is a large class of theorems having this axiom for their basis—theorems which are at present ostensibly based upon the demonstration above shown to be fallacious.
§ 19. But this axiom has far wider and far more important applications. It is the foundation of all Mathematical Analysis. Alike in working out the simplest algebraic equation, and in performing those higher analytical processes of which algebra is the root, it is the one thing perpetually taken for granted. Whilst other axioms are specifically stated, this axiom is tacitly assumed at every step. It is true that the assumption is limited to that particular case of the axiom in which its necessity is so self-evident as to be almost unconsciously recognized; but it is not the less true that this assumption cannot be made without involving the axiom in its entire extent. The successive transformations of an equation we shall find to be linked together by acts of thought, of which this axiom expresses the most general form. Let us take an example and analyse it.
Now it may seem that the only assumptions involved in these three steps are—first, that if equals be added to equals, the sums are equal; second, that the square roots of equals are equals; and third, that if equals be taken from equals, the remainders are equal. But a little reflection will show that the several results reached in virtue of these assumptions lead to no conclusion if they stand alone: and they cannot be co-ordinated to any purpose without some further assumption being made. What is that assumption? As at present written, there is nothing to mark any connexion between the first form of the equation and the last. Manifestly, however, the validity of the inference x = 2, depends upon there being some perfectly specific connection between it and the original premiss x2 + 2x = 8; and this connection implies connections between the intermediate steps. This premised, the real process of thought involved will be at once recognized on inserting the required symbols, thus:—
That only in virtue of the successive cognitions thus represented does the conclusion legitimately follow from the original premiss, cannot fail to be seen, on considering that the argument is worthless unless the value of x in the last form of the equation, is the same as its value in the first; and that this implies the preservation throughout of a constant relation between the function of x and the function of its value under all their transformations—a constancy which is more strictly expressed by saying that their successive relations are equal. But now arises the question—In virtue of what assumption is it that the final relation subsisting between the two sides of the equation is asserted to be equal to the initial one? On this assumption it is that the worth of the conclusion ultimately depends; and for this assumption no warrant is assigned. I answer, the warrant for this assumption is the axiom—Relations that are equal to the same relation are equal to each other. Probably, at first sight, it will not be altogether manifest that this axiom is involved. It needs but to simplify the consideration of the matter, however, to render the fact apparent. Suppose that we represent the successive forms of the equation by the letters A, B, C, D. If now A, B, C, D had represented substantive things; and if, when it had been shown that A was equal to B, and B was equal to C, and C was equal to D, it had been concluded that A was equal to D; what would have been assumed? There would have been two assumptions of the axiom—Things that are equal to the same thing are equal to each other: one to establish the equality of A and C by the intermediation of B; and one to establish the equality of A and D by the intermediation of C. Now, the fact that A, B, C, D do not represent things, but represent relations between things, cannot be supposed fundamentally to alter the intellectual process by which the equality of the first and last is recognized. If, when A, B, C, D represent things, the equality of the first and last can be shown only by means of the axiom—Things that are equal to the same thing are equal to each other; then, manifestly, when A, B, C, D represent relations, the equality of the first and last can be shown only by means of the axiom—Relations that are equal to the same relation are equal to each other.
It is true that in this case the relations dealt with are relations of equality; and the great simplification hence resulting may produce some hesitation as to whether the process of thought really is the one described. Perhaps it will be argued that the successive forms of the equation being all, in virtue of their essential nature, relations of equality, it is known by an act of direct intuition that any one of them is equal to any other; or that if an axiom be appealed to, it is the axiom—All relations of equality are equal to each other. It must, without doubt, be conceded, that relations of equality, unlike all other relations and unlike all magnitudes, are in their very expression so defined as that the equality of any one of them to any other may be foreknown. But admitting this, the objection may be met in two ways. In the first place, it may be replied that every relation of equality can be known to equal every other relation of equality only through the cognition—Relations that are equal to the same relation are equal to each other. For like all general truths it must be originally derived from particular experiences: the particular experience forming the first step to it must be a perception of the equality of some two relations of equality: further progress towards the general truth requires a perception of the equality of one of these to some third relation of equality: and now be it observed that any further carrying out of this process to a fourth and a fifth, cannot lead to the generalization that all relations of equality are equal, until they have been compared in some other than their serial order. As in the case of magnitudes that have been recognized as successively equal, each to the next, the assertion that they are all equal implies an act of thought in which some two that are not adjacent have been perceived to be equal in virtue of their common equality to an intermediate third; so, in the case of relations, however obviously they are all equal, a like act of thought must be gone through. Yet a simpler proof is assignable. As the truth—All relations of equality are equal to each other, is more general than the truth—Relations of equality, that are equal to the same relation of equality are equal to each other; it must include this last; and cannot be reached without presupposing it. If this reply be considered inconclusive—as it will possibly be by those who contend for innate forms of thought—the second reply may be given; namely, that the relation subsisting between the two sides of an equation when reduced to its final form, is known to be a relation of equality only in virtue of its affiliation upon the original relation of equality, by means of all the intermediate relations. Strike out in the foregoing case, the several transformations which link the first and last forms of the equation together, and it cannot be logically known that x is equal to 2. If then this ultimate relation can be known to equal the first, only because it is known to equal the penultimate relation, and the penultimate relation to equal the antepenultimate, and so on; it is manifest that the affiliation of the last relation upon the first, unavoidably involves the axiom—Relations that are equal to the same relation are equal to each other.
It must be admitted that in cases like these in which this general axiom is applied to relations of equality, it seems very much like a superfluity—a formula that is more circuitous than the intuition it represents. And it is doubtless true that in such cases the cognition seems to merge into a simpler order of cognitions, from which it is with difficulty distinguishable. Nevertheless, I think the arguments adduced warrant the belief that the mental process described is gone through; though perhaps almost automatically: and indeed, if, when the relations are not relations of equality, the intuition expressed by this axiom is consciously achieved, it seems unavoidably to follow, that when the relations are those of equality, it is also achieved, even if unconsciously. And for this belief yet further warrant will be found, when, under another head, we come to consider the case of inequations—a case in which no such source of difficulty exists, and yet in which the process of thought is of like nature.
§ 20. Leaving here its several applications, and turning to consider the axiom itself, as being predicable alike of all relations, whether of equality or any degree of inequality, we have now to inquire by what process of thought it is known that relations which are equal to the same relation are equal to each other. We have seen that the fact is not demonstrable, but can be reached only by direct intuition. What is the character of this intuition?
Clearly if the equality of the first and third relations cannot be established by an act decomposable into steps, but can be established only by a single act, that single act must be one in which the first and third relations are brought into immediate relation before the consciousness. Yet any direct comparison of the first and third without the intermediation of the second would avail nothing; and any intermediation of the second would seem to involve a thinking of the three in their serial order—first, second, third; third, second, first—which, even could it be called a single act, would not bring the first and third into the immediate relation required. Hence, as neither a direct comparison of the first and third, nor a serial comparison of the three, can fulfil the requirement, it follows as the only remaining alternative, that they must be compared in couples. And this is what is really done. By the premisses it is known that the first and second relations are equal; and that the second and third relations are equal. There are, therefore, presented to consciousness, two relations of equality between relations. The direct intuition is that these two relations of equality are themselves equal. And as these two relations of equality possess a common term, the intuition that they are equal, involves the equality of the remaining terms. The nature of this mental process will, however, be best expressed by symbols. Suppose the several relations to stand thus:—A : B = C : D = E : F, then the act of thought by which the equality of the first and third relations is recognized may be symbolized thus:—∗
Careful introspection will, I think, confirm the inference that this represents the mental process gone through—that the first and second relations, contemplated as equal, form together one concept; that the third and second, similarly contemplated, form together another concept; and that, in the intuition of the equality of these concepts, the equality of the terminal relations is implied: or that to define its nature abstractedly—the axiom expresses an intuition of the equality of two relations between relations.
Probably to the minds of some readers, this analysis will not at once commend itself. Indeed, as at first remarked, it is an inconvenience attendant on commencing with the most complex intellectual processes, that the propriety of formulating them after a certain manner cannot be clearly perceived until the analysis of the simpler intellectual processes has shown why they must be thus formulated. After reading the next few chapters, the truth of the above conclusion will become manifest. In the meantime, though it may not be positively recognized as true by its perceivable correspondence with the facts of consciousness, it may yet be negatively recognized as true by contemplating the impossibility, lately shown, of establishing the equality of the first and last relations by any other intellectual act.
Before ending the chapter it should be observed, that the relations thus far dealt with are relations of magnitudes; and, properly speaking, relations of homogeneous magnitudes; or, in other words, ratios. In the case of the geometrical reasoning quoted from the fifth book of Euclid, this fact is definitely expressed; and though in the case of the algebraical reasoning it may at first be thought that the magnitudes dealt with are not homogeneous—seeing that the same equation often includes at once magnitudes of space, time, force, value,—yet it needs but to consider that these magnitudes can be treated algebraically only by reducing them to the common denomination of number—only by considering them as abstract magnitudes of the same order, to at once see that the relations dealt with are really those subsisting between homogeneous magnitudes—are really ratios; and might have been so named throughout. The motive for constantly speaking of them under the general name, relations, of which ratios are but one species, will be understood when it is seen, as it presently will be, that only when regarded under this most general form do they permit the intellectual processes by which they are co-ordinated to be brought under the same category with other acts of reasoning.
COMPOUND QUANTITATIVE REASONING (CONTINUED).
§ 21. The results reached in the last chapter do not, apparently, help us very far on the way to a theory of Quantitative Reasoning. Such an intuition as that expressed in the axiom educed, can form but one amongst the many intuitions which, joined together, constitute a mathematical argument. A moment's reflection will show that however many times quoted, or applied in thought, the axiom—Relations which are equal to the same relation are equal to each other, can never do anything else than establish the equality of some two relations by the intermediation of a series of relations severally equal to both: and there are few if any cases, save those furnished by algebraic and allied processes, in which the equality of two relations is the fact to be arrived at; or could be thus arrived at if it were. The proposition—“If two circles touch each other externally, the straight line which joins their centres shall pass through the point of contact,” is one with which such an axiom can have no concern: and the same is manifestly the case with the great majority of geometrical truths. Some more general cognition, then, has to be found.
Guidance in the search for such a cognition, may be drawn from the consideration that if a truly fundamental one, it must be involved not only in all other kinds of quantitative reasoning, but also in the kind exemplified in the preceding chapter. It must underlie both. This being an à priori necessity, it follows that as, in the case of algebraic reasoning, the foregoing axiom expresses in general language the sole cognition by which the successive steps are rationally co-ordinated, the required fundamental cognition must be somehow involved in it. I seems therefore, that our best course will be to continue the line of analysis already commenced.
If then, ceasing to consider in its totality the complex axiom—Relations which are equal to the same relation are equal to each other, we go on to inquire what are the simpler elements of thought into which it is proximately decomposable; we at once see that it twice over involves a recognition of the equality of some two relations. Before it is possible to predicate that the relations A : B and E : F being severally equal to the relation C : D, are equal to each other; it must first be predicated that the relation A : B is equal to the relation C : D; and that the relation C : D is equal to the relation E : F. Hence the intellectual act which we have now to consider, is the establishment of a relation of equality between two relations. And this is the intellectual act of which we are in search. An intuition of the equality of two relations is implied in every step, alike of that quantitative reasoning which deals with homogeneous magnitudes, and that which deals with magnitudes that are not homogeneous—is the ultimate ratiocinative act into which every complete mathematical argument is resolvable. Let us take as our first field for the exemplification of this fact, the demonstration of geometrical theorems.
§ 22. Before analysing the steps by which a proposition is proved, we may with advantage contemplate the substance of a proposition; and consider by what process the mind advances from that particular case of it which the demonstration establishes, to the recognition of its general truth. Let us take as an example, the proposition—“The angles at the base of an isosceles triangle are equal to each other.”
To establish this, the abstract terms are forthwith abandoned, and the proposition is re-stated in a concrete form. Let A B C be an isosceles triangle of which the side A B is equal to the side A C; then the angle A B C shall be equal to the angle A C B. By a series of steps which need not be here specified, the way is found from these premisses to this conclusion. It is definitely demonstrated that the angle A B C is equal to the angle A C B. But now mark what takes place. As soon as this particular fact has been proved, the general fact is immediately re-enunciated and held to be proved. We pass directly from the concrete inference—the angle A B C is equal to the angle A C B, to the abstract inference—therefore the angles at the base of an isosceles triangle are equal to each other. Q. E. D. Be the cogency of every step in the demonstration what it may, the truth of the proposition at large hinges entirely upon the cognition that what holds in this case holds in all cases. What now is the nature of this cognition? It is a consciousness of the equality of two relations: on the one hand, the relation subsisting between the sides and angles of the triangle A B C; and on the other hand, the relation subsisting between the sides and angles of another isosceles triangle, of any isosceles triangle, of all isosceles triangles. Whatever theory be espoused respecting the mode in which we figure to ourselves a class—whether in the present case the abstract fact be recognized only after it has been seen to hold in this isosceles triangle, and in this, and in this; or whether after it has been seen to hold in some ideal type of an isosceles triangle; does not in the least affect the position that the thing discerned is the equality of the relations presented in successive concepts. If we use the letter A to symbolize the premised fact (viz. that in the triangle A B C the sides A B and A C are equal), and the letter B to symbolize the fact asserted (viz. that the angle A B C is equal to the angle A C B); then, after establishing a certain relation (of coexistence) between A and B in this one case, we go on to affirm that the same relation holds between some other A and B, or all As and Bs: or strictly speaking, not the same relation, but an equal relation. And as, for this affirmation, we can assign no reason, it manifestly represents a simple intuition.
But not only do we pass from the special truth to the general truth by an intuition of the equality of two relations: a like intuition is implied in each of the steps by which the special truth is reached. In the demonstration of such special truth, the truths previously established are explicitly or implicitly referred to; and the relations that subsist in the case in hand are recognized as equal to relations which those previously established truths express. This will be at once seen on subjecting a demonstration to analysis. The one belonging to the foregoing theorem is inconveniently long: we shall find a fitter one in Proposition xxxii.
“If the side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.”
“Let A B C be a triangle, and let one of its sides B C be produced to D; then the exterior angle A C D is equal to the two interior and opposite angles C A B, A B C; and the three interior angles of the triangle, namely A B C, B C A, C A B, are together equal to two right angles.”
Thus, alike in each step by which the special conclusion is reached, and in the step taken from that special conclusion to the general one, the essential operation gone through is the establishment in consciousness of the equality of two relations. This is the bare abstract statement of the thing effected. If this is not done, nothing is done. And as, in each such cognition, the mental act is undecomposable—as for the assertion that any two such relations are equal, no reason can be assigned save that they are perceived to be so; it is manifest that the whole process of thought is thus expressed.
§ 23. Perhaps it will be deemed scarcely needful specifically to prove that each step in an algebraic argument is of the same nature. But though, by showing that the axiom—Relations which are equal to the same relation are equal to each other, twice involves an intuition of the above described kind, it may have been implied that the reasoning which proceeds upon that axiom, is built up of such intuitions; yet it will be well definitely to point out that only in virtue of such intuitions do the successive transformations formations of an equation become allowable. Unless it is perceived that a certain modification made in the form of the equation, leaves the relation between its two sides the same as before—unless it is seen that each new relation established is equal to the foregoing one, the reasoning is vicious and the result erroneous. A convenient mode of showing that the mental act continually repeated in one of these analytical processes is of the kind described, is suggested by an ordinary algebraic artifice. When a desired simplification may be thereby achieved, it is usual to throw any two forms of an equation into a proportion: a procedure in which the equality of the relations is specifically asserted. Here is an illustration: not such an one as the algebraist would choose; but one which will serve present purposes.
or, as it is otherwise written,
and if proof be needed that this mode of presenting the facts is legitimate, we may at once obtain it by multiplying extremes and means; whence results the truism—
This clearly shows that the mental act determining each algebraic transformation, is one in which the relation expressed by the new form of the equation is recognized as equal to the relation which the previous form expresses. Only in virtue of this equality is the step valid: and hence the intuition of this equality must be the essence of the step.
IMPERFECT AND SIMPLE QUANTITATIVE REASONING.
§ 24. Ability to perceive equality implies a correlative ability to perceive inequality: neither can exist without the other. But though inseparable in origin, the cognitions of equality and inequality, whether between things or relations, altogether differ in this; that whilst the one is essentially definite, the other is essentially indefinite. There is but one equality; but there may be numberless degrees of inequality. To assert an inequality, involves the affirmation of no fact, but merely the denial of a fact; and hence, as positing nothing specific, the cognition of inequality can never be a premiss to any specific conclusion.
Thus it happens that reasoning which is perfectly quantitative in its results, proceeds wholly by the establishment of equality between relations, the members of which are either equal, or one a known multiple of the other: and that, conversely, if any of the magnitudes standing in immediate relation are neither directly equal, nor the one equal to so many times the other; or if any of the successive relations which the reasoning establishes are unequal; the results are imperfectly quantitative. This truth is illustrated in that class of geometrical theorems in which it is asserted of some thing that it is greater or less than some other; that it falls within or without some other; and the like. Let us take as an example the proposition—“Any two sides of a triangle are together greater than the third side.”
“Let A B C be a triangle; any two sides of it are, together, greater than the third side; namely, B A, A C, greater than B C; and A B, B C, greater than A C; and B C, C A, greater than A B.”
“Produce B A to D, and make A D equal to A C; and join D C.”
It will be observed, that throughout this demonstration, though the magnitudes dealt with are unequal, yet the relations successively established are always equal to certain other relations: though the primary relations (between things) are those of inequality, yet the secondary relations (between relations) are those of equality. And this holds in the majority of imperfectly quantitative arguments. Though, as we shall by and by see, there are cases in which both the magnitudes and the relations are unequal, yet they are comparatively rare; and are incapable of any but the simplest forms.
§ 25. Another species of imperfectly quantitative reasoning occupies a position in mathematical analysis, like that which the foregoing species does in mathematical synthesis. The ordinary algebraic inequation supplies us with a sample of it.
Thus, if it is known that is less than the argument instituted is as follows:—
Now, in this case, as in the case of equations, the reasoning proceeds by steps, of which each asserts the equality of the new relation to the relation previously established: with this difference, that instead of the successive relations being relations of equality, they are relations of inferiority. That the general process of thought, however, is alike in both, will be obvious on considering that as the inferiority of x to y can be known only by deduction from the inferiority of to and as it can be so known only by the intermediation of other relations of inferiority; the possibility of the argument depends upon the successive relations being recognized as severally equal. It is true that these successive relations need not be specifically equal; but they must be equal in so far as they are defined. In the above case, for example, the original form of the inequation expresses a relation in which the first quantity bears a greater ratio to the second, than it does in the subsequent transformations; seeing that when equals are taken from unequals, the remainders are more unequal than before. But though in the degree of inferiority which they severally express, the successive relations need not be equal; yet they must be equal in so far as being all relations of inferiority goes: and this indefinite inferiority is all that is predicated either in premiss or conclusion.
Here, too, should be specifically remarked the fact hinted in a previous chapter; namely, that the reasoning by which one of these inequations is worked out, palpably proceeds upon the intuition that relations which are equal to the same relation are equal to each other. The relations being those of inequality, the filiation of the last upon the first can only thus be explained: and the parallelism that subsists between inequations and equations, in respect of the mental acts effecting their solutions, confirms the conclusion before reached that in equations that intuition is involved, though less manifestly.
It remains to be pointed out that, of imperfect quantitative reasoning, the lowest type is that in which the inequality of the successive relations is expressed in its most general form—a form which does not define the relations as either those of superiority or inferiority. For instance:—
In this case the deductive process is the same as before: the successive relations are perceived to be alike in respect to their inequality; though it is not known whether the antecedents or the consequents are the greater. There is a definite co-ordination of the successive relations; though each relation is itself defined to the smallest possible extent. And, starting from this as the least developed type, we may see that the type previously exemplified, in which the antecedents are known to be greater or less than the consequents, is an advance towards those highest forms in which the antecedents and consequents are either directly equal, or the one equal to some specified multiple of the other.
§ 26. Incidentally, simple quantitative reasoning has been to a considerable extent treated of in the course of the foregoing analyses. The successive steps into which every compound quantitative argument is resolvable are all simple quantitative arguments; and we have already found that they severally involve the establishment of equality or inequality between two relations. It will be convenient, however, to consider by themselves, a class of simple quantitative arguments which are of habitual occurrence in the compound ones: some of them axioms; some nearly allied to axioms.
Let us commence with the familiar one—“Things which are equal to the same thing, are equal to each other.” It may be shown by reasoning like that already used in a parallel case, that this truth is reached by an intuition of the equality of two relations. Thus, putting A, B and C, as the three magnitudes, it is clear that for the equality of A and C to be discerned, they must be presented to consciousness in two states, of which the one immediately succeeds the other. But if A and C are contemplated alone, in immediate succession, their equality cannot be recognized; seeing that it is only in virtue of their mutual equality to B, that they can be known as equal. And if, on the other hand, B is interpolated in consciousness, and the three are contemplated serially—A, B, C, or C, B, A,—then A and C do not occur in the required juxtaposition. There remains no alternative, therefore, but that of contemplating them in pairs, thus:—
When A and B are united together in the single concept—a relation of equality; and when B and C are united into another such concept; it becomes impossible to recognize the equality of these two relations of equality which possess a common term, without the equality of the other terms being involved in the intuition.
But, perhaps, the most conclusive mode of showing that the mental act is of the kind described, will be to take a case in which some of the magnitudes dealt with have ceased to exist. Suppose A to represent a standard unit of measure preserved by the State; and let a surveyor be in possession of a measure B, which is an exact copy of the original one A; suppose, further, that in the course of his survey the measure B is broken; and that in the meantime the building containing the standard measure A, has been destroyed by fire: nevertheless, by purchasing another measure C, which had also been made to match the standard A, the surveyor is enabled to complete his work; and is perfectly satisfied that his later measurements will agree with his earlier ones. What is the process of thought by which he perceives this? It cannot be by comparing B and C: for one of these was broken before he got the other. Nor can it be by comparing them serially—B, A, C, and C, A, B: for two of them have ceased to exist. Evidently, then, he thinks of B and C, as both copies of A: he contemplates the relations in which they respectively stood to A: and in recognizing the sameness or equality of these relations, he unavoidably recognizes the equality of B and C. And here it will be instructive to notice a fact having an important bearing, not only on this, but on endless other cases: the fact, namely, that the mind may retain a perfectly accurate remembrance of a relation, when it is unable to retain an accurate remembrance of the things between which it subsisted. Supposing that in the above case the surveyor has had opportunities, at the respective times when he bought them, of comparing B and C with A. It becomes possible for him, at any time afterwards, to remember with perfect precision the relation of equality in which B stood to A: he can see in thought that exact agreement which they displayed when placed side by side, with as much completeness as though he were again observing it. But it is impossible for him to remember the magnitudes themselves, with anything like this precision. He finds that by figuring in imagination two objects which he has seen at different times, but has never compared, he can form an approximate idea of their relative magnitudes, if they are markedly different; but, if they are nearly of a size, he is as likely to be wrong as right in saying which is the greater. If, then, two magnitudes separately observed, cannot afterwards be so distinctly represented in consciousness as that their equality or inequality can be determined; and if, on the other hand, a relation of equality that was once remarked between two magnitudes can be represented in consciousness with perfect distinctness, and recognized as equal to some other relation of equality; then it becomes manifest that, in cases like the above, the truth perceived cannot be reached by remembering the magnitudes, but can be reached by remembering the relations. And thus we have demonstrative proof that the process of thought is as was stated.
Diverging from this original type are certain intuitions in which the thing cognized is the equality, not of two relations of equality having a common term, but of two relations of inequality having a common term. Thus, if A is greater than B, and B greater than C, then A is greater than C: and the like holds if they are severally less instead of greater. The act of thought may be symbolized thus:—
The relation A to B being given as a relation of superiority, while that of C to B is given as a relation of inferiority, it is known that the relation A to B is greater than the relation C to B; and as the term B, is common to the two relations, the intuition that the relation A to B is greater than the relation C to B, cannot be formed without involving the intuition that A is greater than C.
Diverging again from this type and its converse are others, having in common with it the characteristic that the two compared relations are perceived to be not equal, but unequal. For example, if A is greater than B, and B is equal to C; we know that A is greater than C. Similarly, if A is less than B, we know it is less than C. And if the first relation is one of equality and the second is one of inequality, there is a parallel intuition. In these cases, or rather in the first of them, we may express the mental act thus:—
Here, as before, the magnitude B being common to both, the relation A to B cannot become known as greater than the relation C to B without the superiority of A to C being known. Two relations having a common term cannot be conceived unequal, unless the remaining terms are unequal. And just as two magnitudes placed side by side, cannot be perceived unequal without its being at the same time perceived which is the greater; so, of two conjoined relations, one cannot be perceived greater than the other, without its being at the same time perceived which includes the greater magnitude. Should any one hesitate as to the correctness of these analyses, he has but to revert to the method of inquiry before followed, and consider by what process the conclusion is reached when some of the magnitudes have ceased to exist, to at once see that no other acts of thought can suffice.
The species of intuition serving to establish the equality of the successive forms of an equation—a species of intuition by which are recognized the general truths that the sums of equals are equal; that the differences of equals are equal; that if equals be multiplied by equals the products are equal, and if divided by equals the quotients are equal—is also accompanied by a converse species of intuition, in which the fact recognized is the inequality of two relations. Perhaps the simplest cases are the antitheses of the foregoing ones. They are seen in such axioms as—If to equals, unequals be added, the sums are unequal; and—If equals be divided by unequals, the quotients are unequal. But some of the intuitions of this order exhibit a higher degree of complexity: instance those by which it is known that if from unequals, equals be taken, the remainders are more unequal; and conversely, that if to unequals, equals be added, the sums are less unequal. To which general cases may be added the specific ones in which the first pair of unequals being known to stand in a relation of superiority, the second pair are known to stand in a still greater relation of superiority, or a less relation, according to the operation performed; and similarly, when the relation is one of inferiority. Thus if A + c is greater than B + c, then in a still higher degree is A greater than B—an intuition which may be expressed in symbols as follows:—
For present purposes it is needless to detail the varieties of intuition belonging to this class. It will suffice to remark, alike of these cases in which the thing perceived is the inequality of two relations, and of the antithetical cases in which the equality of two relations is perceived, that they differ from the previous class in this; that the relations are not conjoined ones, but disjoined ones. There are never three magnitudes only: there are always four. Throughout the first series, of which the simplest type is the axiom—“Things which are equal to the same thing are equal to each other,” there is invariably one term common to the two relations; whilst throughout the second series, of which as a typical sample we may take the axiom—“If equals be added to equals, the sums are equal,” the compared relations have no term in common. Hence it happens that in this second series, the relations being perfectly independent and distinct, the mental processes into which they enter are more readily analyzable. It is at once manifest that the groups of axioms above given, severally involve an intuition of the equality or inequality of two relations; and indeed the fact is more or less specifically stated throughout: seeing that in each case there is a certain relation, the terms of which are modified after a specified manner, and there is then an assertion that the new relation is or is not equal to the old one—an assertion which, being based on no argument, expresses an intuition.
One further fact respecting these two groups of intuitions remains to be noticed; namely, that they have a common root with those which proportions express. The one group is related in origin to that species of proportion in which the second of three magnitudes is a mean between the first and third; and the other group to that species in which the proportion subsists between four separate magnitudes. Thus the axiom—“Things which are equal to the same thing are equal to each other,” may, if we call the things A, B and C, be written thus:—
And again, the axiom—“The sums of equals are equal,” may, if we put A and B for the first pair of equals, and C, D for the second pair, be expressed thus:—
This fundamental community of nature being recognized, it will at once be perceived that the intuitions by which proportions are established, differ from the majority of the foregoing ones, simply in their greater definiteness—in their completer quantitativeness. The two compared relations are always exactly equal, whatever the magnitudes may be—are not joined by the indefinite signs meaning greater than or less than: and when the proportion is expressed numerically, it not only implies the intuition that the two relations are equal; but the figures indicate what multiple, or submultiple, each magnitude is of the others.
QUANTITATIVE REASONING IN GENERAL.
§ 27. Leaving details, and considering the facts under their most general aspect, it is to be remarked that Quantitative Reasoning involves, with more or less constancy, the three ideas, coextension, coexistence and connature:∗ or to speak less accurately, but more comprehensibly—sameness in the quantity of space occupied; sameness in the time of presentation to consciousness; and sameness in kind. The germ out of which Quantitative Reasoning grows—the simple intuition of the equality of two magnitudes, necessarily involves all these: seeing that there can be no comparison between them unless they are of the same kind; and their coextension cannot be perceived unless they are coexistent. So too with geometry, throughout its entire range. Each of its propositions predicates the coextension or non-coextension of two or more connatural things which coexist: and its demonstrations proceed by asserting that certain coexistent, connatural things are invariably coextensive, or the reverse; or that certain connatural and coextensive things invariably coexist with certain other things. When the propositions are numerical, and when, as frequently happens in Algebra and the calculus generally duration is one of the elements dealt with, it would appear that coexistence is not involved; and further, that when force and value are the other elements of the question, there is not even any implication of coextension. These, however, are illusions resulting from the abstract character of numerical symbols. Simply representing as these do, equal units, and groups of equal units, of any order whatever; and being, as it were, created at any moment for the purposes of calculation; numerical symbols seem at first sight, independent alike of Space and Time; and able to establish quantitative relations between magnitudes that are not homogeneous. The fact, however, is exactly the reverse. On tracing them back to their origins, we find that the units of Time, Force, Value, Velocity, &c., which figures may indiscriminately represent, were at first measured by equal units of Space. The equality of times, becomes known either by means of the equal spaces traversed by an index, or the descent of equal quantities (space-fulls) of sand or water. Equal units of weight, were obtained through the aid of a lever having equal arms (scales); and were obtainable in no other way. The problems of Statics and Dynamics are primarily soluble, only by putting lines to represent forces. Mercantile values are expressed in units, which were at first, and indeed are still, definite weights of metal; and are therefore, in common with units of weight, referable to units of linear extension. Temperature is measured by the equal lengths marked alongside a mercurial column. And similarly, all the definitely quantitative observations of science, are made by means of subdivisions of linear space. Thus, abstract as they have now become, the units of calculation, applied to whatever species of magnitudes, do really represent equal units of linear extension; and the idea of coextension underlies every process of mathematical analysis. Similarly with coexistence. Numerical symbols are, it is true, purely representative; and hence may be regarded as having nothing but a fictitious existence. But one of two things must be admitted respecting the reasoning processes carried on by means of them. Either these processes imply a conscious reference to the things symbolized—in which case the equalities predicated in them are really those which were previously observed between coexistent things; or else the things symbolized cease to be thought of, and the relations among the symbols are alone considered—in which case these symbols require to be made coexistent to consciousness before their relations can be determined. In fact, the phenomena of motion and sequence can be treated quantitatively, only by putting coexistent magnitudes to represent magnitudes that do not coexist. The relative lengths of two times, not being ascertainable directly, has to be indirectly ascertained, by comparing the spaces which a clock-finger traverses during the two times; that is, by comparing coexistent magnitudes. In brief, regarding it in the abstract, we may say that the Calculus in general is a means of dealing with magnitudes that do not coexist, or are not homogeneous, or both, by first translating them into magnitudes that do coexist and are homogeneous, and afterwards reducing them back to their original form.
But, perhaps, the fact that perfect quantitative reasoning deals exclusively with intuitions of the coextension of coexistent magnitudes that are connatural, will be most clearly seen when it is remarked that the intuitions of coextension, of coexistence, and of connature, are the sole perfectly definite intuitions of which we are capable. Whilst, on applying two equal lines together, we can perceive with precision that they are equal; we cannot, if one is greater than the other, perceive, with like precision, how much greater it is: and our only mode of precisely determining this, is to divide both into small equal divisions, of which the greater contains so many, and the less so many: that is—we have to fall back upon the intuition of coextension. Again, whilst we can perceive with the greatest exactness that two things coexist, we cannot, when one thing follows another, perceive with like exactness the interval of time between them: and our only way of definitely ascertaining this, is by means of a scale of time made up of coextensive units of space. Once more, we can recognize with perfect definiteness, the equality of nature of those things which admit of quantitative comparison. That straight lines are homogeneous, and can stand to each other in relations of greater and less, though they cannot so stand to areas or cubic spaces; that areas are connatural with areas, and cubic spaces with cubic spaces; that such and such are magnitudes of force, and such and such are magnitudes of time—these are intuitions that have as high a degree of accuracy as the foregoing ones—a degree of accuracy which our intelligence cannot exceed. Beyond these three orders of intuitions, however, we have none but what are more or less indefinite. All our perceptions of degree and quality in sound, colour, taste, smell; of amount in weight and heat; of duration; of velocity; are in themselves inexact. Now, as we know that by quantitative reasoning of the higher orders, perfectly definite results are reached; it follows that the intuitions out of which it is built must be exclusively those of coexistence, connature and coextension: an inference which will be confirmed on calling to mind that in any case of imperfect quantitative reasoning, some other species of intuition is palpably involved.
And here, with a view of showing the various combinations into which these intuitions enter, and also with a view of exhibiting sundry facts not yet noticed, it will be well to group, in their ascending order, the successive forms which quantitative reasoning assumes: such repetition as will be unavoidable, being, I think, justified by the completer comprehension to be given, by presenting the phenomena in their genesis and their totality.
§ 28. The intuition underlying all quantitative reasoning is that of the equality of two magnitudes. Now, the immediate consciousness that— implies—first, that A and B shall be coexistent; for otherwise, they cannot be so presented to consciousness as to allow of a direct recognition of their equality—second, that they shall be magnitudes of like kind, that is, connatural or homogeneous; for if one be a length and the other an area, no quantitative relation can exist between them—third, that they shall not be any homogeneous magnitudes, but they shall be magnitudes of linear extension; seeing that these alone admit of that perfect juxtaposition by which exact equality must be determined—these alone permit their equality to be tested by seeing whether it will merge into identity, as two equal mathematical lines placed one upon the other do—these alone exhibit that species of coexistence which can lapse into single existence: and thus the primordial quantitative idea, unites the intuitions of coextension and coexistence in their most perfect forms.
To recognize the negation of this equality—to perceive that A is unequal to B—or, more explicitly, to perceive either that— involves no such stringent conditions. It is true that, as before, A and B must be connatural magnitudes. But it is no longer necessary that they should be coexistent; nor that they should be magnitudes of linear extension. Provided the superiority or inferiority of A to B is considerable, it can be known in the absence of one or both; and can be known when they are magnitudes of bulk, weight, area, time, velocity, &c.
The simplest act of quantitative reasoning, which neither of these intuitions exhibits when standing alone, arises when the two are co-ordinated in a compound intuition; or when either of them is so co-ordinated with another of its own kind. When, by uniting two of the first intuitions thus—
we recognize the equality of A and C; it is requisite, as before, that if the two equalities are to be known immediately, the magnitudes shall be those of linear extension, though, if the equalities have been mediately determined, the magnitudes may be any other that are homogeneous; but it is no longer necessary that all of them shall coexist. At one time A must have coexisted with B; and at one time B must have coexisted with C; but the intuitions of their equalities having once been achieved, either at the same or separate times, it results from the ability which we have to remember a specific relation with perfect exactness, that we can, at any subsequent time, recognize, the equality of the relations A to B and B to C, and the consequent equality of A and C; though part, or even all, of the magnitudes have ceased to exist.
By uniting the first and second intuitions, and by uniting the second with another of its own kind, we obtain the two compound intuitions, formulated as follows:—
In the first of these cases it is requisite, when the relations are immediately established, that the magnitudes be linear; but not so if the equality of A and B has been indirectly established: and whilst A and B must have coexisted, it is not necessary that B and C should have done so. In the second case the magnitudes need not be linear; but, if the inequalities are considerable, may be of any order. Further, it would at first sight appear that they need none of them be coexistent. But this is not true; for if the superiority or inferiority of A to B and of B to C be so great that it can be perceived by comparing the remembrances of them, then the superiority or inferiority of A to C can be similarly perceived, without the intermediation of B; and the reasoning is superfluous. The only cases to which this formula applies, are those in which the inequalities are so moderate, that direct comparison is required for the discernment of them: whence it follows that, as in the third formula, each pair of magnitudes must have been at one time coexistent. And in strictness this consideration applies also to the fourth formula.
The next complication, and the one which characterizes all quantitative reasonings save these simplest and least important kinds just exemplified, is that which arises when, in place of conjoined relations, we have to deal with disjoined relations—when the compared relations instead of having one term in common have no term in common. Wherever this happens—wherever we have four magnitudes instead of three, sundry new laws come into force: the most important of which is, that the magnitudes need no longer be all of the same order. In every one of the foregoing cases, it will be observed that while the intuition of coexistence is sometimes not immediately involved but only mediately so, even where the judgment reached is perfectly quantitative—while, where the judgment is imperfectly quantitative, the intuition of coextension is not involved, save as the correlative of non-coextension—the intuition that is uniformly involved is that of the connature of the magnitudes, their homogeneity, their sameness in kind. Without this, no one of the judgments given is possible. But with disjoined relations it is otherwise. The four magnitudes may be all homogeneous; or they may be homogeneous only in pairs, either as taken in succession or alternately. Let us consider the resulting formulæ.
When all the magnitudes are homogeneous we have for the first group of cases the symbol
in which each of the disjoined relations is one of equality, and the second is some transformation of the first. This, as before shown, represents the mental act taken in every step of an equation; and stands for the several axioms—When equals are added to, subtracted from, multiplied by, or divided by, equals, the results are equal. For the second group of cases we have the symbol
in which each of the relations is one of inequality. This comprehends all the cases of proportion: whether they be the numerical ones in which the degrees of inequality are definitely expressed; or the geometrical ones (as those subsisting between the sides of similar triangles) in which the degrees of inequality, though known to be alike, are not definitely expressed. For the third group of cases, forming the antithesis to the two preceding groups, and being but imperfectly quantitative, we have the symbol
which represents such general truths as that if equals be taken from unequals the remainders are more unequal; that if to equals unequals be added, the sums are unequal; and so forth: and which also stands for the instances in which two ratios differ so widely, that their inequality is at once recognized. It needs only to be further remarked respecting these three groups of cases in which the magnitudes are all homogeneous, that the equality or inequality predicated between the two pairs, always refers directly or indirectly to the space-relations of their components, and not to their time-relations.
Passing to the other disjunctive class, in which the several magnitudes are not all homogeneous, we find that the equality predicated between the relations may refer either to comparative extension or comparative existence. The first group of them, which may be symbolized thus:—
so as to indicate the fact that the magnitudes of the first relation are of one species, whilst those of the second relation are of another species, comprehends cases in which one line is to another line as one area to another area; or a bulk to a bulk, as a weight to a weight—cases like those in which it is seen that triangles of the same altitude are to one another as their bases; or that the amounts of two attractions are to each other inversely as the squares of the distances from the attracting body. Here it is manifest that though the first pair of magnitudes differs in kind from the second pair, yet the antecedent and consequent of the one, bear to each other the same quantitative relation as those of the other; and hence the possibility of ratiocination. The second group of cases is that in which each relation consists of two heterogeneous magnitudes, as a line and an angle; but in which the two antecedents are of the same nature, and the two consequents are of the same nature. It may be formulated thus:—
Here, neither of the compared relations can be a quantitative one: seeing that in neither do the components possess that connature without which relative magnitude cannot be predicated. Hence the two relations can be equal only in respect of the coexistence of their elements; and, as it would seem, considerations of quantity are no longer involved. But though, under the conditions here stated, the reasoning merges into that inferior species remaining to be treated of in the next chapter; there are other conditions under which this form represents reasoning that is truly quantitative: namely, when the coexistence holds only in virtue of certain defined quantitative relations, by which the heterogeneous magnitudes are indirectly bound together. Thus, when the theorem—“The greater side of every triangle has the greater angle opposite to it,” is quoted in the proof of a subsequent theorem, the act of thought implied is of the kind above symbolized. The greater side (A) of a triangle, has been found to stand in a relation of coexistence with the greater angle (b); and in some other triangle the greater side (C) and greater angle (d) are perceived to stand in the same or an equal relation: but this relation is not simply that of coexistence; it is coexistence in certain respective positions: and though there can be no direct quantitative relation between a side and an angle, yet, by being contained between the two lesser sides, the greater angle is put in indirect quantitative relation with the greater side. It may be questioned, however, whether in this, as in the innumerable like cases that occur in geometrical reasoning, A, b, C, and d should not be severally regarded rather as relations between magnitudes, than as magnitudes themselves. To elucidate this question, let us consider the theorem—“The angle in a semicircle is a right angle.” Here the word “semicircle” denotes definitely quantitative relations—a curve, all parts of which are equidistant from a given point, and whose extremities are joined by a straight line passing through that point: the words “angle in a semicircle” denote further quantitative relations: and the thing asserted is, that along with this group of quantitative relations coexists that other quantitative relation which the term “right angle” denotes between two lines containing it. Taking this view, the reasoning will stand thus:—
And this seems to be the more correct analysis of those kinds of quantitative reasoning, in which the antecedents are not homogeneous with the consequents.
The only further complication needing consideration here, is the one arising when, instead of two equal relations, we have to deal with three. As, from that first simple intuition in which two magnitudes are recognized as equal, we passed to the union of two such intuitions into a compound one involving three magnitudes; so again, from the foregoing cases in which two relations are recognized as equal, we now pass, by a similar duplication, to the still more complex case in which three relations are involved. This brings us to the axiom—“Relations that are equal to the same relation, are equal to each other;” formulated, as we before saw after this fashion:—
In which symbol it will be seen that each pair of relations is united in thought, after the same general manner as any of the pairs lately treated of. The various modifications of this form which result when the relations are unequal, it is unnecessary here to detail. And it is also unnecessary to go at length into those yet more complicated forms which result when this conjunctive arrangement is replaced by a disjunctive one—when, in place of three relations, we have to deal with four; as in the case of the axiom given at the outset (§ 17)—“Relations which are severally equal to certain other relations that are unequal to each other, are themselves unequal.” The laws of the evolution have been sufficiently exemplified to render this, and the allied intuitions, readily comprehensible. All that needs further be done, is to point out how, by successive developments, we have progressed from a simple intuition of the equality or inequality of two magnitudes, to a highly complex intuition of the equality or inequality of relations between relations.
§ 29. And, now, having examined quantitative reasoning in its genesis, and found that, either mediately or immediately, it always involves, in their positive or negative forms, some or all of the ideas—sameness in the nature of its magnitudes; sameness in their quantity; sameness in their time of presentation to consciousness; and sameness in degree between relations of the same nature subsisting among them; it will be well, finally, to observe that we may recognise, à priori, the impossibility of carrying on any quantitative reasoning, save by intuitions of the equality or inequality of relations. It is the purpose of a quantitative argument to determine with definiteness the relative magnitudes of things. If these things stand to each other in such wise that their relative magnitudes are known by simple intuition, argument is not involved. There can be argument, therefore, only when they are so circumstanced as not to be directly comparable: whence it follows that their relative magnitudes, if determined at all, must be determined by the intermediation of magnitudes to which they are comparable. The unknown quantitative relation between A and E, can be ascertained only by means of some known quantitative relations between each of them and B, C, D; and it is the aim of every mathematical process to find such intermediate known relations, as will bring A and E into quantitative comparison. Now, no contemplation of magnitudes alone can do this. We might go on for ever considering B, C, and D, in their individual capacities, without making a step towards the desired end. Only by observing their modes of dependence can any progress be made. If A and E are in an unknown quantitative relation, which we desire to determine, we can determine it only as being equal or unequal to certain other relations, which we know mediately or immediately. There is no way, even of specifically expressing the relation, save by this means. The ascertaining what a thing is or is not, signifies the ascertaining what things it is like or not like—what class it belongs to. And when, not having previously known the relation of A to E, we say we have determined it, our meaning is, that we find it to be the same, or not the same, as some relation which is known. Hence it results, à priori, that the process of quantitative reasoning, must consist in the establishment of the equality or inequality of relations.
PERFECT QUALITATIVE REASONING.
§ 30. Thus far we have dealt with reasoning which has for its fundamental ideas, coextension, coexistence, and connature; and which proceeds by establishing cointension∗ in degree, between relations connate in kind. We have now to consider a species of reasoning into which the idea of coextension does not enter; or of which it forms no necessary element: that, namely, by which we determine the coexistence or non-coexistence of things, attributes, or relations that are connatural with certain other things, attributes, or relations. It was pointed out that the intuitions of coextension, coexistence, and connature, are the only perfectly definite ones we are capable of; and the only ones, therefore, through which we can reach exact conclusions. One class of these conclusions in which the quantity of certain existences of determinate quality is predicated, has been examined: we have now to examine a class in which the thing predicated is the quality of certain determinate existences; or the existence of certain determinate qualities.
The last chapter incidentally exhibited the near connection between these kinds of reasoning. It was shown, that when two compared relations severally consist of heterogeneous magnitudes admitting of no quantitative comparison, the two relations can be considered equal, only in respect to the coexistence of the components of each. It was shown that many geometrical theorems simulate this form; expressed by the symbol
the fact predicated being the coexistence of C and d, standing in the same relation as A and b, which were proved coexistent; (say the equiangularity and equilateralness of a triangle.) As was pointed out, however, the terms of each relation are, in these cases, not really heterogeneous magnitudes; but heterogeneous relations amongst magnitudes, having indirect, but definite quantitative connections. But when the terms of each relation are simple heterogeneous magnitudes, or heterogeneous groups of relations having no implied quantitative connections, then we pass to the order of reasoning now to be treated of; in which equality is asserted of two relations that are alike in the nature of their terms, and in the coexistence of each antecedent with its own consequent.
Before going on to particularize, it will be well to meet the objection that may be raised to the use of the word equality in the sense here given to it. Commonly we apply it only to attributes. We speak of equal lengths, breadths, areas, capacities; equal times, weights, velocities, momenta; equal temperatures, sounds, colours, degrees of hardness; and we speak of equal ratios or relations, when the terms are magnitudes; but we do not speak of relations of coexistence as equal. Here, however, we are dealing, not with words in their conventional applications, but with the mental acts which words mark; and these, when they are of essentially the same character, may legitimately be indicated by the same terms. The true interpretation of equality is indistinguishableness. Colours, and sounds, and weights, and sizes, we call equal when no differences can be discerned between them. We assert the equality of two ratios—two relations of magnitude, when the contrast in amount between the first antecedent and its consequent, cannot be distinguished from the contrast between the second antecedent and its consequent. And, similarly, we may assert the equality of two relations of existence, when the one does not differ from the other in respect of time—when each is a relation of coexistence. As two relations of coextension are properly considered equal, though each of them consists of magnitudes that are unlike in everything but length; so, in a more limited sense, two relations of coexistence may properly be considered equal, though the elements of each are unlike in everything but the period of their presentation to consciousness. Or, to put the matter in an à priori form—All things whatever stand to each other in some relation of time. Every phenomenon, when considered in connection with any other, must be cognized either as occurring before it, as being simultaneous with it, or as occurring after it. But all objects of thought, and, amongst others, relations of time, admit of being compared, and their likeness or unlikeness recognized. The time-relation of events that occur simultaneously, is manifestly different from the time-relation of events that occur one after the other. Two sequences are alike in so far as they are sequences; and each of them is unlike a coexistence. Hence, if there are time-relations so completely alike as to be indistinguishable, they may properly be called equal. Such time-relations we have in all coexistences: and thus, when, as in the case of two attributes that invariably coexist, we, in any new case, know that where we see the one we shall find the other; it may as truly be said that the mental act involved, is a recognition of the equality of two relations, as when, in similar triangles of which two homologous sides are known, we infer the area of one triangle from that of the other.
§ 31. Reasonings of this order, in which the thing predicated is not the quantity of certain existences, but either, on the one hand, the existence or non-existence of certain attributes, or group of attributes, or, on the other hand, the simultaneity, or non-simultaneity, of certain changes, or groups of changes—reasonings which, instead of contemplating both space-relations and time-relations, contemplate time-relations only—exhibit, in a large class of cases, that same necessity often ascribed exclusively to quantitative reasonings. This class of cases is divisible into two sub-classes: the one including disjoined relations, and the other conjoined relations—the one always involving four phenomena, and the other only three. The first of these sub-classes—represented by the formula last given, and, like geometrical reasoning, predicating necessary coexistence, but, unlike it, saying nothing of coextension—includes that infinitude of cases in which, from certain observed attributes of objects, we infer the presence of certain other attributes that are inseparable from them. When, on feeling pressure against an outstretched limb, we conclude that there is something before us having extension—when, on seeing one side of an object, we know that there is an opposite side—when, any one necessary property of body being perceived, another is foreseen; this order of reasoning is exemplified. Were it not that perpetual repetition has reduced these cognitions to what may be termed organic inferences, it would be at once seen they stand on an analogous footing with those in which the equilateralness of a triangle is known from its equiangularity, when the coexistence of these has once been recognized. Under another head we shall hereafter have occasion to consider these cases more closely. At present it merely concerns us to notice, that the mental act involved in each of them, is an intuition of the equality of two disjoined time-relations—the one, a known generalized relation of invariable coexistence, ascertained by an infinity of experiences having no exception, and therefore conceived as a necessary relation; the other, a relation of coexistence, in which one term is not perceived, but is implied by the presence of the accompanying term. Or, to formulate an example:—
And similarly in all cases of necessary attributes as distinguished from contingent ones.∗
Of that subdivision of perfect qualitative reasoning which proceeds by recognizing the equality or inequality of conjoined relations, the examples are not very abundant. The fact predicated in them is, either the coexistence or non-coexistence of certain things, as determined by their known relations to some third thing; or else the simultaneity or non-simultaneity of certain events, as determined by their known relations to some third event. If, of two persons together passing the door of a building, the one observes a barrel of gunpowder, and the other a boy with a light in his hand, it is clear that, on immediately hearing an explosion, the adjacent coexistence of the light with the gunpowder is inferable from the facts that the one observed the adjacent coexistence of the light and the building, and the other the adjacent coexistence of the gunpowder and the building. If again, certain two other persons both heard the explosion, and, on comparing notes, found that each was setting out to meet the other at the moment of its occurrence; it is a necessary inference that they set out at the same time. These two classes of cases, dealing respectively with coexistent or non-coexistent things, and with co-occurring or non-co-occurring changes, are so nearly allied, that it is needless to treat of them both. Confining our attention to the latter class, we may represent the subdivision of it above exemplified, thus:—
In this symbol the letters stand, not for objects, but for events: the simultaneity of A and C, being recognized by an intuition analogous to that by which their equality would be recognized, were they magnitudes both equal to a third.
The antithetical group of cases in which, of three events, the first and second being known to occur simultaneously, and the second and third being known to occur non-simultaneously, it is inferred that the first does not occur simultaneously with the third, needs not to be dealt with in detail. But it will be well to notice the more specific cases in which something more than simple non-simultaneity is predicated: those namely, in which it is inferred that one event preceded or succeeded a certain other event. Thus, if A and B go in company to a public meeting; and B on coming away meets C entering the door; then A, on afterwards hearing of this, knows that he was there before C: or if, supposing them all to go separately, C on arriving finds B already present; and B tells him that on his (B's) arrival he found A present; then, though he should not see him, C knows that A was there before himself. Using the letters to stand for the events (not the persons), these cases may be represented thus:—
It is unnecessary to detail the possible modifications of these; or to argue at length that the intuitions must be essentially of the kind thus symbolized; for the cases are so obviously analogous to those previously treated of, in which the relations of two unequal magnitudes are known by the intermediation of a third (§ 24), that the explanation there given may, with a change of terms, be used here. All that it is requisite to observe is the fact, which this analogy itself suggests, that the reasoning exemplified by these last cases is, in a vague sense, quantitative. So long as only coexistence or non-coexistence, simultaneity or non-simultaneity, is the thing predicated, quantity of time can scarcely be said to be involved. But when the ideas before and after enter into the question, there would seem to be a mental comparison of periods; as measured from some common point in time. Particular occurrences in the general stream of events are relatively fixed by means of their respective relations to the past—are regarded as farther, or not so far, down the current of time; and can only be thus regarded by comparing the respective intervals between them and occurrences gone by. Whether, as in the first of the following figures, we represent each of the events A, B, and C, as the terminus to its own particular line of causation; or, whether, as in the second, we represent them simply as unconnected occurrences,—
—it is equally manifest that in determining the unknown relation of A and C, by means of their known relations to B, it is necessary to conceive all their times of occurrence as measured from some past datum—to compare the lengths of these times; and to recognize the inferiority of the length A to the length C, by means of the known relations they respectively bear to the length B. Where this datum is, matters not: for the respective periods measured from it, will retain their several relations of equality, inferiority, or superiority, however far back, or however near it is placed: and hence, perhaps, the reason why we form no definite conception of it. The best proof, however, that the process of thought is as here described, is obtained, when, from these vaguely-quantitative predications expressed by the words before and after, we pass to those definitely-quantitative ones achieved by using space as a measure of time—when we pass to cases in which, by our clocks, we determine how much before or after. For when, on hearing that one event occurred at four and another at five, we know that the one was an hour later than the other; we really recognize their relation in time, by means of their respective relations to twelve o'clock—the datum from which their distances are measured. Similarly with the lapse of time between any two historical events; which we determine by severally referring them to the commencement of the Christian era. And if, to determine specifically the respective positions in time of two events not directly comparable, we habitually compare their distances from some point in the past; it can scarcely be doubted that when we merely determine their positions generally, as before or after, the process gone through is, though vague and almost unconscious, of the same essential nature.
But, whatever may be the detailed analysis of this mental act—and it is not an easy one—the act must necessarily consist in an intuition of the equality or inequality of two relations. If the events A and C stand in just the same time-relation to an event B; or, more strictly—if their time-relations to it are equal; then the cognition that they are simultaneous is involved: they cannot be thought as both occurring at the same time with C; or at equal intervals before it; or after it; without being thought as simultaneous. Conversely, if the events A and C are known to stand in different time-relations to the event B—if their time-relations to it are unequal; then the cognition of their non-simultaneity is involved. Whence it unavoidably follows, that when the difference of the time-relations is expressed more specifically—when the terms before and after are used; the intuition must be essentially of the same character: be the mode in which the comparison of relations is effected, what it may.
§ 32. It seems to me, that to this species of reasoning alone, are applicable the axioms which Mr. Mill considers as involved in the syllogism. If we include simultaneity in our idea of coexistence, it may be said that all the foregoing cases of conjunctive reasoning, severally involve one or other of the two general propositions—“Things which coexist with the same thing coexist with one another,” and—“A thing which coexists with another thing, with which other a third thing does not coexist, is not coexistent with that third thing.” But in no other ratiocinative acts, I think, than those above exemplified, are these self-evident truths implied.
That they cannot be the most general forms of the mental processes commonly formulated by the syllogism, will become manifest on considering that they refer positively or negatively to one time only; whereas, the syllogism, as involving in its major premiss a more or less direct appeal to accumulated experience, refers to two times—to time present and time past. The axiom—“Things which coexist with the same thing coexist with each other,” cannot, however often repeated, help us to any knowledge beyond that of the coexistence of an indefinite number of things; any more than the axiom,—“Things which are equal to the same thing are equal to each other,” can, by multiplied application, do more than establish the equality of some series of magnitudes. But the act of thought which every syllogism attempts to represent, besides involving a cognition of the particular coexistence predicated in the conclusion; involves also, a cognition of those other coexistences which form the data for that conclusion: all of which coexistences may have long since ceased. The two terms of the coexistence predicated, may alone continue in being: the entities presenting parallel coexistences may have been every one annihilated: how, then, can the mental act by which the predication is effected, be formulated in an axiom which involves three coexistent terms?
The fact is, that Mr. Mill has here been misled by a verbal ambiguity of a kind, which he himself has previously pointed out, as one “against which scarcely any one is sufficiently on his guard.” Towards the close of Chapter iii. of his Logic, he says:—“Resemblance, when it exists in the highest degree of all, amounting to undistinguishableness, is often called identity, and the two similar things are said to be the same as when I say that the sight of any object gives me the same sensation or emotion to-day that it did yesterday, or the same which it gives to some other person. This is evidently an incorrect application of the word same; for the feeling which I had yesterday is gone, never to return; what I have to-day is another feeling, exactly like the former perhaps, but distinct from it; By a similar ambiguity we say, that two persons are ill of the same disease; that two persons hold the same office.” Now, that the verbal confusion between identity and exact likeness, thus exemplified, has betrayed Mr. Mill into the above erroneous formula, will, I think, become manifest, on examining the passage which serves to introduce that formula. At page 200 (3rd edition), he says:—
“The major premiss, which, as already remarked, is always universal, asserts, that all things which have a certain attribute (or attributes) have or have not along with it, a certain other attribute (or attributes). The minor premiss asserts that the thing or set of things which are the subject of that premiss, have the first-mentioned attribute; and the conclusion is, that they have (or that they have not) the second. Thus in our former example,—
the subject and predicate of the major premiss are connotative terms, denoting objects and connoting attributes. The assertion in the major premiss is, that along with one of the two sets of attributes, we always find the other: that the attributes connoted by “man” never exist unless conjoined with the attribute called mortality. The assertion in the minor premiss is that the individual named Socrates possesses the former attributes; and it is concluded that he possesses also the attribute mortality.”
Both in the general statement and in the example, I have italicised the words in which the misconception is more particularly implied. Let us confine our attention to the example. Here it will be observed, that in saying, “Socrates possesses the former attributes,” the literal meaning of the words, and the meaning Mr. Mill's axiom ascribes to them, is, that Socrates possesses attributes not exactly like those connoted by the word “man,” but the same attributes. By this interpretation, and only by this interpretation, are the elements of the syllogism reducible to three—1st, the set of attributes possessed by all men and by Socrates; 2nd, the mortality of other men; 3rd, the mortality of Socrates. But is it not clear that in asserting Socrates to possess the attributes possessed by other men—in calling the attributes which constitute him a man, the same as those by which men in general are distinguished; there is a misuse of words parallel to that involved in saying that two persons are ill of the same disease? Persons said to have the same disease, are persons presenting similar groups of special phenomena not presented by other persons. Objects said to have the same attributes (as those of humanity), are objects presenting similar groups of special phenomena not presented by other objects. And if the word same is improperly used in the one case, it must be improperly used in the other. This being admitted, it follows inevitably, that the elements of the syllogism cannot be reduced to less than four. (1). The set of attributes characterizing any or each of the before-known objects that are united into a certain class: which set of attributes must be represented in consciousness, either (plurally) as possessed by every sample of the class that can be remembered, or (singularly) as possessed by some one sample of it, figured to the mind as a type of the class; and which, therefore, cannot be considered as less than one, though it may be considered as more. (2). The particular attribute predicated in the major premiss, as always accompanying this set of attributes: and which, according as we are supposed to think of it as possessed by several remembered samples of the class, or by a typical sample, may be considered as many, or as one; but cannot be less than one. (3). The set of attributes presented by the individual (or sub-class) named in the minor premiss: which set of attributes being essentially like (not the same as) the first-named set of attributes, this individual is recognized as a member of the first-named class. (4). The particular attribute inferred, as accompanying this essentially like set of attributes. And if the elements of the syllogism cannot be reduced to less than four, it is manifest that the axiom—“Things which coexist with the same thing coexist with each other,” which comprehends only three things, cannot represent the mental act by which the elements of the syllogism are co-ordinated. Only to that limited class of conjunctive reasonings lately exemplified, can such an axiom apply.
§ 33. Returning from this parenthetical discussion, there has still to be noticed that further species of perfect qualitative reasoning, in which the thing predicated is some necessary relation of phenomena in succession. In a previous part of the chapter, we have considered cases of unconditional coexistence; and here we have to glance at cases of unconditional sequence. As in the first group, we were concerned only with those relations of coexistence of which the negations are inconceivable; so in the second, we are concerned with those relations of antecedence and sequence which it is impossible to think of as other than we know them. To take a case—If, on entering a room, I find that a chair which I had previously placed in one part of it, is now in another; it is a necessary conclusion that it has traversed the intervening space: it is inconceivable that it should have reached its present position, without having passed through positions intermediate between that and the original one: and further, it is a necessary conclusion that some agency (very probably, though not certainly, human) has produced this change of place: it is inconceivable that there should be this effect without a cause. Here we have nothing to do with the analyses of these inferences further than to observe, that, like the previous ones, they are reached by intuitions of the equality of relations. The relation between this effect as a consequent, and some force as an antecedent, is conceived as one with an infinity of such relations; differing in detail, but alike in presenting uniformity of succession. And similarly with the relation between changed position, and transit through space.
IMPERFECT QUALITATIVE REASONING.
§ 34. Though the line of demarcation between perfect and imperfect qualitative reasoning would seem to be tolerably precise—seeing that whilst the conclusions of the one are of the kind whose negations cannot be conceived, those of the other can have their negations conceived with greater or less difficulty—yet the approximation of the two is practically so close, that some of the second class may readily be mistaken for members of the first. These divisions, convenient, and, indeed, essential as they are, are most of them in some degree artificial. Just as in the last chapter we saw that the distinction between quantitative and qualitative reasoning can scarcely be maintained in cases where the thing predicated is antecedence or subsequence in time; so here, the transition from perfect to imperfect qualitative reasoning, is through cases in which the conclusions, if not absolutely necessary, are almost so. Thus the relation between visible and tangible attributes is such, that on receiving the ocular impressions representing an adjacent object, we cannot help concluding that an adjacent object exists, which, on putting out our hands towards it, will give them sensations of resistance; and there are doubtless many aboriginal minds by which no other conclusion is conceivable. But our experience of looking-glasses and of optical illusions, renders it just possible for us to imagine that where the appearance exists, there may exist no solid substance. Though, judging from the unhesitating confidence with which, from moment to moment, we act out cognitions of this order, they would seem to stand on the same footing with those lately exemplified, in which from the invariable coexistence of tangibility with limiting surfaces, we infer that any particular object must have ends; yet the two classes are found to differ, when thus rigorously analysed. So, again, with cases like that incidentally quoted at the close of the last chapter, in which the mortality of a particular individual is inferred from the mortality of mankind in general. Certain as the inference appears, and next to impossible as it seems for any one to believe of himself, or of another, that he will not die; it is yet not only conceivable that death might be escaped, but history shows us that in times past it was even believable.
The various grades of imperfect qualitative reasoning—beginning with those in which the negation of the inference can be conceived only by the greatest effort; descending through those in which it can be conceived with less and less effort; and ending with those lowest cases of contingent reasoning in which it presents itself to the mind almost as readily as the opposite one—are discriminated from perfect qualitative reasoning, and from quantitative reasoning, by the peculiarity that the compared relations are no longer to be considered as equal or unequal, but as like or unlike. That complete indistinguishableness which characterizes the compared relations of definite necessary reasoning, is found only among the simple phenomena of number, space, time, force,—is not predicable of the relations subsisting among those comparatively complex phenomena whose dependencies cannot be known, or are not yet known, as necessary. The knowledge that the ratio, A : B, is equal to the ratio, is an exact intuition. The contrast in magnitude between A and B is perceived to be indistinguishable from that between half A and half B. The two relations not being each of them made up of sundry component relations, the comparison between them gives a result that is simple and precise. But when, from the general truth that motion is a constant antecedent of sound, we infer, on hearing a sound, that something has moved; or when, from human mortality in general, we infer the mortality of a particular individual; the compared relations cannot be called equal, but can only be called like. The established relation between sound, and motion as its antecedent, is not representable to the mind as one special relation; but as an average of many special relations varying in the amounts, qualities, and intervals of their antecedents and consequents: and hence the particular relation between the sound heard and the motion inferred, cannot be held equal to the general one; seeing that this lacks the definiteness implied by such a predication. Even when, from the nature of the sound, the character of the antecedent motion is known—when, from a loud crash, it is concluded that a heavy body has fallen; there is still only likeness in the compared relations, though it is a likeness that approaches nearer to equality: for though the repeatedly experienced relation between a loud crash and the fall of a heavy body, is far more specific than is the general relation between sound and motion; yet it is not so specific as that either the size or nature of the body can be known with any precision; as it could be were the compared relations equal in the true sense of the word. Similarly in the second case. Though the relation between life and death is such that we can with certainty say of any individual that he will die; yet we cannot with certainty say either the time or the manner. He may die to-morrow by accident; or next year by disease; or fifty years hence of old age. Whilst the generalization from which our conclusion is deduced, is specific in the respect that the phenomena of life are invariably followed by those of death; yet the infinity of cases included in the generalization differ more or less in every other respect than this fundamental one: and, consequently, as the particular relation which the conclusion recognizes, exactly parallels no particular foreknown relation; and has only one peculiarity in common with all foreknown relations of the same order; likeness, only, can be asserted of it, and not equality. Did we regard the relation between life and death in the abstract, as purely one of succession—could we exclude from it all consciousness of the interval, so as to recognize no difference between the death of the infant and that of the centenarian—we might with propriety consider all cases of the relation as equal: but our inability to do this, necessitates the use of the more general word. Indeed, it needs but to observe the contrasted applications we commonly make of these words, to see the validity of the distinction. The things we habitually call equal, are either simple sensations or simple relations. We talk of equal lengths, breadths, and thicknesses; equal weights and forces; equal temperatures and degrees of light; equal times and velocities. When speaking accurately, we do not, in respect to any of these, use the word like, unless in the qualified form “exactly alike,” which is synonymous with equal: nor, when the compared magnitudes of these kinds are almost, though not quite equal, do we allow ourselves to call them like, in virtue of their near approximation. Wherever the terms of the comparison are both elementary—have only one aspect under which they can be regarded; and can be specifically posited either as distinguishable or indistinguishable; we call them either unequal or equal. But when we pass to complex things, exhibiting at once the attributes, size, form, colour, weight, texture, hardness—things which, if equal in some particulars, are rarely if ever equal in all; and therefore rarely if ever indistinguishable—then we use the term like, to express, partly the approximate equality of the several attributes separately considered, and partly the grouping of them after a parallel manner in time and space. Similarly with the relations involved in reasoning. If simple, they are recognized as equal or unequal; if complex, as like or unlike.
§ 35. This premised, it will at once be seen that those cases of imperfect qualitative reasoning commonly given in Treatises on Logic, as illustrating the process of thought said to be expressed by the syllogism, severally exhibit intuitions of the likeness or unlikeness of relations. When, to quote a familiar case, it is said—“All horned animals are ruminants; this is a horned animal; therefore this annual is a ruminant;” the mental act indicated is a cognition of the fact that the relation between particular attributes in this animal, is like the relation between homologous attributes in certain other animals; and may be symbolized thus:—
That this formula—the relation between A and B is like the relation between a and b—substantially represents the logical intuition, will, from our present stand-point, be obvious. For it is manifest—first, that it is only in virtue of the perceived likeness between A and a—the group of attributes involved in the conception of a horned animal, and the group of attributes presented by this particular animal—that any inference can be valid, or can even be suggested: second, that the attributes implied by the term “ruminant,” can be known only as previously observed or described; and that the predication of these as possessed by the animal under remark, is the predication of attributes like certain foreknown attributes: and, third, that there is no assignable reason why, in this particular case, a relation of coexistence should be predicated between these attributes and those signified by the words “horned animal,” unless as being like certain relations of coexistence previously known: nor, indeed, could the predication otherwise have any probability, much less certainty. Or, to state the case with greater precision—Observe, first, that as the unseen attribute predicated, cannot, on the one hand, be supposed to enter the mind, save in some relation to its subject; and that as, on the other hand, the relation cannot be thought of without the subject and the predicated attribute being involved as its terms; it follows that the intuition, which the inference expresses, must be one in which subject, predicate, and the relation between them are jointly represented. Observe next, that while subject and predicate are separately conceivable things, the relation between them cannot be conceived without involving them both; whence it follows that only by thinking of the relation can the elements of the intuition be combined in the requisite manner. And now observe, under what form this relation must be thought. Clearly, since the subject is recognized as like certain others with which it is classed; and since the attribute predicated is conceived as like an attribute possessed by other members of the class; and since the relation between the subject and the predicated attribute is proved, by the truth of the predication, to be like the relation subsisting in other members of the class; it must be by recognizing the relation as like certain foreknown relations, that the conclusion is reached.
This view of the matter will be further elucidated and confirmed, by contemplating the essential parallelism subsisting between the species of reasoning above described, and that species of mathematical reasoning which is confessedly carried on by comparison of relations. The unknown fact predicated in a syllogism, is perfectly analogous to the unknown fourth term in a proportion. Let us take cases.
In each of these acts of ratiocination (mark the word) the fourth term, b, represents the thing inferred: and seeing, not only that it is similarly related to its data in the two cases, but that the data stand in like relations to each other; the essential parallelism of the mental processes will be manifest. No doubt they have their differences: but an examination of these will serve but to show their fundamental agreement. Thus, the fact that the predication in the first is qualitative, whilst in the second it is quantitative, though true in the main, and important as a general distinction, is not true in any literal or absolute sense. For, if strictly analyzed, both are found qualitative, and both in some degree quantitative. A glance at the forms in which the two inferences present themselves to the mind, will render this obvious. The first (that carbonic acid is being evolved) is, in the main, and as verbally expressed, merely qualitative—refers to the nature of a certain process and a certain product; and the second (that a specified portion of time will clapse), though distinguishable as especially quantitative, is by implication qualitative also; seeing that not only is a magnitude predicated, but a magnitude of time: the thing inferred is defined alike in nature and amount. As thus regarded, then, the first inference is qualitative; and the second both qualitative and quantitative. If now, we examine the two inferences still more closely, and, neglecting the words in which they are expressed, consider the mental states those words describe; we shall see a still nearer approximation. For though the first inference as verbally rendered (carbonic acid is being evolved) is in no respect quantitative; yet the idea so rendered, is constantly accompanied by an idea of quantity, more or less definite. The experiences by which it is known that fermenting wort evolves carbonic acid, are accompanied by experiences of the quantity evolved; and vague as these may be, they are yet such that when the brewer predicates a certain vat of fermenting wort to contain carbonic acid, part of the predication, as present to his consciousness, is an idea of some quantity—more, certainly, than a cubic foot; less, certainly, than the total capacity of the vat: and this quantity is intuitively thought of as in some ratio to the quantity of wort. Again, in the second case, though the inference as verbally rendered (the lapse of three minutes and three-quarters) is specifically quantitative; yet the idea so rendered, if examined in its primitive form, is not specifically quantitative; but only vaguely quantitative. A man who has walked a mile in fifteen minutes, and, observing that he has a quarter of a mile still to go, infers the time it will take to reach his destination; does not primarily infer three minutes and three-quarters; but primarily infers a short time—a time indefinitely conceived as certainly less than ten minutes, and certainly more than one. True, he can afterwards, by a process based upon the perceived equality of the relations between time and distance, calculate this time specifically. But, as it will not be contended that he can reach the specific time without calculation; and as it must be admitted that before making the calculation he has an approximate notion of the period he seeks to determine; it must be confessed that though his ultimate inference is definitely quantitative, his original one is but indefinitely quantitative. The two inferences, then, as at first formed, are alike in being qualitative and indefinitely quantitative; and they differ simply in this—that whilst in the one, the quantitative element is neglected as incapable of development, it is, in the other, evolved into a specific form. Seeing, then, that the parallelism between them is so close, it cannot be questioned that as the last is reached by an intuition of the equality of two relations, so the first is reached by an intuition of the likeness of the two relations.∗
It is unnecessary here to give any illustration or analysis of that species of so-called syllogistic reasoning by which negative inferences are reached; and which differs from the foregoing species simply in this; that the fact recognized is not the likeness, but the unlikeness, of two compared relations. Nor is it requisite to give any detailed interpretation of the different forms and modes of the syllogism; which obviously depend, partly upon the order in which the terms of the two relations are contemplated, and partly upon the extent to which the relations hold, as being either universal or partial. All that properly falls within a psychological analysis like the present, is, an explanation of the general nature of the mental process involved. To consider the various possible modifications of this process, would carry us further than is desirable into the province of Logic.
Neither will it be needful to exemplify that compound qualitative reasoning, which occurs in all cases where an inference is reached, not by a single intuition of the likeness or unlikeness of relations, but by a connected series of such intuitions. Analogous as such cases are to those of compound quantitative reasoning, examined in previous chapters; and, like them, consisting of successive inferences that are sometimes severally perfect, and sometimes only part of them perfect; it will suffice to refer the reader to §§ 22, 24, for the general type, and to his own imagination, for instances.
All that it seems desirable to notice, before leaving that division of imperfect qualitative reasoning which proceeds from generals to particulars, is the fact, that, by an easy transition, we pass from the ordinary so-called syllogistic reasoning, to what is commonly known as reasoning by analogy; this last differing from the first simply in the much smaller degree of likeness which the terms of the inferred relation bear to those of the known relations it is supposed to parallel. In the syllogism as ordinarily exemplified, it is to be observed, not only that the objects classed together as the subject of the major premiss, have usually a great number of attributes in common, besides the one more particularly predicated of them; but that the individual or sub-class which the minor premiss names, has also a great number of attributes in common with this class of objects: in virtue of which extensive community of attributes it is, that the inferred attribute is asserted. Thus, when it is argued—“All men are mortal: therefore this man is mortal;” it is clear that the individual indicated, and all the individuals of the class to which he is tacitly referred, exhibit a high degree of similarity. Though they differ in colour, stature, bulk, in minor peculiarities of form, and in their mental manifestations; yet they are alike in such a great number of leading characteristics, that there is no hesitation in grouping them together. When, again, it is argued—“All horned animals are ruminants: therefore, this horned animal is a ruminant;” we see that though the sub-classes—such as oxen, deer, and goats—which are included in the class horned animals, differ considerably in certain respects; and though the particular horned animal remarked upon, as the ibex, differs very obviously from all of them; yet they have sundry traits in common, besides having horns. If, taking a wider case, we reason that as all mammals are warm-blooded, this mammal is warm-blooded, it will be remarked that the class—including as it does, whales, mice, tigers, men, rabbits, elephants—is far more heterogeneous. If, once more, we infer the vertebrate structure of a particular quadruped from the general fact that all quadrupeds are vertebrate, the class, as including most reptiles, is more heterogeneous still. And the heterogeneity approaches its extreme, when we draw inferences from the propositions that all animals contain nitrogen, and that all organisms are developed from fertilized germs. But now let it be noticed that, in these latter cases, in which the objects grouped together have so many points of difference, the probability of the conclusion come to, depends upon the previous establishment of the asserted relation, not simply throughout one, or a few, of the sub-classes thus grouped, but throughout a great variety of those sub-classes. Had only oxen and goats been found ruminant, the presumption that any other species of horned animal was ruminant, would be but weak. The warm-bloodedness of a new kind of mammal, would be but doubtfully inferable, if only a dozen or a score other kinds were known to be warm-blooded; no matter how many thousands of each kind had been tested. If the possession of a spine had been proved to coexist with the possession of four legs, only in every species of quadruped inhabiting this country, it would be hazardous to assert of any and all four-legged creatures found in other parts of the globe, that they had spines. In each of these cases, the reasoning, whilst yet the general fact was unestablished, would be merely analogical; and would be so recognized. Take a parallel instance. The elephant differs from most mammals in having the teats placed between the fore limbs; and also in the structure of the hind limbs, which have their bones so proportioned, that where there is usually a joint bending backwards, there is, in the elephant, a joint bending forwards. In both these peculiarities, however, the elephant is like man and the quadrumana; whilst at the same time it approaches them in sagacity, more nearly than any other creature does. If now, there were discovered some new animal organized after the same fashion, and unusual marks of intelligence were to be expected from it, the expectation would imply what we call an inference from analogy; and vague as this analogy would be, it would not be more vague than that which induced the expectation that other horned animals ruminated, whilst yet rumination had been observed only in oxen, goats, and deer. Add to which, that just as, when to oxen, goats, and deer, were added numerous other species in which the like relation subsisted, the basis of deduction was so far enlarged as to give the inferred rumination of a new horned animal, something more than analogical probability; so, were the relation between special intelligence and physical characteristics above described, found in a hundred different kinds of mammalia, the inference that a mammal possessing these physical characteristics was intelligent, would be an ordinary deduction; and might serve logicians as an example of syllogistic reasoning, equally well with the preceding one. Thus, premising that in the syllogism the word “all” means—all that are known (and it can never mean more), it is clear that ordinary syllogistic deductions differ from analogical ones, simply in degree. If the subjects of the so-called major and minor premisses are considerably unlike, the conclusion that the relation observed in the first will be found in the last, is based on nothing but analogy; which is weak in proportion as the unlikeness is great: but if, everything else remaining the same, the class named in the major premiss has added to it class after class, each of which, though considerably unlike the rest, has a certain group of attributes in common with them, and with the subject of the minor premiss; then, in proportion as the number of such classes becomes great, does the conclusion that a relation subsisting in every one of them subsists in the subject of the minor premiss, approximate towards what we call deduction.
In an order of still more remote analogical reasoning, we find much unlikeness not only between the subjects, but between the predicates. Thus, to formulate an example:—
In this case, the likeness in virtue of which society is referred to the class, organisms, is extremely distant; and there is not much apparent similarity between the progress of organic economy and that of industrial economy: so that the inference could be considered but little more than an idle fancy, were it not inductively confirmed by past and present history.
And now, not to overlook the bearing of these cases on the general argument, let it be remarked—First, that analogical reasoning is the antipodes of demonstrative reasoning, not only in its uncertainty, but also in the dissimilarity of the objects whose relations it recognizes: seeing that whilst, in mathematical and other necessary inferences, the things dealt with have few attributes, and the relations among them are capable of accurate determination as equal, or exactly alike; and whilst, in the imperfect deductive reasoning lately treated of, the things dealt with have many attributes which, though severally differing in some degree, have so much in common, that most of their relations may properly be called like; in analogical reasoning the things dealt with, are, in many respects, conspicuously unlike; and the presumption that they are like in respect of some particular relation, becomes correspondingly feeble. Secondly, let it be remarked, that whilst ordinary class reasoning is, under one aspect, parallel to that species of mathematical reasoning, which recognizes the equality between one relation of 2:3, and all other relations of 2:3; reasoning by analogy is, under the same aspect, parallel to that species of mathematical reasoning which recognizes the equality between the relation 2:3 and the relation 6:9—an equality that is called a numerical analogy. And let it be remarked, in the third place, that as, in the case of analogical reasoning, the likeness of the relations is obviously the thing contemplated,—seeing that it would never occur to any one to consider society as an organism, unless from the perception that certain relations between the functions of its parts were like the relations between the functions of the parts constituting an animal—and as the most perfect mathematical reasoning, namely, that which deals with numbers, confessedly proceeds by intuitions of the equality or exact likeness of relations; we have yet further grounds for holding that all orders of reasoning which lie between these extremes, and which insensibly merge into both, are carried on by a similar mental process.
§ 36. From that species of imperfect qualitative reasoning, which proceeds from generals to particulars, we now pass to that antithetical species which proceeds from particulars to generals; in other words—to inductive reasoning. From our present stand-point, not only the fundamental differences, but the fundamental similarities, of these kinds of reasoning become clearly apparent. Both are seen to be carried on by comparison of relations: and the contrast between them is seen to consist solely in the numerical preponderance of the premised relations in the one case, and of the inferred relations in the other. If the known relations grouped together as of the same kind, outnumber the unknown relations recognized as like them; the reasoning is deductive: if the reverse; it is inductive. In the accompanying formula, arranged with a view of exhibiting this contrast, the whole group of attributes, in virtue of which an object is known as such or such, are symbolized by A or A or a, according as they are thought of as possessed by all, or some, or one; and for the particular attribute or set of attributes predicated as accompanying this group, the letter B or B or b is used, according as the subject of it is all, some, or one.
Or, to give a specific illustration of each,—Like the general observed relation between living bodies and fertilized germs; is the relation between these infusoria and fertilized germs; or is the relation between this entozoon and a fertilized germ: and, conversely—Like the observed relation between the development of this plant and its progress from homogeneity to heterogeneity of structure; or like the observed relation between the development of those animals and their progress from homogeneity to heterogeneity of structure; is the general relation in all organisms between development and progress from homogeneity to heterogeneity of structure.
Some possible criticisms on this exposition may fitly be noticed. In the formula, as well as in the illustration of the inductive process, I have introduced, as it may appear merely to complete the antithesis, the generalization of a whole class of cases, from the observation of a single case—a generalization which seems manifestly illegitimate. To this objection there are two replies. In the first place, it is to be remembered that our immediate subject is not logic, but the nature of the reasoning process; and if, as will not be denied, many people are in the habit of founding a general conclusion upon a solitary instance—if, as must be admitted, the mental process by which they advance from data to inference is the same where the data are insufficient, as where they are sufficient; then, a general account of this mental process may properly include examples of this kind. The second reply is, that throughout a wide range of cases, such inductions are perfectly legitimate. When it has been demonstrated of a particular equilateral triangle that it is equiangular, it is forthwith inferred that all equilateral triangles are equiangular; and numberless general truths in mathematics are reached after this fashion. Hence, then, a formula for induction not only may, but must include the inference from the singular to the universal. A further criticism which will perhaps be passed, is, that in quoting as a specimen of deduction, the argument that infusoria have fertilized germs because living bodies in general have them, a very questionable sample of the process has been given; as is proved by the fact that there are still many by whom the inference is rejected. My answer is again twofold. It is beyond question that the majority of the deductions by which every-day life is guided, are of this imperfect order; and hence, whether valid or invalid, they cannot be excluded from an account of the deductive process. Further, I have chosen a case in which the conclusion is open to a possible doubt, with a view of implying that in all cases of contingent reasoning, the unknown relation predicated, can never possess anything more than a high degree of probability—a degree proportionate to the frequency and uniformity of the parallel experiences.
This doctrine is, I am aware, quite at variance with that held by many logicians, and especially by Sir William Hamilton; who contends not simply that (irrespective of the distinction between necessary and contingent matter), there are both Deductions and Inductions in which the conclusion is absolutely necessitated by the premisses, but that all other Deductions and Inductions are extra-logical. To discuss this question at full length, would involve an undue divergence from our subject. Such brief criticisms only can be set down, as seem requisite for the defence of the opposite doctrine. Among general objections to Sir William Hamilton's argument (see “Discussions,” pp. 156 to 166), may be noted the fact that he uses the word same in place of the word like, after a fashion equally ambiguous with that pointed out in the last chapter. Moreover, he employs the words whole and parts (to stand for a logical class and its constituent individuals) in a mode implying that in thinking of a whole we definitely think of all the contained parts—an assumption totally at variance with fact. No one, in arguing that because all men are mortal, this man is mortal, conceives the whole, “all men,” in anything like a complete circumscribed manner. His conception answers neither to the objective whole (all the men who exist and have existed), which infinitely exceeds his power of knowing; nor to the subjective whole (all the men he has seen or heard of), which it is impossible for him to remember. Yet, unless logical wholes are conceived in a specific manner, Sir William Hamilton's doctrine cannot stand: for the perfect Induction and perfect Deduction, which alone he allows to be the subject-matter of Logic, imply wholes that are known by “enumeration (actual or presumed) of all the parts.” Again; let us consider the results following from this distinction which Sir William Hamilton draws between the logical and the extra-logical. Other logicians, he says, have divided Induction “into perfect and imperfect, according as the whole concluded, was inferred from all or from some only of its constituent parts.” This he considers to involve “a twofold absurdity;” and asserts that that only is logical induction, which infers the whole from the enumerated all. Now, if this be so, there arises the question—What is the nature of that so-called imperfect induction which infers wholes from some only of the constituent parts? Sir William Hamilton says it is extra-logical. Still it is a species of reasoning—a species by which the immense majority of our conclusions are drawn; and rightly drawn. Hence, then, there are two kinds of Induction (as well as of Deduction), one of which is recognized by the science of reasoning, while the other is ignored by it. This implication is of itself sufficiently startling; but it will become still more so on considering the essential nature of the difference, which, according to this hypothesis, exists between the logical and the extra-logical. If, proceeding by the so-called imperfect induction, I infer from the multiplied instances in which I have seen butterflies developed from caterpillars, that all butterflies are developed from caterpillars; it is clear that the inference contains innumerable facts of which I have never been directly cognizant: from a few known phenomena, I conclude an infinity of unknown phenomena. If, on the other hand, proceeding by the so-called perfect induction, which does not allow me to predicate of the whole anything that I have not previously observed in every one of the parts, and which, therefore, does not permit, as logical, the conclusion that all butterflies are developed from caterpillars—if, proceeding by this so-called perfect induction, I say that as each of the butterflies (which I have observed) was thus developed, the whole of the butterflies (which I have observed) were thus developed; it is clear that the so-called conclusion contains nothing but what is previously asserted in the premiss—is simply a colligation under the word whole, of the separate facts indicated by the word each—predicates nothing before unknown. Here, then, are two kinds of mental procedure: in one of which, from something known, something unknown is predicated; in the other of which, from something known, nothing unknown is predicated. Yet both these are called reasoning—the last logical; the first extra-logical. This seems to me an impossible classification. The two things stand in irreconcilable contrast. Agreeing as I do with Sir William Hamilton in considering it as absurd to include in logic both perfect and imperfect induction; I do so on exactly opposite grounds: for this which he calls perfect induction, I conceive to be not reasoning at all, but simply a roundabout mode of defining words. All reasoning whatever, Inductive or Deductive, is a reaching of the unknown through the known; and where nothing unknown is reached, there is no reasoning. The whole process of stating premisses and drawing conclusion, is a wanton superfluity if the fact which the conclusion asserts is already given in experience. Suppose I have noticed that A, B, C, D, E, F, &c. severally possess a given attribute: do I then by this so-called Induction group them together as all possessing that attribute, that I may be subsequently enabled by the so-called Deduction to infer that E or F possesses it? Certainly not. By the hypothesis I have already noticed that E and F possess it; and knowing this by a past perception, have no need to reach it by inference. Yet this ascent from the known constituent parts to the constituted whole, is all that Sir William Hamilton recognizes as logical Induction; whilst the descent from such constituted whole to any, some, or one of such constituent parts, is all that he recognizes as logical Deduction. And thus, in the endeavour to establish necessary logical forms, he exhibits forms which the intellect never does, nor ever can with any propriety, employ.
Returning from this digression, which certain anticipated objections rendered needful, it is to be observed of the inductive process as above formulated, that it applies alike to the establishment of the simplest relations between single properties, and the most complex relations between groups of properties and groups of objects. As is now usually admitted, the process by which a child reaches the generalization that all surfaces returning brilliant reflections are smooth to the touch, is fundamentally like that by which the physiologist reaches the generalization that, other things equal, the temperature of any species of creature is proportionate to the activity of its respiration. Between those earliest and unconsciously formed inductions on which are based the scarcely more conscious deductions that guide our movements from moment to moment, and those latest ones which only the highly cultured natural philosopher is competent to draw, may be placed a transitional series, the members of which differ, partly in the comparative infrequency with which the relations are presented to our observation; partly in the increasing complexity of the terms between which the relations subsist; and partly in the increasing complexity of the relations themselves. Throughout the whole series, however, the essential act of thought is a cognition of the likeness between certain observed relations and certain unobserved relations: the trustworthiness of which cognition varies sometimes according to the numerical ratio between the observed and unobserved relations; sometimes according to the simplicity of their nature; sometimes according to their analogy to established relations; sometimes according to all these.
Any detailed consideration of the conditions under which the inductive inference is valid, would here be out of place. We have now only to examine the nature of the mental act by which such inference is reached; and which is the same whether the data are adequate or not. The rest falls within the province of inductive logic. The only further remark at present called for, is, that (excluding the mathematical inductions before named) when the observed relations are very few in number, or when the terms between which they subsist differ considerably from the terms of the relations classed with them, or both, we have what is known as an hypothesis. Thus, to quote an example from a recent controversy, if we argue that
it is clear that, though inductive reasoning is simulated in form, the presumption that the relations are like is not strong, and nothing but probability can be claimed for the inference. If now, the likeness between the terms of the known and unknown relations were more complete—were all other worlds physically like this world in nearly every particular; the hypothesis would have increased probability: and then, if, of worlds thus physically similar, we ascertained that hundreds, thousands, tens of thousands were inhabited; the inference that all were inhabited, would become an ordinary induction—would approach in validity to the induction which, from the mortality of all known men, concludes that all men are mortal. From which mode of presenting the facts it will become manifest not only that, as we all know, hypothesis must precede induction; but further, that every hypothesis is an induction in the incipient stage: capable of being developed into one if there are facts for it to assimilate; fated to dwindle away if there are none.
§ 37. To the foregoing two orders of imperfect qualitative reasoning—that which proceeds from generals to particulars, and that which proceeds from particulars to generals—has to be added a third order; which Mr. Mill has named, reasoning from particulars to particulars. This, regarded under each and all of its aspects, is the primitive species of reasoning. It is that to which both Induction and Deduction may be degraded by continually diminishing the number of their observed or predicated facts; and which lies midway between them as the common root whence they diverge. It is that habitually displayed by children and by the higher animals. And it is that in which we find the comparison of relations reduced to its simplest shape. In all the examples of imperfect qualitative reasoning hitherto given, either the known relations serving for data were plural; or the unknown relations predicated were plural; or both were plural. But in this aboriginal reasoning, both the premised and the inferred relations are singular. The mental act is an intuition of the likeness (or unlikeness) of one relation to one other relation. The burnt child who, having once experienced the connexion between the visual impression of fire and the painful sensation which fire produces upon the skin, shrinks on again having his hand put near the fire, is mentally possessed by a represented relation between fire and burning, similar to the before presented relation. He thinks of the future relation as a repetition of the past one. He sees, or, more strictly speaking, presumes, that the two relations are alike. In this rudimentary—this most simple and imperfect ratiocination, we may clearly perceive that the thing remembered, which stands for premiss, is a relation; that the thing conceived, which stands for inference, is a relation; that the presentation of one term of this inferred relation (the fire) is followed by the representation of its other term (burning); that the relation thus conceived, is so conceived, solely because there is a past experience of the relation between fire and burning; and that hence, by the very conditions of its origin, the new relation is conceived as like the foreknown one. And it is clear that whilst, by the multiplication of experiences, the known and unknown relations, instead of being respectively one and one, become many and many, and so originate Deduction and Induction, the act of thought by which the inference is reached, must remain throughout fundamentally similar.
REASONING IN GENERAL.
§ 38. Before summing up the evidence, and presenting under its most general form the doctrine which the foregoing chapters develop in detail, it will be well briefly to glance at the current theory of reasoning, with the view of showing its insufficiency.
That so many logicians should have contended that the syllogism exhibits the process of thought by which we habitually reason, would be unaccountable, were it not for the immense influence of authority on men's opinions. Passing over the general objection, that it involves a petitio principii, and cannot therefore represent the mode by which we find our way to new truths, a cursory examination even, will suffice to show that the syllogism is a psychological impossibility. Take a case. When I say,—
and when it is asserted that this describes the mental process by which I reached the conclusion; there arises the very obvious question—What induced me to think of “All crystals”? Did the concept “All crystals,” come into my mind by a happy accident, the moment before I was about to draw an inference respecting a particular crystal? No one will assert such an absurdity. It must have been, then, that a consciousness of the particular crystal identified by me as such, was antecedent to my conception of “All crystals.” This, however, it will be said, is merely a formal objection; which may be met by putting the minor premiss first. True: but this objection is introductory to a fatal one. For the mind being, as we see, necessarily occupied about the individual crystal, before it is occupied about the class; there result the two inquiries—(1), Why, having been conscious of the individual crystal, should I, in this particular case, go on to think of the class crystals; instead of thinking of some other thing? and (2), Why, when I think of the class crystals, should I think of them as having planes of cleavage; instead of thinking of them as angular, or polished, or brittle, or having axes, or in connection with any other attribute? Is it again by a happy accident that, after the individual, the class occurs to my mind? and further, is it by a happy accident that the class is remembered as having the particular attribute I am about to predicate? No one will have the folly to say—yes. How happens it, then, that after the thought—“This is a crystal,” there arises the thought—“All crystals have planes of cleavage;” instead of some other of the thousand thoughts which mental suggestion might next produce? There is one answer, and only one. Before consciously asserting that all crystals have planes of cleavage, it has already occurred to me that this crystal has a plane of cleavage. Doubtless it is the registered experience I have had respecting the cleavage of crystals, which determines me to think of this crystal as having a plane of cleavage; but that registered experience is not present to my mind before the special predication is made; though I may become conscious of it subsequently. The process of thought which the syllogism seeks to describe, is not that by which the inference is reached, but that by which it is justified; and in its totality is not gone through at all, unless the need for justification is suggested. Each may at once convince himself of this by watching how any of his most familiar inferences originate. It is stated that Mr. So-and-so, who is ninety years old, is about to build a new mansion; and you directly say, how absurd it is that a man so near death should make such preparation for life. But how came you to think of Mr. So-and-so as dying? Did you first repeat to yourself the proposition—“All men must die?” Nothing of the kind. Certain antecedents led you to think of death as one of his attributes, without previously thinking of it as an attribute of mankind at large. To any one who considered Mr. So-and-so's folly not demonstrated, you would probably reply,—“He must die, and that very shortly:” not even then appealing to the general fact. Only on being asked why he must die, would you, either in thought or word, resort to the argument—“All men die: therefore Mr. So-and-so must die.” Obviously then, the syllogism in no way represents the ordinary inferential act; which is a single and almost unconscious intuition; but only approximately represents the process by which our inferences are, if need be, consciously verified.
As will of course be perceived, many of the formulas given in preceding chapters, are to be taken with a parallel explanation. They represent, not the primary and direct reasoning, but the secondary, and what we may call, reflex reasoning. To express any deduction by saying of the compared relations that,
is to raise the insuperable difficulty above suggested—that the class, with its appropriate predicate, cannot in order of thought precede the individual and that which we predicate of it; or, in other words—that we do not think of the class of before known relations as like the single present relation; but we think of the single present relation as like the class. Just as, before writing down the proportion I must have already recognized the unknown relation sought, as equal to the known relation premised: otherwise the writing down the premised relation would be unaccountable. Hence it is manifest, that to symbolize the deductive process in a complete manner, the inferred relation must be placed before, as well as after, the class of relations to which it is assimilated; thus—
The first of these three represents that act of thought in which, on the presentation of some object (a) there is suggested to the mind some unseen attribute (b), as possessed by it. This act is simple and spontaneous; resulting, not from a remembrance of the foreknown like relations (A : B); but merely from the influence which, as past experiences, they exercise over the association of ideas. Commonly, the inference thus determined suffices us; and we pass to some other thought: but if a doubt is internally or externally suggested, then the acts of thought represented by the rest of the symbol are gone through; and we have a process of conscious reasoning.
And here, respecting this series of mental acts, there occurs a consideration of some interest and importance. It is universally admitted that in the evolution of reasoning, induction must precede deduction—that we cannot descend from the general to the particular, until we have first ascended from the particular to the general. The fact now to be remarked is, that this is true not only of reasoning considered in its ensemble, but also, in a qualified sense, of each particular ratiocination. It was pointed out a few pages back, that as, in the development alike of the general mind and the individual mind, qualitative reasoning precedes quantitative reasoning; so, each particular act of quantitative reasoning grows out of a preceding act of qualitative reasoning: and in the present case there seems to hold the analogous law, that as, in mental progress, both general and particular, induction precedes deduction; so, every particular act of deduction properly so called, presupposes a preparatory act of induction. For may we not with propriety say, that the mental transition from the spontaneously inferred relation with which every deductive process must commence, to the class of relations it belongs to; parallels the act by which the mind originally passed from particular relations to the general relation? It is true that the particular relation is in this case not an observed one; and in so far the parallel does not hold: but still, it is conceived as existing; and it is only in virtue of being so conceived that the class it is referred to is thought of. The sequence of thought, as it were, follows the channel through which the induction was before reached. In so far as each separate deductive act involves an ascent from the particular to the general, before the descent from the general to the particular; the historic relation between induction and deduction is repeated. In all cases of deduction there is either an induction made on the spur of the moment (which is often the case), or there is a rapid rethinking of the induction before made.
Resuming our more immediate topic—It is to be remarked that the amended, or rather completed, form under which the deductive process is above represented, remains in perfect accordance with the doctrine, developed in foregoing chapters; that reasoning is carried on by comparison of relations. For whether the singular relation is thought of before the plural one; or the plural before the singular; or first one and then the other; it remains throughout manifest, that they are thought of as like (or unlike) relations; and that the possibility of the inference depends on their being so thought of. On the other hand, the syllogistic theory is altogether irreconcilable with the mental processes we have just traced out—irreconcilable as presenting the class, while yet there is nothing to account for its presentation; irreconcilable as predicating of that class a special attribute, while yet there is nothing to account for its being thought of in connexion with that attribute; irreconcilable as embodying in the minor premiss an assertory judgment (this is a man), while the previous reference to the class, men, implies that that judgment had been tacitly formed beforehand; irreconcilable as separating the minor premiss and the conclusion, which ever present themselves to the mind in relation. Whatever merit the syllogism may have as verbally exhibiting the data and conclusion in a succinct form; it wholly misrepresents the mental process by which the conclusion is really reached.
And if the syllogism, considered in the concrete, does not truly display the ratiocinative act; still less do the axiomatic principles reached by analysis of the syllogism, supply anything like a theory of the ratiocinative act. It may be said that it does not fall within the province of Logic to formulate the workings of the intellect—that it is concerned with the objective aspect of reasoning, and not with its subjective aspect, which pertains to Psychology—that all which Logic can do is to reduce overt inductions and deductions to their simplest elements, and to systematic arrangement. And this is true. But there seems to be an undefined yet general impression, that a certain abstract truth said to be involved in every syllogism, is that which the mind recognizes in going through every syllogism; and that the recognition of this abstract truth under any particular embodiment, is the real ratiocinative act. Nevertheless, neither the dictum de omni et nullo—“that whatever can be affirmed (or denied) of a class, may be affirmed (or denied) of everything included in the class;” nor the axiom which Mr. Mill evolves—“that whatever possesses any mark possesses that which it is a mark of;” nor indeed any axiom which it is possible to frame; can express the ratiocinative act. Saying nothing of the special objections to be urged against these or kindred propositions, they are all, in so far as they profess to embody laws of logical thinking, open to the fundamental objection that they are substantive truths perceived by reason; not the mode of rational perception. Each of them describes a piece of knowledge; not a process of knowing. Each of them generalizes a large class of cognitions; but does not by so doing approach any nearer to the nature of the cognitive act. Contemplate all the axioms—“Things that are equal to the same thing are equal to each other;” “Things that coexist with the same thing coexist with each other;” and so forth. Each of these is a rational cognition; and if any supposed logical axiom be added to the number, it, also, must be a rational cognition. But these axioms are manifestly of one family; become known by similar intellectual acts; and no addition of a new one to the list can answer the question—What is the common nature of these intellectual acts? what is the process of thought by which axioms become known? Axioms can belong only to the subject-matter about which we reason; and not to reason itself. They imply cases in which an objective uniformity determines a subjective uniformity; and all these subjective uniformities can no more be reduced to one, than the objective ones can. The utmost that any analysis of reason can effect, is to disclose the form of intuition through which these and all other mediately known truths are discerned: and this we have in the inward perception of likeness or unlikeness of relations. This it is which constitutes, as it were, the common type of rational cognitions, axiomatic or other: and it is manifestly incapable of axiomatic expression; not only because it varies with every variation in the subject-matter of thought; but because the universal process of rational intelligence, cannot become solidified into any single product of rational intelligence.
§ 39. And now, that the truth of the several doctrines enunciated in foregoing chapters may be still more clearly seen, let us glance at the series of special results that have been reached; and observe how harmoniously they unite as parts of one consistent whole.
We noticed that perfect quantitative reasoning, by which alone complete previsions are reached, involves intuitions of coextension, coexistence, and connature in the things reasoned about; besides connature in the compared relations, and cointension in the degree of those relations—equality among the entities in Space, Time, Quality; and among their relations in kind and measure: that thus in the highest reasoning, not only does the idea of likeness rise to its greatest perfection (equality), but it appears under the greatest variety of applications; and that in imperfect quantitative reasoning where non-coextension is predicated, either indefinitely (these magnitudes are unequal) or definitely (this magnitude is greater than that), the idea of exact likeness is no longer so variously involved. We next noticed that in perfect qualitative reasoning, the intuition of coextension ceases to appear; but that there is still coexistence and connature amongst the terms, along with connature and cointension amongst the relations subsisting between those terms: that thus there is a further diminution in the number of implied intuitions of equality; and that in parti-perfect qualitative reasoning, where non-coexistence is predicated either indefinitely (these things do not exist at the same time) or definitely (this follows that), the number of such implied intuitions is still further reduced: though there yet remains equality in the natures of the things dealt with, and in the natures of the compared relations. We have now to notice, what was not noticed in passing, that in imperfect qualitative reasoning we descend still lower; for in it, we have no longer complete equality of nature in the terms of the compared relations. Unlike lines, angles, forces, areas, times, &c., the things with which ordinary class reasoning deals, are not altogether homogeneous. The objects grouped together in an induction are never exactly alike in every one of their attributes; nor is the individual thing respecting which a deduction is made, ever quite indistinguishable in character from the things with which it is classed. No two men, or trees, or stones, have the same absolute homogeneity of nature that two circles have. Similarly with the relations between these terms: though they remain connatural, do not remain cointense. And thus, in our contingent every-day reasoning, we have only likeness of nature in the entities and attributes involved; equality of nature in the relations between them; and more or less of likeness in the degree of those relations. The subjects must be like; the things predicated of them must be like; and the relations must be homogeneous, if nothing more. Even when we come to the most imperfect reasoning of all—reasoning by analogy—it is still to be observed that, though the subjects and predicates have severally become so different that not even likeness of nature can be safely asserted of them; there still remains likeness of nature between the compared relations. If the premised relation is a sequence, the inferred one must be a sequence; or they must be both coexistences. If one is a space-relation and the other a time-relation, reasoning becomes impossible. As a weight cannot be compared with a sound; so, neither can there be any comparison between relations of different orders. And hence, whatever else may disappear, the compared relations must continue to be of like nature. Without this there can be no predication of any other likeness or unlikeness; and therefore no reasoning. This fact, that, as we descend from the highest to the lowest kinds of reasoning, the intuitions of likeness among the elements involved, become both less perfect and less numerous, but never wholly disappear, will hereafter be seen to have great significance.
Passing from the elements of the rational intuitions to their forms, we find that these are divisible into two genera: in the one of which the compared relations, having a common term, are conjoined; and in the other of which the compared relations, having no common term, are disjoined. Let us glance at the several species comprehended under the first of these genera. Having necessarily but three terms, these have for their types the forms If, in the first of these forms, A, B, and C represent magnitudes of any order; then, if they are severally equal, we have the axiom—“Things that are equal to the same thing are equal to each other;” and if they are severally unequal, we have a case of mean proportionals. In the second form, if A, B, and C are magnitudes, we have the converse of the above axiom; whilst the thing determined is the inequality of A and C. And in the third form, the thing determined is the superiority or inferiority of A to C. Again, if A, B, and C instead of being magnitudes are times, either at which certain things continuously exist or at which certain events occur, then the first form represents the axioms—“Things that coexist with the same thing coexist with each other,” and “Events which are simultaneous with the same event are simultaneous with each other.” The second form stands for the converse axioms; and predicates the non-coexistence or non-simultaneity of A and C. While the third symbolizes cases in which A is concluded to be before or after C. To make these facts clear, let us formulate each variety.
It must not be supposed, however, that Time and Space relations are the only ones that can enter into these forms. Relations of Force under its various manifestations, may be similarly dealt with. To use Sir William Hamilton's nomenclature, there is Extensive quantity (in Space); Protensive quantity (in Time); and Intensive quantity (in the degree of the Actions that occur in space and time). It is true, as before shown, (§ 25) that intensive quantities, as those of weight, temperature, &c. cannot be accurately reasoned about without reducing them to equivalent quantities of extension; as by the scales and the thermometer: but it is none the less true that there is a simple order of inferences respecting intensive quantities, exactly parallel to those above given. If, for example, a ribbon matched in colour some fabric left at home; and matches some other fabric at the draper's; it is rightly inferred that these fabrics will match each other: or if, on different occasions, a piece of music had its key note pitched by the same tuning fork; it is to be concluded that the pitch was alike on both occasions. And similarly in various other cases, which it is needless to specify. In all of them, as well as in the various ones above given, the intuition, both in its positive and negative forms, is represented by the symbol
The only further fact of importance to be remarked of them, is, that not only are the two relations homogeneous in nature, but all the three terms are so likewise. Whence, in part, arises the extremely-limited range of conjunctive reasonings.∗
The other genus of rational intuitions, distinguished by having four terms, and therefore two separate or disjoined relations, is represented by the typical forms—
To which must be added the two modified forms which result when the reasoning is imperfect—
If, in the first of these five, the letters represent homogeneous magnitudes; then, when A equals B, and C equals D, we have represented the group of axioms—If equals are added to, subtracted from, multiplied by, &c., equals, the results are equal; as well as all the ordinary algebraic reasonings into which these axioms enter: and when each of the two ratios is not one of equality, we have an ordinary proportion. Supposing that the four terms are not homogeneous throughout, but only in pairs; then the formula stands for common geometrical reasoning: and when the things represented are not magnitudes, but simply entities and attributes that are alternately homogeneous; we have that order of reasoning by which necessary coexistences and sequences are recognized. Again, in the second and third forms—if all the terms are homogeneous magnitudes, then inequations and certain axioms antithetical to the above are symbolized: if the magnitudes are but alternately homogeneous, there is typified that imperfect geometrical reasoning by which certain things are proved always greater or less than certain others: and when the letters stand not for magnitudes but simply for entities, properties, or changes, we have that species of necessary qualitative reasoning which gives negative predications. Lastly, by the fourth and fifth forms are signified all orders of common class-reasoning: from that which is next to necessary to that which is in the highest degree problematical: inclusive alike of Induction, Deduction, Analogy, and Hypothesis. All these sub-genera and species of Disjunctive Reasoning are representable by the one symbol—
And the several varieties may be classified in three distinct modes; according as the basis of classification is—(1) the degree of resemblance between the two relations; (2) the nature of the compared relations; and (3) the comparative number of the premised and inferred relations. Under the first of these classifications, we have the divisions—Positive and Negative; Perfect, Parti-perfect, and Imperfect; Necessary and Contingent; Analogical. Under the second, we have the two great divisions—Quantitative and Qualitative: of which the one may be Proportional, Algebraic, or Geometrical, according as the terms of each relation are or are not homogeneous, and are or are not equal; and of which the other may refer to either coexistences or sequences, whether between attributes, things, or events. Under the third, we have reasoning divided into Inductive, Deductive, Hypothetical; which are classifiable according to the numerical ratio between the premised and inferred relations. Thus, if the inference is
The only further fact to be noted respecting the disjunctive form of reasoning, is, that it includes certain inferences which can be classed neither with the inductive, the deductive, the process from particulars to particulars, nor any of their modifications: inferences namely, that are at once drawn, and correctly drawn, in cases that have not been before paralleled in experience. Thus, if A be but a hundredth part less than B; it is at once inferable that a half of A is greater than a third of B. Neither a general principle nor a particular experience, can be quoted as the premiss for this conclusion. It is reached directly and independently by a comparison of the two relations named; and is satisfactorily explicable neither on the hypothesis of forms of thought, nor on the experience-hypothesis as ordinarily interpreted. We may aptly term it a latent inference; and its genesis, like that of many others, is to be properly understood only from that point of view, whence, as already hinted, these antagonist hypotheses are seen to express opposite sides of the same truth. Of this more in the sequel. Meanwhile let it be observed that while the species of reasoning thus exemplified is obviously effected, like all others, by comparison of relations; it cannot be conformed to any of the current theories.
Respecting those most complex forms of reasoning analyzed in the first chapter, which deal not with the quantitative or qualitative relations of things, but with the quantitative relations of quantitative relations; it is needless now to do more than remind the reader that they arise by duplication of the forms above given; and that in their highest complications they follow the same law. Perceiving as he thus will that the doctrine enunciated applies alike to all orders of reasoning, from the most simple to the most complex—from the necessary to the remotely contingent; from the axiomatic to the analogical; from the most premature induction to the most rigorous deduction—he will see that it fulfils the character of a true generalization: that, namely, of explaining all the phenomena.
§ 40. One other group of confirmatory evidences may with advantage be noticed: those which are supplied by our ordinary forms of speech. Already one or two of them have been incidentally pointed out. They are so numerous and so significant, that even standing alone they would go far to establish the theory that has been developed. Thus we have the Latin ratio, meaning reason; and ratiocinor, to reason. This word ratio we apply to each of the two quantitative relations forming a proportion; and the word ratiocination, which is defined as “the act of deducing consequences from premisses,” is applicable alike to numerical and to other inferences. Conversely, the French use raison in the same sense that ratio is used by us. Throughout, therefore, the implication is that reasoning and ratio-ing are fundamentally identical. Further be it remarked that ratiocination, or reasoning, is defined as “the comparison of propositions or facts, and the deduction of inferences from the comparison.” Now every proposition or asserted fact, involving as it does a subject and a something predicated of it, necessarily expresses a relation: hence the definition may be properly transformed into, “the comparison of relations” &c.: and as the only thing effected by comparison is a recognition of the likeness or unlikeness of the compared things; it follows that inferences said to be deduced from the comparison, must result from the recognition of the likeness or unlikeness of relations. Again, we have the word analogy applied alike to proportional reasoning in mathematics, and to the presumptive reasoning of daily life. The meaning of analogy is, “an agreement or likeness between things in some circumstances or effects, when the things are otherwise entirely different:” and in mathematics, an analogy is “an agreement or likeness between” two ratios in respect of the quantitative contrast between each antecedent and its consequent; though their constituent magnitudes are unlike in amount, or in nature, or in both. So that in either case, to “deny the analogy,” is to deny the assumed likeness of relations. Then we have the common expressions—“by parity of reasoning,” and “the cases are not upon a par.” Parity means equality; and being upon a par means being upon a level; so that here, too, the essential idea is that of likeness or unlikeness. Note also, the familiar qualifications,—”cæteris paribus,” “other things equal;” which are used with the implication that when all the remaining elements of the compared cases stand in like relations, the particular elements in question will stand in like relations. Further, there is the notion of parallelism. It is an habitual practice in argument to draw a parallel, with the view of assuming in the one case what is shown in the other. But parallel lines are those that are always equi-distant—that are like in direction: and thus the fundamental idea is still the same. Once more: not only do men reason by similes of all orders, from the parable down to the mere illustration; but similarity is constantly the alleged ground of inference, alike in necessary and in contingent reasoning. When geometrical figures are known to be similar, and the ratio of any two homologous sides is given; the values of all the remaining sides in the one, may be inferred from their known values in the other: and when the lawyer has established his precedent he goes on to argue, that similarly, &c. Now as, in geometry, the definition of similarity is, equality of ratios amongst the answering parts of the compared figures; it is clear that the similarity on the strength of which ordinary inferences are drawn, means—likeness of relations. Various other phrases, such as, “The comparison is not fair;” “What is true in this case will be true in that;” “Like causes will produce like results;” may be mentioned as having the same implication. Nay more: not only is the process of thought by which both our simplest and our most complex inferences are drawn, fundamentally one with that by which proportional inferences are drawn; but its verbal expression often simulates the same form. Just as in mathematics we say—As A is to B, so is C to D; so in non-quantitative reasoning we say—As a muscle is to be strengthened by exercise, so is the rational faculty to be strengthened by thinking. And indeed, this sentence supplies a double illustration; for not only does each of the two inferences it compares exhibit the proportional form; but the comparison itself exhibits that form. Thus it is throughout manifest, that our habitual modes of expression bear witness to the truth of the foregoing analysis.
§ 41. And now, as an appropriate finish to this somewhat too lengthened exposition, I would briefly point out that the conclusion reached may be established even à priori. When towards the close of this Special Analysis we come to consider the ultimate elements of consciousness; it will be abundantly manifest that the phenomena of reasoning cannot, in the nature of things, be truly generalized in any other way. But without waiting for this simplest and most conclusive proof eventually to be arrived at; it may, even from our present stand-point, be demonstrated by two separate methods, that every inference of necessity involves an intuition of the likeness or unlikeness of relations. Already, incidental reference has been made to these à priori arguments; but they claim a more definite statement than they have hitherto received.
Both of them are based immediately upon the very definition of reason, considered under its universal aspect. What is the content of every rational proposition? Invariably a predication—an assertion that something is, was, or will be, conditioned (or not) in a specified manner—that certain objects, forces, attributes, stand to each other thus or thus, in Time or Space. In other words—the content of every rational proposition is, some relation. But what is the condition under which alone a relation is thinkable? It is thinkable only as of a certain order—as belonging, or not belonging, to some class of before-known relations. It must be with relations as with the terms between which they subsist; which can be thought of as such, or such, only by being thought of as members of this or that class. To say—“This is an animal;” or “This is a stone;” or “This is the colour red;” of necessity implies that animals, stones, and colours have been previously presented to consciousness. And the assertion that this is an animal, a stone, or a colour, is, in such case, a grouping of the new object of perception, with the similar objects before perceived. In like manner the inferences—“That berry is poisonous;” “This solution will crystallize;” are impossible even as conceptions, unless a knowledge of the relations between poison and death, between solution and crystallization, have been previously put into the mind; either immediately by experience, or mediately by description. And if a knowledge of such relations pre-exists in the mind, then the predications—“That berry is poisonous;” “This solution will crystallize;” imply that certain new relations are thought of as belonging to certain classes of relations—as being severally of the same order as one or more relations previously known. It follows, then, that contemplated from this point of view, reasoning is a classification of relations. But what does classification mean? It means the grouping together those that are like—the separation of the like from the unlike. Hence, therefore, in inferring any relation we are necessitated to think of it as one (or not one) of some class of relations; and thus to think of it, is to think of it as like or unlike certain other relations. Inference is impossible on any other condition.
Again, passing to the second à priori argument, let us consider what is the more specific definition of reasoning. Not only does the proposition embodied in every inference, assert a relation; but every proposition, whether expressing mediate or immediate knowledge, asserts a relation. In what, then, does the knowing a relation by reason, essentially differ from the knowing it by perception? It differs by its indirectness. Every cognitive act, consisting as it does in the consciousness of a definite relation between two things, (in contradistinction to that indefinite relation which is already known to obtain between them as severally existing in Space and Time), the process of cognition is distinguishable into two separate kinds; according as the relation is disclosed to the mind directly or indirectly. If the two things are so presented that the relation between them is immediately cognized—if their coexistence, or succession, or juxtaposition, is knowable through the senses; we have a perception: but if their coexistence, or sequence, or juxtaposition, is not knowable through the senses—if the relation between them is mediately cognized; we have a ratiocinative act. Reasoning, then, is definable as the indirect establishment of a definite relation between two things. But now the question arises—By what process can the indirect establishment of a definite relation be effected? There is but one answer. If a relation between two things is not directly knowable; it can be disclosed to the mind only through the intermediation of relations that are directly knowable, or are already known. Two mountains not admitting of a side by side comparison, can have their relative heights determined only by reference to some common datum line; as the level of the sea. The relation between a certain distant sound and the blowing of a horn, can be established in consciousness, only by means of a before-perceived relation between such a sound and such an action. Observe, however, that in neither case can any progress be made so long as the relations are separately contemplated. Knowledge of the altitude of each mountain above the sea, will give no knowledge of their relative altitudes, until their two relations to the sea are thought of together, as having a certain relation. The remembrance that a special kind of sound is simultaneous with the blowing of a horn, will be of no service unless this general relation is thought of in connection with the particular relation to be inferred. Hence, then, every ratiocinative act is the establishment of a definite relation between two definite relations.
These two general truths—That reasoning, whether exhibited in a simple inference, or in a long chain of such inferences, is the indirect establishment of a definite relation between two things; and that the achievement of this, is by one or many steps, each of which consists in the establishment of a definite relation between two definite relations; embody, under the most abstract form, the various results arrived at in previous chapters.∗
CLASSIFICATION, NAMING, AND RECOGNITION.
§ 42. It needs but to read a page of any treatise on Logic, to sec that there is a close alliance between Reasoning and Classification. The alliance is much closer than is supposed. It is not simply that, as every logician holds, Reasoning presupposes Classification; but also that Classification presupposes Reasoning. This statement seems to involve a contradiction; and would do so, were Reasoning and Classification wholly distinct things. But the solution of the apparent paradox, lies in the fact, that they are different aspects of the same mental process—are the necessary complements of each other. Already in describing reasoning as the classification of relations, its near approach to the classification of entities has been implied: and if we remember that whilst, on the one hand, classification of relations involves classification of the things or attributes between which they subsist; on the other hand classification of entities involves classification of the relations among their constituent attributes; the kinship of the two will appear still closer. But let us compare them in detail.
It is self-evident that the idea underlying all classification is that of similarity. When we group an object with certain others, we do so on the ground that in some or all of its characteristics it resembles them. Whether it be in classing together the extremely like individuals constituting a species; whether it be in uniting under the general division, vertebrata, such apparently heterogeneous creatures as a fish and a man, a snake and a bird; or whether it be in regarding both animate and inanimate objects as members of the great class, solid bodies; there is always some community of attributes—always some similarity in virtue of which they are colligated. But, as was lately pointed out, similarity means equality or likeness of relations. When it is said that the two triangles ABC, DEF, are similar; the specific assertion involved is, that AB is to BC, as DE to EF; or, generally, that the quantitative relation between any two sides of the one, is equal to that between the homologous sides of the other. And when the two annexed
shells are classed as of the same species, it is manifest that, as before, the perception of similarity is a perception that the relations amongst the several parts of the one, are equal to, or like, those among the homologous parts of the other; not only in size, but to a great extent in colour, texture, and so on. What, then, is the difference between the acts of thought by which, from the perception of similarity in the triangles, there is evolved an inference respecting the value of some side; and by which, from the perception of similarity in the shells, there is evolved the idea of identity of class? The difference consists simply in this. Similarity has several implications: after the perception of similarity any one of these may present itself to consciousness; and according as one or other of the two leading kinds of implication is thought of, we have, either reasoning or classification. To speak specifically—It is impossible to perceive anything to be similar to another, or others, without, to some extent, thinking of that other, or those others: at the same time it is impossible to perceive similarity between things, without being more or less conscious of that likeness of relations which constitutes their similarity. Either of these two latent implications may become the subject of distinct contemplation. If we consciously recall the things to which this particular one is similar, we classify; if, consciously dwelling upon the likeness of relations, we think of certain implied attributes, we reason.
“But how,” it may be asked, “does this prove that classification presupposes reasoning; as well as reasoning, classification? It may be true that the intuition of similarity is their common root. It may be true that our conscious inferences involve acts of classing. But it does not, therefore, follow that our conscious acts of classing involve inferences.” The reply is, that in all ordinary cases, the majority of the like relations in virtue of which any object is classed with certain before known ones, are recognized, not by perception, but by reason. The structural, tangible, gustable, ponderable, and other sensible attributes, ascribed to an orange, are not included in the visual impression received from the orange; but, as all admit, are inferred from that impression. Yet these various inferred attributes are included in the concept—an orange. When I reach out my hand towards this reddish-yellow something, under the belief that it is juicy, and will slake thirst; I have already, in judging it to be an orange, necessarily conceived it as having various attributes besides the observed ones: every one of which I know to exist, only by the same process that I know the juiciness to exist. The act of classing, then, involves a whole group of inferences; of which the particular inference drawn is only one. And had some other been drawn, as that the taste was sweet, what is now distinguished as the inference would have been one of the data—one of the attributes involved in the judgment—this is an orange. Should any one contend that these various unspecified attributes are not inferred in the act of classing; but that the entire thought implied is—All reddish-yellow, spherical, polished, pitted bodies of a certain size are juicy; the untruth of the position will be at once seen on remembering what takes place, if a mock-orange made of painted stone is laid hold of. The unusual, the unexpected weight, and hardness, instantly lead to a change of classification: it is at once perceived that the body is not an orange. And this fact proves that something else than juiciness had been inferred; had been wrongly inferred; and had involved a wrong classification. Further evidence, were it needed, might be drawn in abundance from those higher processes of classification pursued by men of science, in which the reasoning is conscious and elaborate: the implication being that what is knowingly done in scientific classification, is unknowingly done in ordinary classification.
And herein lies another essential vice of the syllogistic theory. That theory proceeds upon the supposition that the act of referring any individual object to a class, is not an act of inference. The constant assumption is that the minor premiss, “This is a—,” is immediately known; whereas it is always known mediately. The process of reasoning is already involved in the cognition of the very data out of which the reasoning process is said to be evolved. On the hypothesis that the syllogism represents the entire ratiocinative operation, it is contended that its conclusion is necessary. Meanwhile, the all-essential fact which it posits as the foundation of that conclusion, is itself known by an unexpressed ratiocination. The concluded fact, and the fact from which it is concluded, stand on the same footing. The proposition—That which I see is an orange; has no greater certainty than the proposition—That which I see is juicy. The visual impressions of form, size, colour, and surface, received from it, form the sole ground for both propositions. The wider inference—It is an orange; can give no extra-validity to the narrower inference—It is juicy; seeing that for the first there is no more evidence than for the last. Yet the doctrine of the syllogism implies that the one is the warrant for the other—implies that I can directly know that this something belongs to the class, oranges, and, by so doing, can indirectly know that it is juicy!
No such insuperable difficulty, however, stands in the way of the theory now enunciated. A perception of similarity—an intuition of likeness of relations, underlying at once the act of classification, or general inference, and the act of ratiocination which gives any special inference, is the basis of either or both, as the case may be. Along with the visible attributes of an orange, may be represented to the mind in various degrees of distinctness, some, many, or all of the attributes before found in relation with such visible attributes; and, according to the mode in which they are represented, the thing predicated is the class, or some one or more of the attributes. If the various unperceived attributes are thought of in their totality, and no one of them becomes specially prominent to consciousness; then, the object in being mentally endowed with all the characteristics of its class, is conceived as one of that class, or is classified. But if one, or a group, of the unperceived attributes arrests the consciousness, and occupies it to the partial exclusion of the other unperceived attributes; then, we have a special inference, or what is verbally embodied as such. Of course the two processes being thus related, run into each other so readily and rapidly, that probably neither ever occurs without the other. It is scarcely possible that the aggregate of unperceived attributes should be thought of without some of them being represented to the mind more vividly than the rest; and it is scarcely possible that any one of them should so completely engross the mind as totally to banish all others. Always the special attribute inferred has for its indistinct background, those many accompanying attributes which constitute the conception of the object as one of a class; and always among the many attributes united in this classing conception, some one or more attributes stand out as incipient inferences. A latent classing accompanies the inferential act: latent inferences accompany the act of classing: and each continually arousing the other, alternates with it in consciousness. Thus we see that whilst likeness of relations is the intuition common to reasoning and classification; it results in one or the other, according as the relations thought of are total or partial.
§ 43. If we regard the name of a thing as a kind of conventional attribute, it will be manifest that, on the presentation of the thing to the mind, this conventional attribute becomes known, as any unseen real attribute becomes known—by an act of inference. The immediately perceived properties are thought of as standing towards various unperceived properties in relations like those previously experienced; and amongst these unperceived properties, is that of calling forth from human beings a certain articulate sound—the name. It is true that this property is not inherent; but depends on an almost accidental relation established between the thing and a limited class of minds. But the like is true of various other properties which we commonly ascribe to the thing itself. As all admit, the so-called secondary qualities of body are not intrinsic; but are the affections produced in our organs by unknown agents; and they so vary, that the same thing may be warm or cold, loud or low, pleasant or disagreeable, according to the character or state of the individual. If, then, these subjective and partially incidental affections, are regarded as attributes of the objects affecting us, and are often ascribed to them inferentially; we may say that the yet more purely subjective and incidental affections which an object produces on us when it suggests its name, is also in a strained sense an attribute, and becomes known by a similar mental process.
But it is by no means necessary to the argument that names should be thus considered as factitious attributes, dependent for their production, like secondary ones, upon organic conditions; though conditions that are far less constant. The fact, that the name of an observed object becomes present to consciousness after the same manner that an unperceived attribute does, may be rendered manifest without seeking any similarity between the things themselves. Observe what happens with a child. The name orange, which it probably first hears on a sample of that fruit being given to it, and which is often repeated in connection with similar visible and tangible attributes, is established in its mind as a phenomenon having a more or less constant relation to the various phenomena which the orange presents. Not having as yet any notions of necessary and accidental relations, the particular sound accompanying these particular appearances, is as much grouped with them as the particular taste is. When the particular appearances recur, a relation (like the previously experienced relation) between them and this allied sound, is as likely to enter into the mind, as a relation between them and the allied taste. The mental act is essentially the same; and though subsequent experiences modify it in so far as the resulting conception is concerned, they cannot alter its fundamental nature. The genesis of the thought by which a thing is named must ever remain identical in nature; and to the last, as at the first, likeness of relations must be the intuition implied in it.
Still more manifest will become the close kinship between naming and reasoning, when we call to mind that aboriginally, a name is a copy of some real attribute of the thing named. It is inferable alike from the prattling of children and from the speech of savages, that all language is in the beginning mimetic. Wherever we can trace out the origin of symbols used to convey thoughts—whether it be in the infantine habit of naming animals by imitating their cries, or in that of senselessly repeating the articulate sounds made by persons around; whether it be in the signs spontaneously hit upon by deafmutes, or those by which travellers in strange lands express their wants; whether it be in the dramatic gestures with which the uncivilized man ekes out his imperfect vocabulary, or in the simulative words of which that vocabulary so largely consists—we see, not only that the notion of likeness underlies all language, but that the symbols of thought, both vocal and mechanical (and even literal also), are at first, merely reproductions of the things signified. And if, as no one who has examined the facts can question, names, in their earliest unmodified forms, are either directly or metaphorically descriptive of one or more distinctive attributes; then, it is clear that primarily an act of naming is simply an inference becoming vocal. If a Bosjesman, catching sight of some wild animal, conveys the fact to his fellows by pointing towards it and mimicking the sound it is known to make; beyond doubt this sound came into his mind as an inferred attribute. And it differs from any other inferred attribute solely in this; that instead of being simply represented to his consciousness, it is further re-represented by his voice: the inference, instead of remaining ideal, becomes, in a sense, real. Not only, then, is it true, that by ourselves the name of a thing is always thought of in the same way that any inferred attribute is thought of; but we find that, originally, a name was literally an inferred attribute transformed—an inference which, arising in the mind of the individual by a representative act, is forthwith presentatively conveyed by him to other minds. It is scarcely needful to add that, developing as language does by insensible modifications and complications out of this primitive process of naming; it follows throughout the same general law. Almost losing, though it ultimately does, the marks of its inferential genesis; it needs but to watch the use of new metaphors and the coining of new words, to see under a disguised form, the same fundamental intuition of likeness of relations.
§ 44. From the acts of Classification and Naming, let us now pass to the act of Recognition. When the relations subsisting among any group of attributes, are not simply like the relations subsisting among some before-known group, but are in most, if not in all respects, equal to them; and when the attributes themselves (as those of height, breadth, colours, &c.) are also equal; then we conclude the object presenting them to be the same object that we before knew. Recognition differs from classification, partly in the fact that the two compared groups of relations usually present a much higher degree of likeness; but mainly in the fact that not only are the relations alike, but the constituent attributes are alike. There are two kinds of difference which objects present: difference in one or more of their sensible properties, as considered severally and separately; and difference in the mode in which these sensible properties are co-ordinated, or related to each other. If the relations differ, the objects are known to be of different species. If the relations are alike, but the properties as individually considered different; the objects are of the same species. And if the relations are alike, and the individual properties are alike—that is, if there is no discernible difference; we know the object as one previously perceived—we identify it—we recognize it. To speak more specifically—If, passing over all those wider classes, such as minerals, plants, &c., whose members present very few relations in common; and those narrower but still very comprehensive ones, such as houses, crystals, quadrupeds, which have a more decided similarity; and again, those yet narrower ones that are called genera—if, passing over all these, we confine our attention to those narrowest and most precise classes which unite individuals of the same kind, as asses, firtrees, balloons; we see that whilst in respect of each particular attribute, there need not be anything like equality, there must be equality, or at least extreme likeness, in respect of the mode in which the attributes are combined. Whether the ass be six feet long or four feet long—whether dark brown or light brown, does not affect the classification; providing the proportions of its body and limbs in their ensemble and details, are indistinguishable, or next to indistinguishable, from those of other asses. It matters not whether the fir-tree be one foot high or a hundred feet; it is still classed as a fir-tree, if the relations of the branches to each other and to the stem, in position, direction, and length, together with the proportions and grouping of the pin-shaped leaves, are like those of fir-trees in general. But that a particular person or place should be identified as a person or place before seen, implies in the great majority of cases, not only that the elements which compose the perception should stand to each other in relations that are indistinguishable from the remembered relations; but further, that each of the elements individually, should be indistinguishable from the remembered clement.
I say in the majority of cases, because, though this is the fundamental prerequisite to recognition, it is not always rigorously fulfilled. Were not objects liable to change, it might be affirmed without qualification. But our general experience of the changeableness of things, often leads us to predicate identity where there is not only some failure of likeness between the perceived and the remembered attributes, but when even the relations in which they stand to each other are no longer quite the same. Though, if the body be inanimate, we look for sameness in the dimensions and their several ratios, we are not prevented from knowing it again, by the absence of a corner, by some change of colour, by the loss of polish, and so on. And an animate body may be recognized as a particular individual, even though it has greatly altered in bulk, in colour, and even in proportions—even though a limb has disappeared, the face become thin, and the voice weak. But when, as in these instances, the identity is perceived, in virtue of some very distinctive attributes and relations which remain unaltered; it is manifest that the particular perceptions are interpreted by the help of sundry generalizations respecting the changes to which certain classes of bodies are liable; and that thus the act of simple recognition, properly so called, is greatly disguised. It should be remarked too, that in cases of this kind the distinction between Recognition and Classification is very liable to disappear. It frequently becomes a question whether the observed object is the identical one before seen, or another of the same class. Both which facts further confirm the definitions above given.
But perhaps the antithesis will be most clearly exhibited, by choosing a case in which recognition is impossible, in consequence of the extreme likeness of the individuals constituting the class. Suppose, while taking a needle from among sundry others of the same size, the whole paper-full is dropped on the floor. To fix upon the one which was about to be taken, is known to be hopeless. Why? Because the needles are so exactly alike in all respects, that no one of them is distinguishable from the others. Classification and Recognition here merge into one: or rather, there is no recognition of the individual, but only of the species. Suppose now, that the selected needle is a larger one than the rest. What follows? That it can be readily identified. Though it may be perfectly similar to the others—though the ratios of the several dimensions to each other may be exactly like the homologous ratios in the rest—though there may be complete equality of relations among the attributes; yet these attributes, separately considered, differ from the corresponding attributes in the others: and hence, the possibility of recognition. And in this case we see, not only the positive conditions under which only recognition can take place, but also the negative conditions. We see not only that the object identified must re-present a group of phenomena just like the group before presented; but also that there must be no other object presenting an exactly parallel group.
One further fact to be noticed is, that Recognition, in common with Classification, is a modified form of reasoning. It is not simply that reasoning is involved in cases where great change has taken place; as where a tree that has wholly outgrown recollection is identified, in virtue of its relative position to surrounding objects; but it is that where the recognition is of the simplest kind—where the recognized object is absolutely unaltered, there is still a ratiocinative act implied in the very predication of its identity. For what do we mean by saying of any particular thing, that it is the same which we before saw? And what suffices us as proof of the sameness? The conception indicated by the word same, is that of a perfectly definite assemblage of correlated phenomena not similar to a before-known assemblage, but indistinguishable from a before-known assemblage. On perceiving a group of attributes answering in all respects to a group perceived on a previous occasion, and differing in some respects from all allied groups, we infer that there coexists with it a group of unperceived attributes that likewise answer, in all respects, to those previously found to coexist with the perceived group. And should any doubt arise as to the identity of the object, then, by more closely inspecting it, by feeling it, by examining its remote side, by looking for a particular mark before observed, we proceed to compare the inferred attributes with the actual ones: and should they agree, we say the object is the same. This is the sole content of our notion of sameness. Whilst from minute to minute throughout our whole lives we are presented with groups of phenomena differing more or less from all previous ones; we are also continually presented with groups of phenomena that are absolutely indistinguishable from groups before presented. Experience teaches us that when the perceived portion of one of these groups is indistinguishable from the corresponding portion of one before perceived; then, the remaining portions of the two are also indistinguishable. And the act of recognition is simply an inference determined by this general experience, joined to that particular experience which the recognition presupposes.
From all which it is manifest that, regarding them both as forms of reasoning, Recognition differs from Classification, simply in the greater speciality and definiteness of the inferred facts. Whilst, on the one hand, in classing an observed object as a book, the implied inference is, that along with certain visible attributes there coexist such others as the possession of white leaves covered with print; on the other hand, in the recognition of that book as So-and-so's Travels, the implied inference is, that these white leaves are covered with print of a particular size, divided into chapters with particular titles, containing paragraphs that express particular ideas. Thus the likeness of relations involved in the intuition, is both more exact and more detailed.
§ 45. The general community of nature thus shown in mental acts called by different names, may be cited as so much confirmation of the several analyses. As, in preceding chapters, we saw that all orders of Reasoning—Deductive and Inductive, Necessary and Contingent, Quantitative and Qualitative, Axiomatic and Analogical—come under one general form; so here, we see both that Classification, Naming, and Recognition are nearly allied to each other, and that they also, are severally modifications of that same fundamental intuition out of which all orders of reasoning arise. Not only are Classification and Naming both of inferential nature; but they are otherwise allied as different sides of the same thing. Naming presupposes Classification; and Classification cannot be carried to any extent without Naming. Not only is it that Recognition and Classification are modes of ratiocination; not only is it that they often merge into each other, either from the extreme likeness of different objects, or the changed aspect of the same object; but it is that while Recognition is a classing of a present impression with past impressions, Classification is a recognition of a particular object as one of a special group of objects. And the weakening of these conventional distinctions—the reduction of these several operations of the mind, in common with all those hitherto considered, to variations of one operation, is to be expected as the natural result of analysis. For it is a characteristic of advancing science, continually to subordinate the demarcations which a cursory examination establishes; and to show that these pertain, not to nature, but to our language and our systems.
THE PERCEPTION OF SPECIAL OBJECTS.
§ 46. The several mental processes treated of in the last chapter, must be briefly glanced at under their obverse aspect. We analysed Classification and Recognition as particular forms of the act by which surrounding things become known to consciousness. It remains to be pointed out that surrounding things can become known to consciousness, only by acts of Classification or Recognition. Every perception of an external body involves a presentation of it to the mind as such or such—as a something more or less specific; and this implies, either the identification of it as a particular thing, or the ranging of it with certain like things. As there can be no Classification or Recognition of objects without Perception of them; so there can be no Perception of them without Classification or Recognition. Every complete act of perception implies an expressed or unexpressed “assertory judgment”—a predication respecting the nature of the perceived entity; and as is generally admitted, the saying what a thing is, is the saying what it is like—what class it belongs to. The same object may, according as the distance or the degree of light permits, be identified as a particular negro; or more generally as a negro; or more generally still as a man; or yet more generally as some living creature; or most generally as a solid body: in each of which cases the implication is, that the present impression is like a certain order of past impressions. The instances in which, from mental distraction, we go on searching for something we have in our hands, or overlook that which is directly under our eyes, clearly show that the mere passive reception of the visual image or group of sensations produced by an object, does not constitute a perception of it. A perception of it can arise only when the group of sensations is consciously co-ordinated and their meaning understood. And as their meaning can be understood only in virtue of those past experiences in which similar groups have been found to imply such and such facts; it is clear that the understanding of them—the act of perception, involves the assimilation of them to those similar groups—involves the thinking of them as like those groups, and as having like accompaniments. The perception of any object, therefore, is impossible save under the form either of Recognition or Classification.
The only qualification of this statement, that may seem in strictness required, concerns cases in which some species of thing is presented to consciousness for the first time—cases, therefore, in which a thing is known not as like, but as unlike, the things previously known. Though, however, it may appear that there is here no Classification—seeing that there exists no previously-formed class—further consideration will show that there is a classification of a general, though not of a special kind. Suppose the object to be a new animal. Though in the act of perception it may not be thought of under the class, mammals, or the class, birds; it is still thought of under the class living beings. Suppose there is doubt whether the object is animate or inanimate. It is nevertheless, perceived as a solid body, and classed as such. The primary act then, is still a cognition of likeness of a more or less general kind; though there may subsequently arise a cognition of a subordinate unlikeness to all before-known things. Whether this law holds when we descend to the simplest kinds of cognition, it would be premature here to inquire; for at present we have to do only with those more complex cognitions, by which surrounding objects are severally distinguished in their totality. To cover all possible criticisms, however, the statement may be qualified by saying, that a special perception is possible, only as an intuition of the likeness or unlikeness of certain present attributes and relations, to certain past attributes and relations.
§ 47. It requires further to be observed, that the perception by which any object is known as such or such, is always what is called an acquired perception. The truth exhibited at length in the last chapter—that Classification and Recognition are inferential acts—is even deducible from the current theory that inferences are implied in the interpretation of every group of sensations. All psychologists concur in the doctrine that most of the elements which go to make up the cognition of an observed object, are not known immediately through the senses, but are mediately known by an instantaneous and unconscious ratiocination. Before a mere visual impression can be developed into a perception of the thing causing it, there must be added in thought those attributes of solidity, trinal extension, size, quality of surface, &c. &c., which when united, constitute the nature of the thing as it is known to us. Though these seem to be given in the visual impression, it is demonstrable that they are not so; but have to be reached by inference. And the act of knowing them is termed acquired perception, to signify the fact that whilst really mediate, it appears to be immediate.
Not only, however, do the Classification and Recognition of individual objects imply acquired perceptions; but acquired perceptions are implied in the Classification and Recognition of those various actions and changes which objects exhibit. If an adjacent person at whose back we are looking, suddenly turns half round; the only thing immediately known is the sudden change in the character of the visual impression. Standing alone this change has no meaning; and comes to have one, only when by accumulated experiences it is found, that all such changes are accompanied by alterations in the relative positions of the parts, as ascertained by touch. We do not see the turning: we infer the turning. We conceive a certain relation between visual and mechanical changes like the numberless previously experienced relations; we classify the present relation with a series of past relations; and we signify it by a word like the words used to signify those past relations. The visible transformation which a piece of melting lead undergoes, can convey no knowledge, unless it is before known that certain appearances always coexist with fluidity. And what seems to be a perception of the melting is, in reality, a rational interpretation of the appearances—a classing of them with the like appearances before known, and an assumption that they stand towards certain mechanical phenomena in relations parallel to the before-known ones. Endless illustrations to the same effect might be cited; but the above will suffice to indicate that those apparently simple though really complex cognitions, by which we guide ourselves from moment to moment, in the house and in the street—cognitions which chase each other through consciousness too rapidly even for enumeration—are all of them acquired perceptions; all of them involve the classification or recognition of attributes, groups of related attributes, and the relations between such groups; all of them embody inferences; all of them imply intuitions of likeness or unlikeness of relations.
§ 48. And here we see again illustrated, the fact, that the divisions we make between the various mental processes have merely a superficial truth. At the conclusion of Chapter VII. Reasoning was defined as the indirect establishment of a definite relation between two things; in contrast to Perception, in which the relation is established directly. But now we find that all those Perceptions by which complex objects become specifically known to us, also involve the indirect establishment of relations. Though, if uncritically received, the verdict of consciousness would seem to be, that on contemplating the lights and shades and perspective outlines of a building, the fact that it is a solid body is immediately known; yet analysis proves that its solidity is known mediately. And this analysis is fully confirmed by the stereoscope, which, by simulating the evidence of solidity, induces us to conceive as solid, that which is not solid. It would appear, therefore, that practically, the indirect is merged into the direct by long-continued habit. Just as the meaning of a word in a new language, though at first remembered only by the intermediation of the equivalent word in a known language, by and by comes to be remembered without this intermediation; so, by constant repetition, the process of interpreting our sensations becomes so rapid, that we appear to pass directly to the facts which they imply. Still more manifest will appear the purely relative truth of this division, when it is observed, not only that what are known to be indirect cognitions become direct by habit, but that what seem unquestionably direct cognitions are united by insensible gradations with indirect ones. Thus, if I stand a hundred yards from the front of a house, the shape of that front seems to be known immediately: the relations of the parts are all directly presented to consciousness: nothing is inferred. But if I stand within a yard of the front and look up at it, the outlines, as then presented to my eye, are not in the least like those seen from a distance; and any conception which I may now form of the shape of the front, must be inferred from the greatly distorted outlines I see. Yet between a hundred yards and one yard, there are ten thousand points from which may be had as many views, each differing inappreciably from its neighbours. Evidently, then, the transition from the directly perceived shape to the indirectly perceived shape is insensible. And when to facts of this kind, we add the familiar fact that in reasoning we constantly skip the intermediate steps of an habitual argument, and pass at once from the premisses to a remotely involved conclusion—when we thus see that in conscious reasoning also, the tendency is for indirect processes to become more and more direct; it becomes manifest that from the most elaborate demonstration, down to the simplest intuition, the directness or indirectness with which the relation is established, is wholly a matter of degree; that the extremes are united by a series of insensible transitions; and that thus it is only relatively, and not absolutely, that Reasoning is distinguished from Perception by its indirectness.
THE PERCEPTION OF BODY AS PRESENTING DYNAMICAL, STATICO-DYNAMICAL, AND STATICAL ATTRIBUTES.∗
§ 49. That relation between object and subject which is established in the act of perception, is of a threefold kind. It assumes three distinct aspects, according as there is some species of activity on the part of the object; on the part of the subject; or on the part of both. If, while the subject is passive, the object is working an effect upon it—as by radiating heat, giving off odour, or propagating sound—there results in the subject, a perception of what is usually termed a secondary property of body; but what may be better termed a dynamical property. If the subject is directly acting upon the object by grasping, thrusting, pulling, or any other mechanical process; and the object is reacting, as it must, to an equivalent extent; the subject perceives those variously modified kinds of resistance which have been classed as the secundo-primary properties; but which I prefer to class as statico-dynamical. And if the subject alone is active—if that which occupies consciousness is not any action or reaction of the object, but something discerned through its actions or reactions—as size, form, or position; then the property perceived is of the kind commonly known as primary, but here named statical.
The three classes of attributes thus briefly defined, which will hereafter be successively considered at length, are, for the most part, presented to consciousness, not separately, but together. Extension, and all the space-attributes, are unknowable, save through the medium of resistance and the other force-attributes. Tangible properties are generally perceived in connection with form, size, and position. And of the non-tangible ones, colour is mostly known as pertaining to the surfaces of solids; and cannot be conceived apart from extension of two dimensions. An object that is simultaneously held in the hands and regarded by the eyes, presents to consciousness all three orders of attributes at once. It is known as something resisting, rough or smooth, elastic or unelastic; as something having both visible and tangible extension, form, and size; as something whose parts reflect certain amounts and qualities of light; and, on further examination, as something specifically scented and flavoured.
In conformity with the method hitherto pursued, of taking first the most complex phenomena, resolving these into simpler ones, and these again into still simpler ones; our analysis of the perception of body will be best initiated by taking one of these total, exhaustive perceptions, and considering what are the relations that subsist among its various elements. And with a view of simplifying the problem, it will be well first to consider those contingent attributes known as secondary, and here called dynamical; so that after having duly analysed these in themselves, and in their relations to the necessary attributes, we may proceed to deal with the perception of necessary attributes as divested of everything that is extraneous.
§ 50. Beginning with these contingent attributes as contemplated in themselves, let us, in the first place, consider the propriety of classing them as dynamical. The most familiar liar ones are obviously manifestations of certain forms of force. Of sound, we know, not only that it becomes sensible to us solely through vibrations of the membrana tympani—not only that these vibrations are caused by waves in the air; but we know that the body whence they proceed must be thrown into a vibratory state by some mechanical force—that it must propagate undulations through surrounding matter—and that in this purely dynamical action consists the production of sound. Respecting heat, we know, both that it may be generated mechanically, as by compression or friction; and that, conversely, it is itself capable of generating mechanical force: further, that in its reflections and refractions, it conforms to the law of composition of forces; whilst, by the now established undulatory theory, its multiplied phenomena are resolved into dynamical ones: and yet, further, that on holding a thermometer near the fire, the same agent which produces in us a sensation of warmth, produces motion in the mercury. The phenomena of colour, again, are reducible to the same category. The reflections and refractions of light are inexplicable, save mechanically; and only on the theory of undulations can polarization, diffraction, &c., be accounted for. In common with heat, light varies inversely as the square of the distance; as gravitating force does, and as every force proceeding in all directions from a centre must do. On the now currently received hypothesis of the correlation of the physical forces, light is regarded as one form of the primordial force, which may otherwise manifest itself as attraction, as sensible motion, as electricity, as heat, as chemical affinity. In the fact that high temperature produces luminosity, joined to the fact that high temperature may be generated mechanically, we clearly trace the transformation; whilst, conversely, we find light producing a dynamic effect, alike in all photographic phenomena, and in those changes of atomic arrangement which it causes in certain crystals. Add to which, that though, under ordinary circumstances, matter only reflects and modifies the rays falling upon it; yet under fit chemical conditions, it becomes an independent source of light. Though not the immediate effects of radiant forces, odours are demonstrably dynamic in their origin. In conformity with the established doctrine of evaporation, that continuous giving off of particles in which odoriferousness consists, must be ascribed to atomic repulsion. And as the diffused molecules constituting the scent of a body, must have been propelled from the surfaces of that body, before they can act upon our nostrils; it follows that a certain form of activity in the object, is the efficient cause of a sensation of smell in the subject. The only secondary attribute of matter not obviously dynamic is that of taste. But the close alliance existing between taste and smell, is almost of itself sufficient to prove that if one is dynamic, so also is the other. Moreover, when we bear in mind that for a body to have any gustable property, implies some degree of solubility in the saliva, without which its particles cannot be carried by endosmose through the mucous membrane of the tongue, and cannot therefore be tasted; and when we further bear in mind that the diffusion of particles through liquid, is so far analogous to their diffusion through air, that the atomic repulsion causing the last, very probably has its share in the first; we shall see still further reason to consider the sensation of taste as due to an objective activity. But the dynamic nature of this, as well as of the other secondary attributes, is most clearly seen when, instead of contemplating the object as acting, we contemplate the subject as acted upon. An inappreciable quantity of strychnine, furtively conveyed into an infant's mouth, will produce a wry face; and, as all can testify, the flavours of certain drugs are so persistent as to continue to give us feelings of disgust, long after the drugs themselves have been swallowed. A pungent odour will cause a sneeze. The smell from a slaughterhouse or boneyard, creates a nausea that so tyrannizes over the consciousness, as to exclude every thought but that of escape. A flash of lightning, or any sudden change in the amount or quality of the light surrounding us, instantly changes the current of our thoughts. While sitting alone, and perhaps diligently occupied, any such alteration in the distribution of light and shade as is produced by the movement of an adjacent body, even when quite on the outskirts of the visual field, will cause us to start and turn the head. And still more significant is the fact that a strong glare abruptly thrown upon his face, will often awaken a sleeping person. Similarly with the changes of temperature. Any one standing with his hands behind him cannot have a red-hot iron put close to them without his ideas being at once directed into a new channel. If the degree of heat passes a certain point, he will draw away his hands automatically; and a forced submission to such extreme degree of heat, produces both a violent nervous excitement and a violent muscular action. So, too, is it with sounds. They may create either pleasurable or painful states of consciousness: they often distract our attention against our will: when loud, they cause involuntary starts in those who are awake; and either waken those who sleep, or modify their dreams. If, then, in these extreme cases, the so-called secondary attributes of body are unquestionably dynamic, they must be so throughout. If we see the eyes made to water by mustard taken in excess; vomiting excited in squeamish voyagers by the smell of the cabin; a blinking of the eyes, and a painful sense of dazzling, caused by looking at the sun; a scream called forth by a scald or burn; and an involuntary bound produced by an adjacent explosion; it becomes an unavoidable conclusion that those properties of things which we know as tastes, scents, colours, temperatures, sounds, are effects produced in us by forces in the environment. The subject undergoes a change of state, determined in him by some external agency directly or indirectly proceeding from an object. Though, immediately after that change of state has been produced, there may arise in the subject, during the interpretation of its outward cause, various internally-determined states; yet, in so far as the change itself is concerned, the subject is simply recipient of an objective influence. In respect to all these so-called secondary attributes, the object is active and the subject is passive. Or, in other words, they are dynamical attributes.
Let us next observe that, with the exception of taste, which is in some respects transitional, these dynamical attributes are those by which objects act upon us through space. By means of the light it radiates or reflects, an outward thing renders itself visible to us when afar off. Objects in a state of sonorous vibration arrest our attention at various degrees of remoteness. We are made aware of the presence of odoriferous substances whilst only in their neighbourhood. And masses of hot matter affect us not only when touching our bodies, but when near to them. Unlike hardness, softness, flexibility, brittleness, and all the statico-dynamical attributes, which are cognizable by us only through actual contact, either immediate or mediate; unlike the statical attributes, shape, size, and position, which do not in themselves affect us at all, but can become known only by acts of constructive intelligence; these dynamical attributes modify our consciousness at all distances from that of a star downwards. Eyes, ears, nose, and the diffused nervous agency enabling us to appreciate temperature, are inlets to the influences of objects more or less removed from us; and the ability that objects have thus to transmit their influence through space, again exhibits their inherent activity.
These attributes are further distinguished from all others by the peculiarity that they are, in a sense, separable from what we commonly call body; and may be perceived independently of it. Light in varying intensities is known as pervading surrounding space. The many tints assumed by the sky are not, in .so far as our senses are concerned, the attributes of matter. And by casting the prismatic spectrum upon a succession of neighbouring surfaces, we may readily convince ourselves that colour, in its various qualities and degrees, exists apart from them. Again, the like holds good with respect to the relation between sounds and vibrating objects which we learn only by a generalization of experiences. To the incipient intelligence of the infant, noise does not involve any conception of body. In an often-recurring echo, the sound has come to have an existence separate from the original concussion. We frequently hear sounds produced by things that are at the time neither visible nor tangible to us, but are simply inferred. And by the phrase,—“What's that?” commonly uttered on hearing an unusual noise, it is clearly implied that the noise has been identified as such, whilst yet no object has been thought of as causing it. Odours, also, are often perceived when wafted far from the substances diffusing them. A room scented by something that has been placed in it, may retain the scent long after the thing has been removed. We may be strongly affected by an entirely new smell, whilst wholly ignorant what produces it, or from which side of us it comes. So, too, is it with heat. In a cloudy August we occasionally experience marked changes of temperature that are not traceable to any special object. The warmth of a room heated by hot-water pipes may be felt for some time before it is discovered whence the warmth proceeds. So even is it with gustable properties. Though ordinarily the things which we taste are simultaneously known to us as fluid or solid matters; yet it needs but to note the strong effects produced upon the tongue by pungent chemicals given in intangible quantities, or to remember the persistence of disagreeable flavours even after the mouth has been rinsed, to at once perceive that sapidity can be dissociated from body. Here again, then, the dynamical attributes stand apart from the statico-dynamical and statical ones; for none of those modifications of resistance constituting the one class, nor those tangibly perceived modes of extension constituting the other (visible extension being but symbolical of tangible extension), can be recognized apart from the objects to which they belong.
Note again that these dynamical or secondary attributes are incidental—that not only do different bodies exhibit them in all degrees and combinations, but that each body exhibits them more or less, or not at all, according as surrounding conditions determine. In the dark all things are colourless: in the light their appearances vary as the light varies in kind and degree. The colour of a dove's neck changes with the position of the observer's eye: that of some crystals and fluids is reversed when the light is transmitted instead of reflected. Under ordinary circumstances most objects are silent: those that emit sound do so only under special influences: and the sound that any one of them emits is in great measure determined by the nature or intensity of the influences. A great number of bodies are inodorous; and of the rest, the majority cannot be perceived to have any smell, unless held quite close to the nostrils. Things that are almost scentless at low temperatures will become strongly scented at high ones; and things that have strong scents become for a time relatively scentless if continuously smelt at. Very many bodies have no taste whatever; and the sapid qualities of others vary according as they are hot or cold. The temperatures of things may be such as to give us sensations of greater or less heat; or such as to give us no appreciable sensations at all; or such as to give us sensations of greater or less cold: and things of the same temperature produce different impressions upon us according as they are good or bad conductors, and according as our temperature is high or low. Thus the incidental character of these attributes is manifest. To a person specially circumstanced, an object may be at once colourless, soundless, scentless, tasteless, and of such temperature as to produce no thermal effect upon him; or the object and the circumstances may be such that he shall be affected by one, or two, or three, or four, or all of these dynamic attributes in endless degrees and combinations. But it is otherwise with the statico-dynamical and statical attributes. For while different bodies present different amounts of resistance and extension; and while in the same body the resistance and extension admit of more or less variation; there is no body without resistance and extension.
Lastly, let it be noticed that these so-called secondary attributes of body, which we find distinguishable from the rest as being dynamical; as acting through space; as cognizable apart from body; and as manifested by body only incidentally; are not, in any strict sense, attributes of body at all. It is not simply that being dissociable from body, body can readily enough be conceived without them; nor is it that what we call colour, sound, and the rest are subjective effects produced by unknown powers in the objects; but it is that these unknown powers are literally not in the objects at all. Rightly understood the so-called secondary attributes are every one of them manifestations of certain forces which pervade the universe in general; and which, when they act upon bodies, call forth from them certain reactions. On being struck, a gong vibrates; and by communicating its vibrations to the air, or any intermediate substance, affects an auditor with a sensation of sound. What now is the active cause of that sensation. It is not the gong: it is the force which, being impressed upon the gong, is changed by its reaction into another shape. Let the sun shine upon any mass of matter, and some of his rays will be absorbed while some are reflected. In most cases the light being decomposed, will, in its changed form, affect us as colour; and by special masses of matter it will be refracted or polarized. That is, a certain force emanating from the sun, impresses itself upon matter, and is, by the counter-action of matter, more or less metamorphosed. The heat given off by burning coal, by boiling water, and by a briskly hammered piece of iron, are so many reactions produced by external actions: in the first case by the chemical action of the surrounding oxygen; in the second by the action of neighbouring hot bodies; in the third by mechanical pressure. The slightly smelling substances around us, in common with the fluid extracts of the perfumer, are forced to send off their molecules by the heat which they receive from neighbouring objects. The atomic repulsion from which odoriferousness results, is one of the reactions consequent on the action of thermal force—is known to vary more or less as the thermal force varies; and could thermal force be altogether withdrawn, odours would cease. Throughout, therefore, these attributes are, it considered in their origin, activities pervading space; and can be ascribed to body only in the sense that body when exposed to them, reacts upon them, modifies them, and by implication is known to us through these modifications. Properly understood, any one of these simple sensations of colour, sound, scent, and the rest, involves a series of actions and reactions of which the object proximately producing it, manifests but the last. The light, or mechanical force, or heat serving as its efficient cause, itself resulted from previous actions and reactions, which, if traced, lead us back into an indefinite past filled with like changes. But confining our attention to the elements with which we have immediately to deal, we see that rightly to understand one of these dynamic attributes, implies the contemplation of three things: first, a force, either diffused as light and heat, or concentrated as momentum; second, an object on which some of that force is impressed, and which, in so far as it is a recipient of force, is passive, but in so far as it reacts and determines that force into new forms and directions, is active; and third, a subject on whom some of the transformed force expends itself in producing what we term a sensation, and who, as the recipient of this transformed force, is passive, but who may be rendered active by it.
Strictly speaking, then, the so-called secondary attributes are neither objective nor subjective; but are the triple products of the subject, the object, and the environing activities. Sound, colour, heat, odour, and taste, can be called attributes of body, only in the sense that they imply in body certain powers of reaction which appropriate external actions call forth. These, however, are neither the attributes made known to us as sensations, nor those vibrations, or undulations, or atomic repulsions in which, as objectively considered, these attributes are commonly said to consist; but they are the occult properties in virtue of which, body modifies the forces brought to bear upon it. Nevertheless, it remains true that these attributes, as manifested to us, are dynamical. And, in so far as the immediate relation is concerned, it remains true that, in respect of these attributes, the object is active, and the subject is passive.
§ 51. Having thus gained a precise conception of these so-called secondary attributes, which we find to be dynamical; to act through space; to be separable from body; to be really environing activities modified by the reactions of body; and to be severally contingent both upon the special constitution of the body and its special circumstance; let us now proceed to define the perception which we have of a body presenting these non-necessary attributes, in conjunction with the necessary attributes: that is—a body as ordinarily perceived.
On taking up and contemplating an apple, there arises in consciousness, partly by presentation through the senses, and partly by representation through the memory, what seems to be one state; but what analysis proves to be an extremely complex group of many states, combined after a special manner. The greater number of these remain to be considered analytically in subsequent chapters; and can here be simply enumerated. Among them we have primarily, the coexistence in time of the contemplating subject and the contemplated object; we have further that relative position of the two in space which we call proximity; that group of impressions on the finger-ends, in virtue of which we conceive the object as not only having a position in space, but as occupying space, and a certain limited amount of space; that more complex group of tactile and motor impressions gained by moving the fingers about it, and constituting our notion of its tangible form; that supplementary group of impressions by which we recognize its surface as smooth; and that yet other group by which we form an idea of its hardness. Passing from these fundamental data acquired through the tactile and muscular senses, to those serving as symbols of them, we have to note the impressions through which the apple's coexistence in time and adjacency in space, are visually as well as tactually known; those which go to make up our conception of its visible bulk and figure; and those which indicate to us a correspondence between the data received through the eyes and those received through the fingers. But now, along with these statical and statico-dynamical attributes, primarily known through variously modified and combined sensations of resistance and motion, and some of them re-known through certain combined ocular sensations of light, shade, and focal adjustment, we find certain other attributes standing in various orders of relation. Indissolubly joined with the visible attributes of position, size, and form, is that of colour (including in the word all possible modifications of light), recognized as coexistent in time and coincident in space with those statical attributes visually perceived by means of it. This relation admits of some variation however. For though, when our consciousness of colour entirely ceases, our consciousness of visible form, size, and place, ceases with it; yet by alterations in the amount and quality of the light, our impression of colour may be changed in various ways and degrees, and made almost to disappear, without any change being produced in our impressions of form, size, and place. The relation, though generically absolute, is specifically conditional. Observe now, however, that the relation of coincidence in time and space between the several impressions we have of the visible attributes, and those we have of the tangible ones, is entirely conditional. It depends on the presence of light; on the opening of the eyes; and on the object being within the field of view. Unless each of these three conditions is fulfilled, no relation of coincidence in time and space between these two sets of attributes, can be established. Similarly with the odour. This, being but weak, cannot be known as accompanying the other attributes, unless the apple be placed close to the nostrils and air be drawn in. The presence of a certain taste is in like manner unknowable, save through actions similarly special. Thus, the common characteristic of the dynamical attributes, as perceived to coexist with the statico-dynamical and statical ones, is, the extreme conditionality of their coexistence, in so far as our consciousness is concerned. Though our perceptions of the softness, roughness, flexibility, &c. of any body examined by the fingers, are conditional, both upon the nature of the body and upon our performance of certain manipulations; yet the general perception of resistance is wholly unconditional. Though our perceptions of the specific extension of the body—its size and shape—are similarly conditional upon its character and upon our acts; yet the general perception of extension is wholly unconditional. Some resistance and some extension are the invariable and necessary elements of the cognition. Be the body what it may, and be the part of our surface which it touches what it may, if it is perceived at all, it is perceived as something resisting and extended. But the perception of the dynamical attributes as coexistent with the rest, is conditional, not only upon the nature of the object and upon our acts, but also upon the exposure of the object to certain agencies pervading the environment.
Hence then, leaving out details, any total perception in which the three orders of attributes are jointly known, is a composite state of consciousness in which, along with certain general impressions of resistance and extension, unconditionally standing to each other and the subject in relations of coexistence in time and adjacency in space; and along with certain specialized impressions of resistance and specialized impressions of extension, conditionally standing to each other and the subject in similar space-relations, and slightly modified time-relations; there are presented certain further impressions, standing in a doubly conditional manner to the previous ones, to the subject, and to each other, in space and time relations still further modified. This definition must not, however, be taken as anything like an accurate or exhaustive one: for nothing is said of all the inferred facts inextricably bound up with the perceived ones; nothing of those many minor conditions and accompaniments, to describe which completely would take pages. It is intended simply to exhibit, in as precise a way as the present stage of the analysis admits, the general mode in which our cognitions of the several orders of attributes are united in ordinary perception—simply to display the relationship in which, as known to us, the dynamical attributes of body stand to its other attributes: so that having duly contemplated the connection, we may go on to analyze the perception of the statico-dynamical and statical attributes by themselves.
§ 52. The mental operation, however, by which one of these perceptions is effected, still remains to be described. So far, we have considered only the several elements which compose the perception; and there has yet to be considered the process by which they are co-ordinated. This is what may be termed a process of organic classification.
As explained in preceding chapters, the “assertory judgment” involved in every perception of an object, is an act of either classification or recognition. The perception, according as it is more or less specific, involves the thought,—“This is a dog;” or, “This is something alive;” or, “This is a solid body.” It is not requisite that the assertory judgment should be verbally expressed, either outwardly or inwardly; but that the perceived object must be more or less consciously referred to its class, is manifest from the fact, that when, after some ordinary thing has been put under his eyes, a person cannot subsequently tell what it was, we say that he did not perceive it. Though he received all the needful impressions, he did not so attend to them as to become conscious of what they imported. Had he done so, his subsequent ability to name the thing would imply that, verbally or not verbally, he had recognized its nature; that is, its class. Now this semi-conscious classification which every complete perception of an object involves, is necessarily preceded by a still less conscious classification of its constituent attributes, of the relations in which they stand to each other, and of the conditions under which such attributes and relations become known. At first sight, this will appear to be an incredible proposition—incredible both as asserting what self-analysis gives no evidence of, and as implying a mental activity inconceivably rapid. Nevertheless, inquiry will show both that, à priori, the perception of an object is not otherwise possible, and that direct experience, not less than analogy, implies that some such spontaneous assimilation takes place.
Observe first the necessities of the case. If, instead of that which I perceive to be an apple, there had been presented something having like form and colours, but measuring a yard in diameter; I should not have concluded it to be an apple. Or if, while the bulk and colours were as usual, the form were cubical or pyramidal; I should certainly have regarded it as something else than an apple. And similarly, if, though like in other respects, it were sky-blue; or covered with spines; or as heavy as lead. What now is implied by these facts? Clearly it is implied that before the object is recognized as an apple, each of the chief constituent attributes is recognized as like the homologous attributes in other apples. The bulk is perceived to be like the bulk of apples in general; the form like their forms; the colour like their colours; the surface like their surfaces; and so on: that is, each of the several elements constituting the total perception, is classed with the before-known like elements; just as the entire group of elements is afterwards classed with the before-known like groups. Moreover, there is a classing not only of the constituent attributes, but of their relations. If the apple be one marked with streaks of red; then it is requisite that these should run in certain directions. Were they to run equatorially, it would be at once decided that the object was not an apple; as also, if the stem and the remnant of the calyx did not stand towards each other, and towards the rest of the mass, in specific positions. That is, the relations of coexistence, and proximity, and arrangement, subsisting among the constituent attributes, must also be recognized as like certain before-known relations—must be classed with them. And yet further, not only must the attributes and relations be thus classed, but also the conditions under which they become known. The colours and visible form of an apple being perceivable only during the presence of light, it results that a cognition of its presence, regarded as a condition like the before-known conditions, becomes an indirect component of the perception: to prove which, it needs but remember that the form and colours of an apple, if seen in the dark, would be regarded not as an apple, but as an optical illusion. Its weight, again, is perceived as coexistent with its tangible properties; but only when it is lifted: and no sensation of weight, save one obtained under this condition, like certain remembered conditions, could be ascribed to the apple, or become an element in the perception of it. Thus then, there is a classing of the several attributes, with the like foreknown attributes; of the relations subsisting among them, with like foreknown relations; and of the conditions under which they are perceived, with like foreknown conditions. And the classification of the object as an apple is the cumulative result of these constituent classifications.
“But how,” it will be asked, “is it possible that such a complicated group of mental acts should be performed so rapidly as to leave no trace in our consciousness?” I have already, by using the phrase “organic classification,” indicated what I conceive to be the solution of this difficulty; and it needs but to glance at the phases through which our acts of classing pass from the conscious to the unconscious, to see that the facts point to this solution. Let any one walking through the Zoological Gardens, meet with an animal he has not before seen, but knows only by description. By what process does he endeavour to determine its kind? He considers its separate characteristics—thinks successively of its size, its general shape, its head, its feet, its tail, its hair, its colour, its walk and actions—classes these respectively as large, as broad, as pointed, and so forth—does, in a less definite way, what a zoologist in a parallel case does systematically; and if he succeeds in classing the creature, does so by thus thinking of the likeness of its constituent parts to those of creatures he has heard of, read of, or seen drawings of. Let him now pass on to some before seen, but not familiar creature, as the hippopotamus. His first sight of it is accompanied by a distinct act of classing; and by a repetition of the name, either aloud or to himself. Let him walk by those cages whose inmates he has often seen, as the lions, and the act of classing will obtrude upon his consciousness much less distinctly. Let him leave the gardens, and though, on passing the horses standing at the gates, he will be conscious that they are horses, he will not specifically identify them as such in any deliberate act of thought. And when he reaches the crowded thoroughfares, though each of the hundred individuals passing him every minute is distinguished as man, woman, boy, or girl, or is classed, the mental act is yet performed so rapidly, so automatically, as scarcely to interrupt the current of his thoughts. Now this ever-increasing facility and quickness in classing complex groups of attributes, implies an ever-increasing facility and quickness in that classing of the attributes themselves, their relations and conditions, which begins with the first days of infancy. Forms, sizes, distances, colours, weights, smells, and the rest, though once consciously classed, gradually during childhood come to be classed less and less consciously; and this classification beginning as it does earlier than any other, being most frequently repeated, and in its nature much simpler, necessarily grows more rapid, more automatic, more organic than any other; and eventually becomes imperceptible to consciousness.
But this view of the matter will be most clearly realized, when each remembers that he has, within his own experience, a case in which the entire progress from conscious to unconscious classification is traceable. When learning to read, the child has to class each individual letter by a distinct mental act. This symbol A, has to be thought of as like certain others before seen; and as standing for a sound like certain sounds before heard. By continued practice these processes become more and more abbreviated and unconscious. Presently the power is reached of classing by one act a whole group of such symbols—a word; and eventually an entire cluster of such words is taken in at a glance. Now, were it not that these steps can be recalled, it would seem absurd to say that when the reader, by what appears almost a single cognition, takes in the sentence—“This is true,” that he not only classifies each word with the before-known like words, but each letter with the before-known like letters. Yet, as it is, he will see this to be an unavoidable inference. For, as it is undeniable that such acts of classing were performed at first; and as no time can be named at which such acts were given up; it follows that the entire change has arisen from their immensely increased rapidity—from their having become automatic or organic. And if this result has taken place with acts of classing that were commenced so late as five or six years old, still more must it have taken place with those much simpler ones which were commenced at birth.
Hence, therefore, the foregoing definition of the perception of body as presenting the three orders of attributes, requires to be supplemented by the explanation, that the several attributes, the relations in which they stand to each other and the subject, and the conditions under which only such attributes and relations can be perceived, have to be thought of as like before-known attributes, before-known relations, and before-known conditions.
THE PERCEPTION OF BODY AS PRESENTING STATICO-DYNAMICAL AND STATICAL ATTRIBUTES.
§ 53. If we imagine a human being without sight, hearing, taste, smell, or the sense of temperature, and having no channels through which to receive impressions of the outer world, save the tactile and muscular senses; then the only attributes of body cognizable by him, will be the statico-dynamical and the statical. All the knowledge which he can gain of things, by touching, pressing, pulling, and rubbing them, and by moving his limbs or body, or both, in contact with them, comes under these heads: the one comprehending that knowledge gained by an activity on his part, and a reactivity on the part of the things; the other comprehending that knowledge gained by his independent internal activity in putting together certain of the impressions he has received,—knowledge in respect of which the things themselves are altogether passive.
These statico-dynamical and statical attributes of body are usually presented to consciousness closely united. When in the dark any object is examined by the hands, more or less definite perceptions of its softness, smoothness, elasticity, &c., are joined with more or less definite perceptions of its position, size, and form. These two classes of perceptions may accompany each other with various degrees of incompleteness: but some connection between them is invariable. As will hereafter be shown, it is questionable whether primordially they are perceived in this relation; but without doubt by the adult human consciousness, all tactile resistances are unconditionally known as coexistent with some extension; and all tactile extensions are unconditionally known as coexistent with some resistance.
In pursuance of the method hitherto followed, we have now to analyze one of these complex tactile perceptions in its totality. And as in the last chapter we directed our attention mainly to a certain contingent class of attributes, and their relations to these essential ones, with a view of subsequently leaving them out of consideration; so here, it will be best to treat more especially of the resistance-attributes, so that having examined the mode in which we perceive them and their relations to the extension-attributes, we may proceed to deal with the extension-attributes by themselves.
§ 54. Observe in the first place, why these resistance-attributes which have been termed secundo-primary, may be more appropriately termed statico-dynamical. They are all of them known as manifestations of mechanical force. They are all, considered in themselves, the results of attraction, or repulsion, or that property of body in virtue of which its reaction upon a disturbing agent varies as the quantity of motion which that disturbing agent impresses upon it.∗ They are the attributes of body involved alike in its standing and in its acting. That capacity which matter has of passively retaining, while undisturbed, its size, figure, and position, may rightly be regarded as statical; while that capacity which it has of opposing a counteracting force to any force brought to bear upon it, must be considered as dynamical; and the fact that these capacities cannot be dissociated, but are two sides of the same capacity, is expressed by uniting the descriptive terms. The duality of aspect demands duality of name. Add to this, that if we class those attributes in respect of which the object is active while the subject is passive, as dynamical; and if we class as statical, those in respect of which the subject is active while the object is passive; then we must class as statico-dynamical, those in respect of which subject and object are both active.
These attributes that have for their common element some manifestation of mechanical force, and that are severally known to us through impressions of which resistance is the essential element, are more numerous than would be supposed. The opposition which objects offer to force tending to raise them—their weight—originates only the attributes of Heavy and Light; which simply indicate certain relative amounts of gravitative force. But the opposition which objects offer to compression or extension, is distinguishable, not only in its relative amounts, but in its kinds. Of bodies that resist in different modes as well as in different degrees, we have the Hard and Soft; the Firm and Fluid; the Viscid and Friable; the Tough and Brittle; the Rigid and Flexible; the Fissile and Infissile; the Ductile and Inductile; the Retractile and Irretractile; the Compressible and Incompressible; the Resilient and Irresilient; and (combined with figure) the Rough and Smooth.∗ Of these pairs of attributed qualities, several are purely relative—are simply degrees of the same. This is manifestly the case with Hard and Soft, Firm and Fluid, Compressible and Irrecompressible. But there are some, as Ductile and Inductile, which are not united by insensible gradations.
To determine the modes in which we perceive these attributes, it is requisite that we should first consider the several distinct sensations resulting from the direct action of body upon us; together with those which accompany our direct action upon body. There are two in respect of which body is active, and we are passive; and two in respect of which we are active and body is passive. Those which we may class as of objective origin, are the sensations of touch and pressure: those which originate subjectively are the sensations of muscular tension and muscular motion. Let us consider them seriatim.
When one of the fingers is brought very gently in contact with anything; or when a fly settles upon the forehead, or a hair gets into the mouth; we have the sensation of touch proper. This sensation is undecomposable—is not accompanied by any sensation of pressure; and though we always ascribe it to some object capable of exercising more or less resistance, we cannot properly say that the resistance is given in the sensation. Though we know the sensation to be caused by mechanical force, it is not immediately, but mediately, that we know this. Mechanical force is immediately knowable to us only as that which opposes our muscular action; and as, in this case, muscular action is not called forth, mechanical force can only be inferred.
If the hand be opened out upon the table, and a weight be placed on one of the fingers, there results the sensation of pressure, which is clearly distinguishable from the last. In most of our tactile impressions, the two are so mixed as to be with difficulty discriminated. But if we compare the feeling caused by a fly on the forehead, with that caused by a weight on the finger, we shall perceive that no increase in the intensity of either will produce the other. And that the two differ not in degree but in kind, will be yet more clearly seen on remembering that the sensation of tickling, which a continuity of touch proper produces, is the strongest when the touch is extremely light; and that when the touch becomes heavier, the sensation of tickling wholly ceases, and is replaced by another. Contrasting them physiologically, we may presume that the sensation of touch proper results from a stimulation of the nerves of the skin, while that of pressure results from a stimulation of nerves in the subjacent tissues; that hence, by very gentle contact the nerves of the skin are alone affected, while by a rougher contact the nerves of both are affected; that consequently, in passing from gentle to rough contact by degrees, the single feeling at first experienced becomes masked by another feeling that arises by insensible gradations; and that thus results the habitual confusion of the two. It remains to be noticed that the sensation of pressure, though often associated with that of muscular tension, often exists apart from it; as in the example above given, and as in our ever-present experience of the reactive pressure of the surface supporting our bodies.
The sensation of muscular tension also, is capable of existing separately from the others. On raising the arm to a horizontal position and keeping it so, and still more on dealing similarly with the leg, a sensation is felt, which, tolerably strong as it is at the outset, presently becomes unbearable. If the limb be uncovered, and be not brought against anything, this sensation is associated with no other, either of touch or pressure.
Allied to the sensation accompanying tension of the muscles, is that accompanying the act of contracting them—the sensation of muscular motion. Concerning the state of consciousness induced by muscular motion, and concerning the ideas of Space and Time which are connected with it in adult minds, something will be said hereafter. For present purposes it will suffice to notice, that while, from the muscles of a limb at rest no sensation arises; while from the muscles of a limb in a state of continuous strain, there arises a continuous sensation which remains uniform for a considerable time; from the muscle of a limb in motion, there arises a sensation which is ever undergoing increase or decrease or change of composition.
The several sensations thus distinguished, and more particularly the last three, are those which, by their combination in various degrees and relations, constitute our perceptions of the statico-dynamical attributes of body. Let us consider some of these perceptions as thus constituted.
§ 55. When we express our immediate experiences of a body by saying that it is hard, what are the experiences implied? First, a sensation of pressure of considerable intensity is implied; and if, as in most cases, this sensation of pressure is given to a finger voluntarily thrust against the object, then there is simultaneously felt a correspondingly strong sensation of muscular tension. But this is not all: for feelings of pressure and muscular tension may be given by bodies which we call soft, provided the compressing finger follows the surface as fast as it gives way. In what then consists the difference between the perceptions? In this; that whereas when a soft body is pressed with increasing force, the synchronous sensations of increasing pressure and increasing muscular tension are accompanied by sensations of muscular movement; when a hard body is pressed with increasing force, these sensations of increasing pressure and tension are not accompanied by sensations of muscular movement. Considered by itself then, the perception of softness may be defined as the establishment in consciousness of a relation of simultaneity between three series of sensations—a series of increasing sensations of pressure; a series of increasing sensations of tension; and a series of sensations of motion. And the perception of hardness is the same with omission of the last series. As, however, hardness and softness are names for different degrees of the same attribute, these definitions must be understood in a relative sense.
Take again the attribute of resilience, as displayed in such a body as indian rubber. The perception of it manifestly includes as one component, the perception of softness; but it includes something more. While, when the finger is thrust against some soft but irresilient body, as wet clay, the three simultaneous series of sensations of pressure, tension, and motion, are followed (on the withdrawal of the finger) by sensations of motion only; when it is thrust against a piece of indian rubber, these three simultaneous series of sensations are followed by three other series in the reverse order. Following the retiring finger, the indian rubber gives a decreasing series of sensations of pressure, and a decreasing series of sensations of tension. Thus the perception of resilience is definable as the establishment in consciousness, of a relation of sequence between the group of co-ordinated sensations constituting the perception of softness, and a certain other group of co-ordinated sensations similar in kind but opposite in order.
The perceptions of roughness and smoothness, referring as they do, not to the degree or kind of cohesion subsisting among the particles of a body, but to the quality of its surface, have little in common with the foregoing. The motion by which either of them is gained, is not in the line of pressure; but at right angles to it. The accompanying sensations of pressure, or of touch proper, do not form either an increasing or a decreasing series; but are either uniform (as when smoothness is perceived) or irregularly varied (as when roughness is perceived). The perception of smoothness, then, consists in the establishment in consciousness of a relation of simultaneity between a special series of sensations of motion, and a uniform sensation of touch proper, or pressure, or both. While in the perception of roughness, the like sensations of motion are known as simultaneous with a broken series of sensations of touch, or pressure, or both.
It is as unnecessary as it would be tiresome, thus to analyze our perceptions of all the statico-dynamical attributes above enumerated. What has been said renders it sufficiently manifest, that they severally consist in the establishment of relations of simultaneity and sequence among our sensations of touch, pressure, tension and motion; experienced as increasing, decreasing or uniform; and combined in various modes and degrees: and this is all which it here concerns us to know.
§ 56. Passing from these preliminary analyses to the general subject of the chapter—the perception of body as presenting statico-dynamical and statical attributes, or in other words—the perception of body obtained through the tactile and motor organs alone; we find that it is made up of the following elements. The relations between subject and object, of coexistence in time and adjacency in space; the combined impressions which make up our ideas of a more or less specific size and a more or less specific shape; the further impressions included in our notions of surface; those included in our notions of texture; and those many others signified by the terms ductility, elasticity, flexibility, &c.—all of them referred to one place in time and space. Not to dwell upon these several constituents of the perception, which were to some extent incidentally described in the last chapter, it now remains to specify more definitely than before, the kind of union subsisting among them. When in the dark the presence of some object is revealed to us by accidental collision, we have, along with certain unexpected sensations of pressure and muscular tension, a more or less vague conception of a something extended; and, as previously explained, this relation of coexistence between resistance and extension is unconditional—is independent alike of the will of the subject and the quality of the object. But if the nature of the object is to be ascertained, its reactions must be called forth by certain appropriate actions of the subject. The sensations it gives us must become known as sequent to certain sensations we give ourselves. There must be particular kinds of volition and the particular changes of internal state that follow them, before the changes resulting from external impressions can be received. It is true that some of the resistance-attributes, as hardness and softness, usually become involuntarily known in the act of collision; though this is not necessary, seeing that when moving with outstretched hands, the gentlest touch suffices to prove to us that there is something, before yet we can know aught of its nature. But to determine whether the body is rough or smooth, flexible or rigid, ductile or inductile, &c. manifestly presupposes subjective activities of a complicated kind: and the modifications of consciousness accompanying these, must become essential elements of the perceptions. Hence, a statico-dynamical attribute is perceived through a union of internally-determined impressions with externally-determined impressions; which combined group of impressions is known as the consequent of those internally-determined impressions constituting volition.
Defined in its totality then, the perception of body as presenting statico-dynamical and statical attributes, is a composite state of consciousness, having for its primary elements the impressions of resistance and extension unconditionally united with each other and the subject in relations of coincidence in time and adjacency in space; having for its secondary elements the impressions of touch, pressure, tension, and motion, variously united with each other in relations of simultaneity and sequence that are severally conditional on the nature of the object and the acts of the subject, and all of them conditionally united with the primary elements by relations of sequence; and having for its further secondary elements certain yet undefined relations (constituting the cognitions of size and form, hereafter to be analyzed), which are also conditionally united alike with the primary elements and the other secondary elements.
Such being the constituents of the perception, it only requires to remind the reader that, as shown at length in the last chapter, the act of perception consists in the classing these constituents, each with others of its own order. No one of them can be known for what it is, without being assimilated to the before-known ones which it resembles. And from the classing of each impression with like remembered impressions; each relation with like remembered relations; and each condition with like remembered conditions; results that classing of the object in its totality which is synonymous with a perception of it.
THE PERCEPTION OF BODY AS PRESENTING STATICAL ATTRIBUTES.
§ 57. From that class of attributes known to us solely through one or other kind of objective activity; and from that further class known to us through some objective reactivity called forth by a subjective activity; we now pass to that remaining class known to us through a subjective activity only. In respect of its space-attributes—Bulk, Figure, and Position—body is altogether passive: and the perception of them is wholly due to certain mental operations, certain acts of thought. Unlike heat, sound, odour, &c., which are presented to consciousness by no acts of our own, but often in spite of them—unlike roughness, softness, pliability, &c., of which we become conscious by the union of our own acts with the acts of things; the phenomena of extension in their several modifications, are cognizable entirely through an internal co-ordination of impressions: a process in which the extended object has no share. Though the data through the interpretation of which its extension is known, are supplied by the object; yet, as those data are not the extension; and as until they are combined in thought the extension is unknown; it follows that extension is an attribute with which body does not impress us, but which we discover through certain of its other attributes. To an uncritical observer, the visible outlines of an object will perhaps seem to be as much thrust upon his consciousness by the object itself, as its colour is. But on remembering that these visible outlines are revealed to him only through certain modifications of light; that these modifications are produced not by the outlines, but by certain occult properties of the substance having these outlines; and that were these occult properties absent the outlines would be invisible; it will be seen that the outlines are known not immediately but mediately. And when it is further remembered that in the absence of light, the outlines of an object are knowable only through a series of tactile and muscular sensations gained by acts of exploration; and that consciousness of the outlines depends on the thinking of these in certain relations; it will no longer be questioned that in the perception of the space-attributes, the object is wholly passive, and the subject alone is active.
The propriety of distinguishing Bulk, Figure and Position as statical attributes, may perhaps be questioned: seeing that as applied in mechanics to signify respectively the phenomena of forces that produce equilibrium, and the phenomena of forces that produce motion, statics and dynamics are allied in nature, and pass the one into the other by insensible steps; whereas the attributes that are here classed as statical, differ wholly and irreconcilably from those classed as dynamical. The reply is, that the terms as now used are to be understood, not in the mechanical sense, but in a more general sense. The statical attributes are those which pertain to body as standing or existing. The dynamical ones are those which pertain to it as acting. Since it will not be denied that the so-called secondary attributes of body, which, as we find, imply its activities, are rightly termed dynamical; it must be admitted that the so-called primary ones, which, as implying passivity, are their antitheses, may be properly distinguished as statical.
§ 58. Whether the space-attributes of body are any of them knowable through the eyes alone, has been a disputed question. That our perceptions of distance are not originally visual, but result from muscular experiences, which visual ones serve to symbolize, is admitted. And that at least one out of the three dimensions of body, involving as it does the idea of greater or less remoteness from us, can be known only through muscular experiences, must also be admitted. But our inability to conceive of colour save as having extension of two dimensions, seems to imply that superficial magnitude is to a certain extent knowable by sight. Though it is perfectly manifest that superficial magnitude as known by sight, is purely relative—that the same surface, according as it is placed quite close to the eye or a quarter of a mile off, may occupy the whole field of view, or but an inappreciable portion of it; yet as, while an object is visible at all, it must present some length and breadth, it may be argued that superficial extension in the abstract, is originally perceivable through the eyes, as much as colour is. This conclusion, however, may be proved erroneous.
A little thought will show, that visible superficial extension is inconceivable without a simultaneous conception of distance. Imagine a surface a foot square to be placed a yard from the eye, at right angles to the axis of vision; and imagine further that four straight lines are drawn from its angles to the centre of the eye. Suppose now that a surface of six inches square be interposed at half the distance, so as to subtend to the eye the same apparent area; and that another of three inches square be interposed between this and the eye in the same manner; and so on continuously. It is manifest that were it possible to repeat this process ad infinitum, the area subtended by the four converging lines would disappear at the same moment that the distance from the point of convergence disappeared; and that hence, all our experiences conforming as they must to the laws of convergent rays, we can have no conception of a visible superficies without an accompanying conception of a distance between that superficies and the sentient surface. Or, to state the case more simply, and at the same time to avoid certain objections that may else be made—superficial extension cannot be conceived, except as the attribute of something separate from consciousness—something belonging, not to the mind, but to an object out of the mind. That is to say, it implies the idea of outness; or in other words the idea of distance. Hence, as it is admitted that distance is knowable only through experiences of motion, it follows that visible extension also, is knowable only through such experiences.
But a clearer understanding of the matter will be obtained, if we consider what is really given in a visual impression. The retina, as examined microscopically, presents, among other elements, a tesselated pavement made up of minute rods packed side by side, with their ends exposed so as to form its surface. As far as can be made out, each of these rods is supplied by a separate nerve; and is, as must be supposed, capable of independent stimulation. Though the hypothesis is not without difficulties, yet it is hardly doubted that these are the agents through whose joint action our visual impressions of form, &c., are obtained. That this joint action may be the more easily comprehended, let us suppose an analogous structure on a large scale. Imagine that an immense number of fingers could be packed side by side, so that their ends made a flat surface; and that each of them had a separate nervous connection with the same sensorium. If anything were laid upon the flat surface formed by these finger-ends, an impression of touch would be given to a certain number of them—a number great in proportion to the size of the thing. And if two things successively laid upon them differed not only in size but in shape, there would be a difference not only in the number of finger-ends affected, but also in the kind of combination. But now, what would be the interpretation of any impression thus produced, while as yet no experiences had been accumulated? Would there be any idea of extension? I think not. To simplify the question, let the first object laid upon these finger-ends be a straight stick; and let us name the two finger-ends on which its extremes lie A and Z. If now it be said that the length of the stick will be perceived, it is implied that the distance between A and Z is already known; or in other words, that there is a pre-existent idea of a special extension: which is absurd. If it be said that the extension is implied by the simultaneous excitation of B, C, D, E, F, and all the fingers between A and Z, the difficulty is not escaped; for no idea of extension can arise from the simultaneous excitation of these, unless there is a knowledge of their relative positions; which is itself a knowledge of extension. By what process then can the length of the stick become known? It can become known only after the accumulation of certain experiences, by which the series of fingers between A and Z becomes known. If the whole mass of fingers admits of being moved bodily, as the retina does; and if, in virtue of its movements, something now touched by finger A is next touched by finger B, next by C, and so on; and if these experiences are so multiplied by motion in all directions, that between the touching by finger A and by any other finger, the number of intermediate touches that will be felt is known; then the distance between A and Z can be known—known, that is, as a series of states of consciousness produced by the successive touchings of the intermediate fingers—a series of states comparable with any other such series, and capable of being estimated as greater or less. And when, by numberless repetitions, the relation between any one finger and each of the others is established, and can be represented to the mind as a series of a certain length; then we may understand how a stick laid upon the surface so as at the same moment to touch all the fingers from A to Z inclusive, will be taken as equivalent to the series A to Z—how the simultaneous excitation of the entire range of fingers, will come to stand for its serial excitation—how thus, objects laid upon the surface will come to be distinguished from each other by the relative lengths of the series they cover; or when broad as well as long, by the groups of series which they cover—and how by habit these simultaneous excitations, from being at first known indirectly by translation into the serial ones, will come to be known directly, and the serial ones will be forgotten: just as in childhood the words of a new language, at first understood by means of their equivalents in the mother tongue, are presently understood by themselves; and if used to the exclusion of the mother tongue, lead to the ultimate loss of it. The greatly magnified apparatus here described, being reduced to its original shape—the surface of finger-ends being diminished to the size of the retina; the things laid upon that surface being understood as the images cast upon the retina; and its movements in contact with these things, as the movements of the retina relatively to the images—some conception will be formed of one part of the process by which our ideas of visual extension are gained.
I say one part of the process, because this analysis carries us but a little way towards the solution. Those motions of the eye required to bring the sentient elements of the retina successively in contact with different parts of the image, being themselves known to consciousness, become components of the perception. So too do those motions required to produce due convergence of the visual axes; and those further motions required to adjust each eye to the proper focus. And even when the several series of states of consciousness thus resulting, have been combined with those which proceed from the retina itself, they can give no idea of extension as we understand it, until they are united with those locomotive experiences through which we gain the idea of outness or distance; and these are impossible without those accompanying tactile experiences that give the limits to distance. To examine in detail these various groups of elements which go to make up our perception of visible extension, would take up more space than can here be spared. Nor is it needful for the establishment of general principles that they should be thus examined. The foregoing analysis shows that leaving out of view other requirements (all of which involve motion, and the accompanying states of consciousness), no image cast upon the retina can be understood, or even distinguished from another image widely different in form, until relations have been established between the separate sensitive agents of which the retina is constructed; that no relation between any two such agents can be known otherwise than through the series of sensations given by intervening agents; that such series of sensations can be obtained only by motion of the retina; and that thus the primitive element out of which our ideas of visible extension are evolved, is a cognition of the relative positions of two states of consciousness in some series of such states consequent upon a subjective motion. Not that such relation between successive states of consciousness gives in itself any idea of extension. We have seen that a set of retinal elements may be excited simultaneously, as well as serially; that so, a quasi single state of consciousness becomes the equivalent of a series of states; that a relation between what we call coexistent positions thus represents a relation of successive positions; that this symbolic relation being far briefer, is habitually thought of in place of that it symbolizes; and that, by the continued use of such symbols, and the union of them into more complex ones, are generated our ideas of visible extension—ideas which, like those of the algebraist working out an equation, are wholly unlike the ideas symbolized; and which yet, like his, occupy the mind to the entire exclusion of the ideas symbolized.
The fact however which it now more particularly behoves us to remember, is, that underlying all cognitions of visible extension, is the cognition of relative position among the states of consciousness accompanying motion.
§ 59. Leaving here the visual perception of body as presenting statical attributes, let us pass to the tactile perception of it—to such perception of Form, Size, and Position, as a blind man has. And before proceeding to deal with this perception in its totality, let us look at its components: considering these first as known to us; and then in our mode of knowing them.
It is an anciently established doctrine that Form or Figure, which we may call the most complex mode of extension, is resolvable into relative magnitude of parts. An equilateral triangle is one of which the three sides are alike in magnitude. An ellipse is a symmetrical closed curve, of which the transverse and conjugate diameters are one greater than the other. A cube is a solid having all its surfaces of the same magnitude, and all its angles of the same magnitude. A cone is a solid, successive sections of which, made at right angles to the axis, are circles regularly decreasing in magnitude as we progress from base to apex. Any object described as narrow, is one whose breadth is of small magnitude when compared with its length. A symmetrical figure is a figure in which the homologous parts on opposite sides are equal in magnitude. Figures which we class as similar to each other, are such that the relation of magnitude between any two parts of the one, is equal to the relation of magnitude between the corresponding parts of the other. Add to which, that an alteration in the form of anything, is an alteration in the comparative sizes of some of its parts—a change in the relations of magnitude subsisting between them and the other parts; and that by continuously altering the relative magnitudes of its parts, any figure may be changed indefinitely. Hence, figure being wholly resolvable into relations of magnitude, we may go on to analyze that out of which these relations are formed—magnitude itself.
Though, in passing from a mode of extension which consists in relations of magnitude, and going on to consider magnitude itself, it would seem that relativity is no longer involved, this is not really the case. Of absolute magnitude we can know nothing. All magnitudes as known to us are thought of as equal to, greater than, or less than, certain other magnitudes—can be conceived in no other way. Not only is it that in speaking of a house as great, we mean, great in comparison with other houses; that in calling a man short, we mean, short in comparison with most men; and that in describing Mercury as small, and a certain pin's head as large, we mean, in comparison with planets and pins' heads respectively; but it is that no notion of magnitude can be formed, save one constructed out of the magnitudes given to us in experience, and therefore, thought of in relation to them. In what then consists the difference between figure and size as known to us? Simply in this: that whereas, in thinking of a thing's figure, we think of the relations of magnitude which its constituent parts bear to each other; in thinking of its size, we think of the relation of magnitude which it, as a whole, bears to other wholes. Still however, there remains the question—What is a magnitude considered analytically? The reply is—It consists of one or more relations of position. When we conceive anything as having a certain bulk, we conceive its opposite limiting surfaces as more or less removed from each other; that is—as related in position. When we think of a particular area, we think of a surface whose boundary lines stand to each other in specific degrees of remoteness; that is—are related in position. When we imagine a line of definite length, we imagine its termini as occupying points in space having some positive distance from each other; that is as related in position. As a solid is decomposable into planes; a plane into lines; lines into points; and as adjacent points can neither be known nor conceived as distinct from each other, except as occupying different places in space—that is, as occupying not the same position, but relative positions—it follows that every cognition of magnitude, is a cognition of one or more relations of position, which are presented to consciousness as like or unlike one or more other relations of position.
This analysis of itself brings us to the remaining space-attribute of body—Position. Like Magnitude, Position cannot be known absolutely; but can be known only relatively. The notion of position, is, in itself, the notion of relative position. The position of a thing is inconceivable, save by thinking of that thing as at some distance from one or more other things. The essential elements of the idea will be best seen, on observing under what conditions only, it can come into existence. Imagine a solitary point A, in infinite space; and suppose it possible for that point to be known by a being having no locality. What now can be predicated respecting its place? Absolutely nothing. Imagine another point B, to be added. What can now be predicated respecting the two? Still nothing. The points having no attributes save position, are not comparable in themselves; and nothing can be said of their relative position from lack of anything with which to compare it. The distance between them may be either infinite or infinitesimal, according to the measure used; and as, by the hypothesis, there exists no measure—as space contains nothing save these two points; the distance between them is unthinkable. But now imagine that a third point C, is added. Immediately it becomes possible to frame a proposition respecting their positions. The two distances A to B, and A to C, serve as measures to each other. The space between A and B may be compared with the space between A and C; and the relation of position in which A stands to B, becomes thinkable as like or unlike the relation in which A stands to C. Thus then, it is manifest that position is not an attribute of body in itself, but only in its connection with the other contents of the universe.
It remains to add, that relations of position are of two kinds: those which subsist between subject and object; and those which subsist between either different objects, or different parts of the same object. Of these the last are resolvable into the first. It needs but to remember, on the one hand, that in the dark a man can discover the relative positions of two objects only by touching first one and then the other, and so inferring their relative positions from his own position towards each; and on the other hand, that by vision no knowledge of their relative positions can be reached save through a perception of the distance of each from the eye; to see that ultimately, all relative positions may be decomposed into relative positions of subject and object.
These conclusions—that Figure is resolvable into relative magnitudes; that Magnitude is resolvable into relative positions; and that all relative positions may finally be reduced to positions of subject and object—will be fully confirmed on considering the process by which the space-attributes of body become known to a blind man. He puts out his hand, and touching something, thereby becomes cognizant of its position with respect to himself. He puts out his other hand, and meeting no resistance above, or on one side of, the position already found, gains some negative knowledge of the thing's magnitude—a knowledge which three or four touches on different sides of it serve to render positive. And then, by continuing to move his hands over its surface, he acquires a notion of its figure. What, then, are the elements out of which, by synthesis, his perceptions of magnitude and figure are framed? He has received nothing but simultaneous and successive touches. Each touch established a relation of position between his centre of consciousness and the point touched. And all he can know respecting magnitude and figure—that is, respecting the relative positions of these points to each other—is necessarily known through the relative positions in which they severally stand to himself.
Our perceptions of all the space-attributes of body, being thus decomposable into perceptions of position like that gained by a single act of touch; we have next to inquire what is contained in a perception of this kind. A little thought will make it clear that to perceive the position of anything touched, is really to perceive the position of that part of the body in which the sensation of touch is located. Whence it follows that our knowledge of the positions of objects, is built upon our knowledge of the positions of our members towards each other—knowledge both of their fixed relations, and of those temporary relations they are placed in by every change of muscular adjustment. That this knowledge is gained by a mutual exploration of the parts—by a bringing of each in contact with the others—by a moving over each other in all possible ways; and that the motions involved in these explorations, are known by their reactions upon consciousness; are propositions that scarcely need stating. But it is manifestly impossible to carry the analysis further without analysing our perception of motion. Relative position and motion are two sides of the same experience. We can neither conceive motion without conceiving relative position, nor discover relative position without motion. For the present, therefore, we must be content with the conclusion that, whether visual or tactual, the perception of every statical attribute of body is resolvable into perceptions of relative position which are gained through motion.
§ 60. Before defining in its totality, the perception of body as presenting statical attributes, it is necesssary to remark that the resisting positions which, as co-ordinated in thought, constitute our ideas of Figure or Magnitude, must be aggregated—must be continuous with an indefinite assemblage of intermediate resisting positions. If they are discontinuous—if they are separated by positions that do not resist, we have a perception not of one body, but of two or more.
Premising this, and omitting as doubly mediate our visual perceptions of extension in its several modes, we may say that the perception of body as presenting statical attributes, is a composite state of consciousness, having for its primary elements the indefinite impressions of resistance and extension, unconditionally united with each other and the subject in relations of coincidence in time and adjacency in space; and having for its secondary elements a series of relations between resisting positions, variously united with each other in relations of simultaneity and sequence that are severally conditional on the nature of the object and the acts of the subject, and all of them conditionally united with the primary elements by relations of sequence.
To which there is only to add, as before, that these being the materials of the perception, the process of perception consists in the unconscious classing of these impressions, relations, and conditions, with the like before-known ones.
THE PERCEPTION OF SPACE.
§ 61. By implication something has been said in the last chapter, respecting our perception of Space. The consideration of occupied space cannot be dissociated from the consideration of unoccupied space. Body and Space being distinguished as resistant extension and non-resistant extension, it is impossible to treat of extension in any of its modes, without virtually treating of them both. Substantially, therefore, the inquiry on which we are now to enter, must be a continuation of the one just concluded. Before commencing it, however, there seems a need for some comments on the position of those who, holding that Space is a form of thought, consider all attempts to analyze our cognition of it as absurd.
Foremost among these, is Sir William Hamilton; who says that, “it is truly an idle problem to attempt imagining the steps by which we may be supposed to have acquired the notion of extension; when in fact we are unable to imagine to ourselves the possibility of that notion not being always in our possession.”
Granting, for argument's sake, this alleged impossibility of conceiving ourselves ever to have been without the notion of extension, it does not necessarily follow either that extension is a form of thought, or that we are disabled from analyzing the notion we have of it. In a preceding criticism of the Kantian doctrine (§ 12), it was pointed out that our inability to banish from our minds the idea of space, was readily to be accounted for on the experience-hypothesis: seeing that if space be an universal form of the non-ego, it must produce some corresponding universal form in the ego—a form which, as being the constant element of all impressions presented in experience, and therefore of all impressions represented in thought, is independent of every particular impression; and consequently remains when every particular impression is banished. And then, to the argument that whether extension is a form of thought or not, our inability to conceive ourselves as ever being without it, disables us from analyzing it, I reply, that though we may be disabled from analyzing it directly, we may still remain able to analyze it indirectly. Though, in any subjective examination of our mental processes, we may fail in finding any anterior elements of thought out of which to construct the idea; yet, by examining mental processes objectively, we may gain the means of conceiving how our own consciousness of space was originally constructed.
But what is here granted for argument's sake, may be denied. This alleged impossibility of conceiving ourselves ever to have been without the notion of extension, I, for one, do not admit. It appears to me quite possible for a man to think of himself as having possessed states of consciousness not involving any notion of extension; or, what is the same thing—it is quite possible to imagine trains of thought in which space is not implied. And indeed, it would be strange that the contrary should be asserted, were it not that we are so tyrannized over by the almost indissoluble associations which experience establishes, and so habitually carry them with us in all our thinkings, as to be constantly in danger of attributing to the undeveloped mind, ideas which only the developed mind possesses. It needs, however, but to figure ourselves as devoid of certain perceptions that are known to be acquired, and it at once becomes easy to conceive ourselves as having thoughts that do not imply space. Remembering that, as Sir William Hamilton expresses it, “we are never aware even of the existence of our organism, except as it is somehow affected;” let any one imagine a human being in that early stage in which he is yet unacquainted with his own body—in which he has had no experiences. It is admitted by Kantists that space being but a form of thought cannot exist before thought—cannot be known in itself antecedently to experience; but that it is disclosed to consciousness in the act of receiving experiences. They assert that the matter of perception being given by the non-ego, and the form by the ego, the form and the matter come into consciousness simultaneously. In the supposed case, therefore, there is yet no idea of space. Let now the first impressions received, be those of sound. No one will allege that sound as an affection of consciousness, has any space-attributes. And even those who have little considered such questions, will admit that our knowledge of sound as coming from this or that point in space, is a knowledge gained by experience—is a knowledge quite separate from the sound itself—is a knowledge inferred from certain modifications of the sound; and that primarily the sound is known only as a pure undecomposable sensation. Further, let it be observed that the sensation of sound is of a kind that does not in itself make us “aware of the existence of our organism, as somehow affected.” Only by experience do we learn that we hear through the ears. Aural impressions are so indistinctly localized, that, in spite of their associations, most adults even will perceive that were it not for their acquired knowledge, they would not know whereabouts on the surface of the body they were sentient. Hence, in the supposed state of nascent intelligence, sensations of sound, not having in themselves any space-attributes, and not in themselves disclosing any part of the organism as affected, would be nothing more than simple affections of consciousness, having no space implications; and would admit of being remembered and compared, without any idea of extension being involved. Having duly contemplated the case thus objectively presented, any one ordinarily endowed with imagination, will, I think, by closing his eyes, arranging his body so as to give as few disturbing sensations as possible, and banishing as much as he can all remembrance of surrounding things, be enabled to conceive the possibility of a state in which a varied series of sounds known as severally like and unlike, and thought of solely in respect to their mutual relations, should be the entire contents of consciousness.
With such further reasons for holding that Space is not a form of thought, but a form of the non-ego disclosed to us by experience, we may be encouraged to continue that analysis of our perception of it collaterally entered upon in the last chapter.
§ 62. Starting afresh from the conclusions there reached—that, whether visual or tactual, every perception of the space-attributes of body is decomposable into perceptions of relative position; that all perceptions of relative position are decomposable into perceptions of the relative position of subject and object; and that these relations of position are knowable only through motion—the firszt question that arises is—How, through experiences of occupied extension, or body, can we ever gain the notion of unoccupied extension, or space? How, from the perception of a relation between resistant positions, do we progress to the perception of a relation between non-resistant positions? If all the space-attributes of body are resolvable into relations of position between subject and object, disclosed in the act of touch—if, originally, relative position is only thus knowable—if therefore position is, to the nascent intelligence, incognizable except as the position of something that produces an impression on the organism; how is it possible for the idea of position ever to be dissociated from that of body? how can the germinal notion of empty extension ever be gained?
This problem, though apparently difficult of solution, is really a very easy one. If, after some particular motion of a limb there invariably came a sensation of softness; after some other, one of roughness; after some other, one of hardness—or if, after those movements of the eye needed for some special act of vision, there always came a sensation of redness; after some others, a sensation of blueness; and so on—it is manifest that, in conformity with the known laws of association, there would be established a constant relation between such motions and such sensations. If positions were conceived at all, they would be conceived as invariably occupied by things producing special impressions; and it would be impossible to dissociate the positions from the things. But as, in our experience, we find that a certain movement of the hand which once brought the finger in contact with something hot, now brings it in contact with something sharp, and now with nothing at all; and that a certain movement of the eye which once was followed by the sight of a black object, is now followed by the sight of a white object, and now by the sight of no object; it results that the idea of the particular position accompanying each one of these movements, is, by accumulated experiences, dissociated from objects and impressions, and comes to be conceived by itself; it results that as there are endless such movements, there come to be endless such positions conceived as existing apart from body; and it results that as in the first and in every subsequent act of perception, each position is known as coexistent with the subject, there arises a consciousness of endless such coexistent positions; that is—of Space. This is by no means offered as an ultimate analysis, or rather synthesis, of the idea; for, as before admitted, the difficulty is to account for our notion of relative position. All that is here attempted is, partially to explain, how, from that primitive notion may be derived the materials of which our cognition of Space in its totality is built.
Carrying with us this idea, and calling to mind the description given in the last chapter of the mode in which the retina is constructed, and the relations among its elements established, it will, I think, become possible to conceive how that wonderful perception which we have of visible space, is generated. It is a peculiarity of sight, as contrasted with all the other senses, that it makes us partially conscious of many things at once. On now raising my head, I take in at one glance, desk, papers, table, books, chairs, walls, carpet, windows, and sundry objects outside; all of them simultaneously impressing me with various details of colour, which more or less tend to suggest surface and structure. It is true that I am not equally conscious of all these things at the same time. I find that some one object to which my eyes are directed, is more distinctly present to my mind than any other; and that the one point in this object on which the visual axes converge, is more vividly perceived than the rest. In fact, I have a perfect perception of scarcely more than an infinitesimal portion of the whole visual area. Nevertheless, I find that even while concentrating my attention on this infinitesimal portion, I am in some degree aware of the whole. My complete consciousness of a particular letter in the title on the back of a book at the other side of the room, does not seem to exclude a consciousness that there are accompanying letters—does not seem to exclude a consciousness of the book—does not even seem to exclude a consciousness of the table on which the book lies—nay, does not even seem entirely to exclude a consciousness of the wall against which the table stands. Of all these things I feel myself conscious in different degrees of intensity—degrees that become less, partly in proportion as the things are unobtrusive in colour and size, and partly in proportion as they recede from the centre of the visual field. Not that these various surrounding things occupy consciousness in the sense of being definitely known as such or such; for I find, on experiment, that while keeping my eyes fixed on one object, I cannot make that assertory judgment respecting any adjacent object which a real cognition of it implies, without becoming, for the moment, imperfectly conscious even of the object on which my eyes are fixed. But notwithstanding all this, it remains true that these various objects are in some sense present to my mind—are incipiently perceived—are severally tending to fill the consciousness—are each of them partially exciting the various mental states that would arise were it to be distinctly perceived.
This peculiarity in the faculty of sight—to which there is nothing analogous in the faculties of taste and smell; which, in the faculty of hearing, is vaguely represented by our appreciation of harmony; and which is but very imperfectly paralleled in the tactile faculty by the ability we have to discern numerous irregularities in a rough surface on which the hand is laid—is clearly due to the structure of the retina. Consisting of an immense number of separate sensitive elements, each of them capable of independent stimulation, it results that when, as in any ordinary act of vision, a cluster of images is simultaneously cast on the retina, all of those numberless sensitive elements upon which the variously modified rays of light fall, are severally thrown into a state of greater or less excitement. Each of them, as it were, touches some particular part of one of the images; and conveys to the sensorium the feeling produced by the touch. But now, let it be remembered that, in the manner before explained, each retinal element has come to have a certain known relation to every one of those which surround it—a relation such that their synchronous excitation serves to represent their serial excitation. Lest this symbolism should not have been fully understood, I will endeavour yet further to elucidate it. Suppose a minute dot to be looked at—a dot so small that the image of it, cast upon the retina, covers only one of these sensitive elements, A. Now suppose the eye to be so slightly moved that the image of this dot falls upon the adjacent element B. What results? Two slight changes of consciousness: the one proceeding from the new retinal element affected; and the other from the muscles producing the motion. Let there be another motion, such as will transfer the image of the dot to the next element C. Two other changes of consciousness result. And so on continuously: the consequence being that the relative positions in consciousness of A and B, A and C, A and D, A and E, &c., are known by the number of intervening states. Imagine now that instead of these minute motions separately made, the eye is moved with ordinary rapidity; so that the image of the dot passes successively over the whole series A to Z, in an extremely brief space of time. What results? It is a familiar fact that all impressions on the senses, and visual ones among the number, continue for a certain brief period after they are made. Hence, when the series of retinal elements A to Z, are excited in rapid succession, the excitation of Z commences before that of A has ceased; and for a short time the whole series A to Z remains in a state of excitement together. This being understood, suppose a line to be looked at whose image is long enough to cover the whole series A to Z. What results? There is a simultaneous excitation of the series A to Z, differing from the last in this; that it is continuous, and that it is unaccompanied by sensations of motion. But does it not follow from the known laws of mental suggestion, that as the simultaneous excitation is common to both cases, it will, in the last case, tend to arouse in consciousness that series of states that accompanied it in the first? Will it not as it were tend to consolidate the entire series of such states into one state? and will it not insensibly come to be taken as the equivalent of such series? There cannot I think be a doubt of it. And if not, then it becomes comprehensible how an excitement of consciousness by the coexistent positions constituting a line, serves as the representative of that serial excitement of it which accompanies motion along that line. Returning now to the above described state of the retina as occupied by a cluster of images—remembering that the relations of coexistent position which we have here considered in respect to a particular linear series, are similarly established throughout countless such series in all directions over the retina, so as to put each element in relation with every other—remembering further that in virtue of a process analogous to that described, the state of consciousness produced by the adjustment of the eyes to a particular focus has become a symbol of the series of coexistent positions between the eyes and the point to which they are directed—remembering all this, the genesis of our visual perception of space will begin to be vaguely comprehensible. Every one of the retinal elements simultaneously thrown into a state of partial excitement, producing as it does a partial consciousness not only of itself as excited, but also of the many relations of coexistent position established between it and the rest, which are all of them similarly excited and similarly suggestive; there tends to arise a consciousness of a whole area of coexistent positions. Meanwhile the state of consciousness produced by the focal adjustment of the eyes, calling up as it does the line of coexistent positions lying between the subject and the object specially contemplated; and each of the things, and parts of things not in the centre of the field, producing, by the greater or less definiteness of its image, an incipient consciousness of its distance, that is, of the coexistent positions lying between the eye and it; there arises an indistinct consciousness of a whole volume of coexistent positions—of Space in three dimensions. Along with a complete consciousness of the one position to which the visual axes converge, arises a nascent consciousness of an infinity of other positions—a consciousness that is nascent in the same sense that our consciousness of the various objects out of the centre of the visual field is nascent. To all which it may be added, that as the innumerable relations subsisting between these coexistent positions were originally established by motion; as each of these relations of coexistent positions came by habit to stand for the series of mental states accompanying the motion which measured it; as every one of such relations must, when presented to consciousness, still tend to call up, in an indistinct way, that train of feelings, that sense of motion, which it represents; and as the simultaneous presentation of an infinity of such relations will tend to suggest an infinity of such experiences of motion, which, as being in all directions, must so neutralize each other as to prevent any particular motion being thought of; there will arise, as their common resultant, that sense of ability to move, that sense of freedom for motion, which forms the remaining constituent in our idea of Space.
Should any still find it difficult to conceive how, by so elaborate a process as the one described, there should be reached an idea apparently so simple, so homogeneous, as that which we have of Space; they will perhaps feel the difficulty somewhat diminished on remembering:—first, that this process commences at birth; second, that every day throughout our lives, and throughout the whole of each day, we are, from moment to moment, repeating our experiences of these innumerable coexistences of position and their several equivalences to the serial states of feeling accompanying motions; and third, that these experiences invariably agree—that these relations of coexistent position are unchangeable—are ever the same towards each other and the subject—are ever equivalent to the same motions. By duly contemplating this early commencement of these experiences, this infinite repetition of them, and their absolute uniformity; and at the same time remembering the power which, in virtue of its structure, the eye possesses of partially suggesting to the mind countless such experiences at the same moment; it will become possible to conceive how we acquire that consolidated idea of space in its totality, which at first seems so inexplicable. And if, to develop somewhat further a late illustration, we call to mind the mode in which we regard long used symbols—how by habit each of the groups of letters now before the reader has acquired a seemingly inherent meaning—has ceased to be a mere series of straight and bent strokes, and has actually, as it were, absorbed some of the thought for which it stands; and if further we remember how, in our intellectual operations, these words have come to be the elements with which we think—how we cannot definitely realize to ourselves any proposition without putting it into words—and how the words are so habitually thought of to the exclusion of the things they signify, as to cause frequent mistakes; if we call to mind these facts, it will not be difficult to understand how, with symbols learnt much earlier, symbols incomparably more simple, uniform, and exact, symbols used every instant of our waking lives, a like transformation should have been carried much further. And this being understood, it may also be understood how the state of consciousness answering to any group of coexistent positions made known by the senses, has supplanted in our minds the series of states of consciousness to which it was equivalent; and how, consequently, our space-perceptions have become a language in which we think of surrounding things, without at all thinking of those experiences of motion which this language expresses.
§ 63. Strong confirmations of this analysis may be drawn from certain peculiarities in our perception of space. If the reader whilst looking at his hand, or any equally close object, will consider what kind of knowledge he has of the space lying between it and his eyes, he will perceive that his knowledge of it is, as it were, exhaustive. He is conscious of the minutest differences of position in it. He has an extremely complete or detailed perception of it. If now he will direct his eyes to the farther side of the room, and contemplate an equal portion of that more remote space, he will find that he has but a comparatively vague cognition of it. He has nothing like so intimate an acquaintance with its constituent parts. If, again, he will look through the window, and observe what consciousness he has of a space that is a hundred yards away, he will discover it to be a still less specific consciousness. And on gazing at the distant horizon he will perceive that he has scarcely any perception of that far off space—has rather an indistinct conception than a distinct perception. This now is exactly the kind of knowledge that would result from the organized experiences above described. Of the space that is so close to us as to be within the range of our hands, we have the most complete perception, because we have had myriads of experiences of relative positions within that space. And of space as it recedes from us we have a less and less complete perception, because our experiences of the relative positions contained in it have been fewer and fewer.
The disordered feelings accompanying certain abnormal states of the nervous system, furnish similar evidence. De Quincey, describing some of his opium-dreams, says that “buildings and landscapes were exhibited in proportions so vast as the bodily eye is not fitted to receive. Space swelled, and was amplified to an extent of unutterable infinity.” It is not at all an uncommon thing with nervous subjects to have illusive perceptions in which the body seems enormously extended: even to the covering an acre of ground. Now the state in which these phenomena occur, is one of exalted nervous activity—a state in which De Quincey depicts himself as seeing in their minutest details the long-forgotten events of his childhood. And if we consider what effect must be produced upon the consciousness of space, by an excitement during which forgotten experiences are revived in extreme abundance and vividness, we shall see that it will cause the illusion of which he speaks. Of the myriad experiences of surrounding positions accumulated throughout life, we manifestly remember but a part. In common with all other experiences they severally tend to fade from the mind; and the perception of space would in the end become indistinct, were it not that they are day by day refreshed, or replaced by new ones. Imagine now, that these innumerable experiences of relative positions, which have been hourly registered in the mind from infancy upwards, and of which the earliest are quite effaced, while intermediate ones continue in various degrees of faintness—imagine these innumerable fading experiences suddenly to revive, and become definitely present to consciousness. What must result? It must result that space will be known in comparatively microscopic detail. Within any portion of space ordinarily thought of as containing a certain quantity of positions, an immensely greater quantity of positions will be thought of. Between the eye and each point looked at, whose distance is commonly conceived as equivalent to a certain series of positions, a far more extensive series will be conceived; and as the length of each such series is the mind's measure of the distance, all distances will appear increased, all points will appear more remote, and it will seem that space has “swelled,” as De Quincey expresses it.
Yet another fact having the same implication, is supplied by that striking change in our cognition of space which results during a temporary inability to see. Any one guided into a totally dark place with which he is unacquainted, and of which there are consequently no recollected visual impressions to occupy his imagination, will find that he almost loses his ordinary idea of space—that he almost ceases to be conscious of it as an infinity of coexistent positions, and remains conscious of it only as permitting freedom of movement. Even on merely closing the eyes for a few minutes, and, as far as may be, excluding from the mind all recollection of adjacent objects, it will be perceived that distant space cannot be thought of at all, except by remembering the cognition of it gained through the eyes; and that the space near at hand, is presented to the mind more as a negation of resistance than anything else. Most persons on several times repeating this experiment, and critically observing their ideas, will, I think, find, that could they move their limbs without imagining the visible changes accompanying the motions, this negation of resistance would be almost their sole cognition of space; and that until, after the manner of the blind, they had developed their tactual experiences of positions, they would be unable to think of space as they at present think of it. Now these are just the mental conditions to which the foregoing analysis points. The infinity of coexistent positions suggested by any visual impression, having become by habit the language in which we think of space, to the exclusion of those motor experiences which this language represents; it results that in proportion as we are deprived of this language, are we disabled from thinking of space: just as we should be almost incapacitated for reasoning, by the loss of our words.
And here let it be further observed, that while these several phenomena perfectly conform to the experience-hypothesis, they are irreconcilable with the antagonist one. The fact that our idea of adjacent space differs in completeness from our idea of remote space, is wholly at variance with the hypothesis that space is a form of thought; which implies a perfect homogeneity in our idea of space. That in morbid states of the brain, space should appear “swelled,” is, on the Kantian theory, unaccountable: seeing that the form of thought should remain constant, whether the thought itself be normal or abnormal. And similarly inconsistent with his theory, is the change in our cognition of space caused by a temporary privation of vision; which, if space were a subjective condition, would cause no change.
§ 64. Leaving here the inquiry into our perception of space in its totality, a few further words are called for respecting that relation of two coexistent positions, in our consciousness of which, the problem ultimately centres. From time to time in the progress of the argument, something has been done towards explaining the nature of this consciousness—towards showing that it is a state of consciousness serving to symbolize a series of states to which it is found equivalent. But, as before said, it is desirable to postpone the more definite analysis of this perception of coexistent positions, until the perception of motion is dealt with. At present the only reason for recurring to it, is to point out the indissoluble union between the cognition of space and the cognition of coexistence; and afterwards what is implied by this.
Not only is it that the idea of space involves the idea of coexistence; but it is that the idea of coexistence involves the idea of space. Fundamentally, space and coexistence are two sides of the same cognition. On the one hand space cannot be thought of without coexistent positions being thought of: on the other hand coexistence cannot be thought of without at least two points in space being thought of. A relation of coexistence implies two somethings that coexist. Two somethings cannot occupy absolutely the same point in space. And hence coexistence implies space. If it be said that one body can have coexistent attributes, and that therefore two attributes can coexist in the same place; the reply is, that body itself is unthinkable except as presenting coexistent positions—a top and a bottom, a right and a left. Body cannot be so diminished, even in imagination, as to present only one position; or, in other words—in ceasing to present in thought more than one position, it ceases to be body. And as attributes imply body—as a mere position in space can have no other attribute than that of position, it follows that a relation of coexistence, even between attributes, is inconceivable without an accompanying conception of space. Space can be known only as presenting relations of coexistence: relations of coexistence can be known only as presented in space.
If now it should turn out under an ultimate analysis, that a relation of coexistence is not directly cognizable, but is cognizable only by a duplex act of thought—only by a comparison of experiences; the question between the transcendentalists and their opponents will be set finally at rest. When, after it has been shown, as above, that our cognition of space in its totality is explicable upon the experience-hypothesis, and that all the peculiarities of the cognition confirm that hypothesis, it comes to be shown that the ultimate element into which that cognition is decomposable—the relation of coexistence—can itself be gained only by experience; the utter untenableness of the Kantian doctrine will become manifest. That this will be so shown, the reader must at present take for granted. I am obliged thus to forestall the argument, because it would be inconvenient, during an analysis of the several orders of relations, to recur at any length to the controversy respecting space.
§ 65. To complete the chapter it needs but to say, that the process of organic classification, shown in previous cases to constitute the act of perception, is very clearly exhibited in the perception of space. The materials of the perception having been gained in the way described, the co-ordination of them into any particular perception, consists in the assimilation of each relation of position to the like before-known relations. In every glance we cast around, the distinct consciousness of the distance of each thing specially looked at, and the nascent consciousness of the distances of various neighbouring things, alike imply a classing of present distances with remembered distances. These distances being one and all unknowable under any other condition, there is no alternative but to admit this. And the seemingly incomprehensible fact that numberless such classings should be simultaneously made by us without attracting our attention, simply shows to what perfection the process of automatic classification is brought by infinite repetition.
THE PERCEPTION OF TIME.
§ 66. The near relationship between our notion of Time and our notion of Space, is implied in various current forms of speech. In the phrase—“a space of time,” a magnitude of one is expressly used to signify a magnitude of the other. Conversely, the Swiss tourist whose inquiries respecting distances are answered in stunden, or hours; and the savage who, in common with the ancient Hebrew, has a place described to him as so many days' journey off; find times used to express spaces. The like reciprocity of symbolism is visible in science. Not only is it that a second of time is a function of the length of the pendulum, and that our hours are measured by spaces on the dial; but it is that, in astronomy, a degree, which was originally a day's journey of the sun along the ecliptic, has become the name of an angular space.
Joined to the arguments contained in the last chapter, these facts will be seen to possess considerable significance. That in early ages, and in uncivilised countries, men should have expressed space in terms of time, and that afterwards, as a result of progress, they should have come to express time in terms of space; is a circumstance giving strong support to the views recently developed: not only because it shows conclusively that the phenomena of coexistence, and those of sequence, are made to stand for each other in the mind; but because it shows, repeated, as it were, on a higher platform, that gradual supplanting of mental sequences by their equivalent coexistences, lately described as the process by which our cognition of space is acquired. Just as the series of states of consciousness accompanying any motion—a series which at first formed the sole representative of space—was described as becoming consolidated into a quasi single consciousness of the coexistent positions traversed during that motion, which single consciousness afterwards expresses to the mind the series it was equivalent to; so, that series of states of consciousness implied by “a day's journey”—a series which, in early ages, formed the only definite representative of a great space—is seen to have become, in process of time, consolidated into a consciousness of the coexistent positions traversed (measured by miles or leagues); and this practically single state of consciousness has, more or less, supplanted in thought and word the series of states represented by it. And if any one, wishing yet further illustration of this process of mental substitution, will observe to what an extent he has acquired the habit of thinking of the spaces on the clock-face instead of the periods they stand for—how, on suddenly discovering it to be half an hour later than he supposed, he does not distinctly realize the half-hour in its duration, but scarcely passes beyond the sign of it as marked by the finger; he will be enabled still more clearly to conceive that the use of coexistences to symbolize sequences, which in these complex cases has become so habitual, has in the simplest cases become organic.
This reciprocity between our cognitions of Space and Time, alike in their primitive and most developed forms, being perceived; and the consequent impossibility of considering either of them entirely alone, being understood; let us go on to deal more particularly with Time.
§ 67. As the ideas of Space and Coexistence are inseparable, so also are the ideas of Time and Sequence. It is impossible to think of Time without thinking of some succession: and it is equally impossible to think of any succession without thinking of Time. Time, like Space, cannot be conceived except by the establishment of a relation between at least two elements of consciousness: the difference being, that while, in the case of Space, these two elements are, or seem to be, present together, in the case of Time they are not present together.
The doctrine that Time is knowable to us only by the succession of our mental states, is so old and well established a one as to call for little exposition. All that seems necessary, is, so far to modify the statement of it as will bring out its harmony with the foregoing doctrines. And to this end, it will be well first to call to mind a few facts illustrating the entirely relative character of the cognition.
Every one remembers that in childhood, when, from the novelty of surrounding things and events, the number of vivid impressions made in a given period was much greater than in after life, time seemed to go much more slowly. The observation is common, that a week spent in travelling or sight-seeing, and therefore unusually full of mental excitements, appears in retrospect far longer than one spent at home; and that, similarly, a road followed for the first time, apparently takes longer to traverse than when it has become familiar. The phenomena accompanying morbid conditions of the brain, supply analogous illustrations. Describing the worst stage of his opium-dreams, when “the sea appeared paved with innumerable faces, imploring, wrathful, despairing, surging upwards by thousands, by myriads, by generations, by centuries”—when architectural imagery, presented with insufferable vividness and splendour, had a “power of endless growth and self-reproduction”—when, therefore, the mental impressions were immensely numerous and extremely distinct, De Quincey says, that he sometimes seemed “to have lived for 70 or 100 years in one night;” nay, to have had “feelings representative of a millennium passed in that time, or, however, of a duration far beyond the limits of any human experience.” Even persons in health occasionally have, in the course of a doze lasting but a few minutes, dreams that appear to occupy considerable periods. And yet still more significant is the fact, to which there are many testimonies, that a sleeper suddenly awakened by a loud noise, may be able to recount some dream to which a loud noise was the expected termination, and which was evidently heard, but which was suggested by the noise, yet be one seeming to have extended over hours or days.
From all which it is manifest, that our notion of any period of time, is wholly determined by the length of the series of remembered states of consciousness that have occurred during that time. I say remembered states of consciousness, because, as any series of states of consciousness can be known only by memory; and as any of the states that have occurred, but are not represented in memory, cannot become members of the series; it results that the series of remembered states can alone serve as the measure between a past and a present state And hence the explanation of all such facts as that any interval looked back upon by a child, appears longer than the same interval looked back upon by an adult: seeing, that out of the same series of domestic and other experiences, many which are novel to the child, and therefore make a deep impression upon it, are so familiar to the adult as to make scarcely any impression at all. And the length of the series of remembered states of consciousness being thus our measure of time, we have no longer any difficulty in understanding cases in which vivid ideas, following each other with extreme rapidity, cause a night to seem like a hundred years, or, as in some drowning persons, a few minutes to represent a whole life.
When, however, we say that the time between two events is recognized by the series of remembered states of consciousness intervening, what do we more specifically mean? These two events are known to us by the states of consciousness they produce. Before the first of them there were countless other states of consciousness: since the last of them there have been others: and between them there were others. We know them, therefore, as having certain places in the whole series of states of consciousness experienced during our lives. The time at which each occurred is known to us as its position in the series. And by the time between them, we mean their relative positions in the series. As any relation of coexistent positions—any portion of space, is conceived by us as such or such, according to the number of other positions that intervene; so, any relation of sequent positions—any portion of time, is conceived by us as such or such, according to the number of other positions that intervene. Thus, a particular time, is a relation of position between some two states in the series of states of consciousness. And, in the abstract, Time, as known to us, is, relativity of position among the states of consciousness.
§ 68. From this analysis it will perhaps be inferred, that whether Space be, or be not, a form of thought, Time must necessarily be one. As there can be no thought without a succession of states of consciousness; and as there can be no succession of states of consciousness except in Time; Time must be a condition of thought, or a form of thought. This, however, is not what the Kantian hypothesis means. It is not simply alleged that thought is possible only in Space and in Time: this no one questions. But it is alleged that the cognitions of Space and Time are necessary constituents in all other cognitions—that they are disclosed to consciousness along with the concrete elements of every idea—that notions of Time and Space of the same nature as the adult possesses, are simultaneous with the first perceptions—are the all-essential framework of them—are the forms of them. This is the sense in which the transcendental doctrine is understood; and it may be shown from the foregoing analysis that in this sense it is not true.
It is, doubtless, to be concluded, either from what has been said above, or from other data, that even in the first stages of intelligence, successive states of consciousness must be severally recognized as standing to each other in certain relations of position—as either occurring next to each other, or as separated by one or more intervening states. Though at first, probably no considerable portion of the series of states can be contemplated at once, and no distant members of it brought into relation, yet the simplest cognition implies that sundry of the proximate members of it are co-ordinated in thought, and their respective places therefore known. But neither the contemplation of any two states of consciousness that stand in certain relative positions, nor the thinking of their relation of position as like some other relation of position, gives, in itself, the notion of time: although it is the raw material out of which that notion is constructed. Time, as conceived by us, is not any one relation of position in the series; nor any relation between two such relations; but is the abstract of all such relations—is the idea of relationship of position in the series: and cannot possibly be conceived until a great number of individual relations have been known and compared. To elucidate this, let us consider a parallel case. Suppose an incipient intelligence to receive two equal impressions of the colour red. No other experiences having been received, the relation between these two impressions cannot be thought of in any way: seeing that there exists no other relation with which it can be classed, or from which it can be distinguished. Suppose two other equal impressions of red to be received. There can still exist no idea of the relation between them: seeing, that though there is a repetition of the previously experienced relation, yet, since no thing can be cognized save as of some kind; and as, by its very nature, kind implies the establishment of difference; there cannot, while only one order of relation has been experienced, be any cognition of it—any thought about it. Suppose, now, that two unequal impressions of red are received. There is now experienced a second species of relation. And if there are afterwards presented a number of such pairs of impressions, that are severally equal and unequal, it becomes possible for the constituents of each new pair to be vaguely thought of as like or unlike, and as standing in relations like or unlike previous ones. I say vaguely thought of, because, while various impressions of the colour red are the sole things known, the cognition of them as like or unlike, will not be distinctly separable from the impressions themselves. When, however, other series of impressions come to be received—as of the colour green in different intensities—the occurrence among these also of some that are like, and of others that are unlike, will tend to dissociate these relations from the colours green and red. And gradually as, by the accumulation of experiences, there are found to be like and unlike sounds, tastes, smells, sizes, forms, textures; the relationships which we signify by these words like and unlike, will be more and more dissociated from particular impressions; and the abstract ideas likeness and unlikeness will come into existence. Manifestly, then, the ideas of likeness and unlikeness are impossible until after multitudes of things have been thought of as like and unlike. Similarly in the case before us. After various relations of position among the states of consciousness have been contemplated, have been compared, have become familiar; and after the experiences of different relations of position have been so accumulated as to dissociate the idea of the relation from all particular positions; then, and not till then, can there arise the abstract notion of relativity of position among the states of consciousness—the notion of Time.
Thus, so far is it from being true that Time, as conceived by us, is a form of thought; it turns out, contrariwise, not only that there can be thoughts while yet Time has not been conceived, but that there must be thoughts before it can become conceivable.
§ 69. The necessary dependence of Time upon Motion is a doctrine taught by Aristotle, who asks—“How can time be when motion is not?” and who argues that, “if time is a numeration of motion, and if time be eternal, motion must be eternal.”
Whether or not the objective relation between Time and Motion be, as is here asserted, indissoluble; it is beyond question that, subjectively, the two cannot be separated. Motion, as understood by the developed mind, is inconceivable without an accompanying conception of Time; and Time can be disclosed to us only through Motion. Though, when once we have accumulated a stock of ideas that can follow one another through consciousness even when the senses are in repose, we can recognize Time apart from any perceived motion; yet, it needs but to consider that all these ideas were gained through motion—that had neither we nor surrounding things ever moved, we should have had no ideas at all, and therefore no conception of Time—to see clearly that Time is knowable only through motion. As, according to the foregoing analysis, our notion of Time is the notion of relativity of position in the series of states of consciousness; as this presupposes a series of such states; as this presupposes successive changes of state; it follows that that which is required to produce changes of state, is that through which Time is disclosed. And it needs but a little reflection to see, that without motion, subjective or objective, no changes of consciousness could ever have been generated.
Respecting the perception of any particular portion of time (or conception it might perhaps more strictly be called; seeing that the majority of its constituents are represented, rather than presented, to consciousness) it only needs saying that it consists in the classing of the relation of position contemplated, with certain before-known relations—the cognition of it as like such before-known relations.
THE PERCEPTION OF MOTION.
§ 70. Our ideas of Motion, Time, and Space, are so intimately connected, that it is extremely difficult to disentangle them. On the one hand, preceding chapters have shown that Space and Time are knowable only through Motion: on the other hand, it is by some contended, with great apparent truth, that Motion is unknowable except as in Space and Time; and that, therefore, notions of Space and Time must pre-exist. Taking which two positions together, there would really seem no course left but to adopt the Kantian hypothesis; and conclude that Time and Space are forms of sensibility, that are disclosed to consciousness in the act by which Motion is perceived. A closer consideration, however, will show that there is an alternative.
For though Motion, as known by the developed mind, cannot be conceived without accompanying conceptions of Space and Time; it does not therefore follow that Motion, as known by the undeveloped mind, cannot be conceived without such accompaniments. It does not follow that because the connection between the ideas is, in adult life, indissoluble, it was always so. The whole confusion has arisen from the totally unwarrantable assumption, that certain impressions received through the senses, were originally understood in a way just like that in which they are understood after the accumulation of an infinity of experiences—an assumption at variance with the established facts of Psychology. Do we not know that the daily rising and setting of the sun, are thought of in completely different ways by the clown and by the astronomer? Do we not know that the adult and the juvenile differ widely in the conceptions suggested to them by the action of a lever, a pulley, or a screw? Do we not know that the form of a house is comprehended by the child, after a manner in which the infant cannot comprehend it? Moreover, is it not admitted that much of our acquired knowledge becomes so consolidated as to disable us from dissociating its elements in our minds—that on grasping an apple we cannot, without great difficulty, so confine our consciousness to the sensations of touch, as to avoid thinking of the apple as spherical—that we find it utterly impossible, when looking at a neighbouring object, to shut out all thought of the distance, and attend only to the visual sensations? And when we unite these two general facts—first, that by the putting together of experiences the mind acquires conceptions quite different from those it originally had; and, second, that experiences which have been from the beginning invariably connected, and perpetually connected, become fused into conceptions that are undecomposable by any subjective contemplation of them—does it not become manifest, both that the adult's idea of Motion is entirely distinct in nature from the infant's idea of Motion, and that it has become impossible for the adult to think of Motion as the infant thought of it? The candid inquirer cannot doubt it. And not doubting it, he will see the vice of the assumption that what are necessities of thought to us, are therefore necessities of thought in the abstract. He will see that the phenomena must be dealt with, not by subjective analysis, but must be analyzed objectively—must be considered, not as they present themselves to our consciousness, but as they would present themselves to a consciousness unoccupied by foregone conclusions.
“But how,” it may be asked, “is it possible for us thus to deal with the phenomena? How can we legitimately speak of Motion as known in some form different from that in which we know it? How can we treat of a conception which we cannot ourselves have?” Very readily. For though in our adult consciousness of Motion, the ideas of Space and Time are inextricably involved; yet there is another element in that consciousness which we can very clearly perceive would remain, were the ideas of Space and Time absent. Though it is perfectly true that on moving my arm, even when in the dark, I cannot become conscious of the motion without being simultaneously conscious of a space traversed and a time occupied in traversing it; yet I find that the muscular sensations accompanying the motion, are altogether distinct in nature from the ideas of Space and Time associated with them. I find no difficulty in so far isolating these sensations in thought, as to perceive that the consciousness of them would remain were my ideas of Space and Time abolished. And I find no difficulty in conceiving that Motion is thinkable by the infant as consisting of these sensations, while yet the notions of Space and Time are undeveloped. Seeing then that Space and Time are knowable only through Motion; and seeing that the primitive consciousness of Motion may readily be conceived to have contained but one of the elements ultimately included in it; we are warranted in the inquiry whether, out of such a primitive consciousness of Motion, the consciousness we have of it may be evolved.
§ 71. To open this inquiry systematically, let us first look at the several data furnished by preceding chapters.
We saw that our conception of Space is a conception of the relativity of coexistent positions; that the germinal element of the conception is the relation between two coexistent positions; that every relation between two coexistent positions is resolvable into a relation of coexistent positions between the subject and an object touched; that this relation of coexistent positions between subject and object, is equivalent to the relation of coexistent positions between two parts of the body; and that thus the question—How do we come by our cognition of Space? is reducible to the question—How do we discover the relation of coexistent positions between two sentient points on our surface?
Our conception of Time we saw to be that of relativity of sequent positions—relativity of position in the series of the states of consciousness. We saw that the germinal element out of which this conception is developed, is a relation of position between two states of consciousness; and that every relation of position between two states of consciousness is known by the number of remembered intervening states.
Respecting Motion, we know that as, through it only are changes in consciousness originally produced, through it only can relations of sequent positions among states of consciousness be disclosed; and that for the same reason, through it only can be disclosed the relations of coexistent positions. At the same time we know that whether Motion is or is not originally cognizable in any other way, it is from the beginning cognizable through the changes of consciousness it produces. If it be subjective motion, as that of a limb, it is present to the mind as a continuous but varying series of sensations of muscular tension. If it be objective motion, as that of something traversing the surface of the body, or as that of something passing before the eyes, it is still present to the mind as a continuous series of sensations: in the one case the tactual sensations that result from touching a succession of points on the skin; in the other case the visual sensations that result from exciting a succession of points on the retina. And if the motion be both subjective and objective, as when one part of the body is drawn over another part, or when a limb is extended within view of the eyes, then it is present to the mind as a double series of sensations: in the one case, as a series of muscular sensations joined with a simultaneous series of tactual sensations; in the other case, as a series of muscular sensations joined with a simultaneous series of visual sensations. Finally, when the hand is moved over the body within view of the eyes, motion is present to the mind as a triple series of sensations—muscular, tactual, visual—occurring simultaneously.
Omitting for the present all consideration of the visual phenomena, let us now turn our attention to the question in which centres the whole controversy respecting the genesis of our ideas of Motion, Space, and Time: the question namely—How do we become cognizant of the relative positions of two points on the surface of the body? Such two points considered as coexistent, involve the germinal idea of Space. Such two points disclosed to consciousness by two successive tactual sensations proceeding from them, involve the germinal idea of Time. And the series of muscular sensations by which, when self-produced, these two tactual sensations are separated, involve the germinal idea of Motion. The questions to be considered then, are—In what order do these germinal ideas arise? and—How are they developed?
Already, in treating of visible extension (§ 58), and the visual perception of space (§ 62), and in showing how serial states of consciousness are consolidated into simultaneous states which become their equivalents in thought, the way has been prepared for answering these questions. The process of analysis partially applied to retinal impressions, has now to be applied, after a more complete manner, to impressions on the body at large. To this end, taking for our subject a newly-born infant, let us call the two points on its body between which a relation is to be established, A and Z. Let us assume these points to be anywhere within reach of the hands—say upon the cheek. By the hypothesis, nothing is at present known of these points; either as coexisting in Space, as giving successive sensations in Time, or as being brought into relation by Motion. If now, the infant moves its arm in such a way as to touch nothing, there is a certain vague reaction upon its consciousness—a sensation of muscular tension. This sensation has the peculiarity of being indefinite in its commencement; indefinite in its termination; and indefinite in all its intermediate changes. Its strength is proportionate to the degree of muscular contraction. Whence it follows that as the limb starts from a state of rest, in which there is no contraction; and as it can reach a position requiring extreme contraction only by passing through positions requiring intermediate degrees of contraction; and as the degree of contraction must therefore form a series ascending by infinitesimal increments from zero; the sensations of tension must also form such a series. And the like must be the case with all subsequent movements and their accompanying sensations; seeing that, be it at rest or in action, a muscle cannot pass from any one state to any other without going through all the intermediate states. Thus, then, the infant, on moving its arm backwards and forwards without touching anything, is brought to what we may distinguish as a nascent consciousness—a consciousness not definitely divisible into states; but a consciousness the variations of which pass insensibly into each other, like undulations of greater or less magnitude. And while the states of consciousness are thus incipient—thus indistinctly separated, there can be no clear comparison of them; no classing of them; no thought, properly so called; and consequently, no ideas of Motion, Time, or Space, as we understand them. Suppose, now, that the hand touches something. A sudden change in consciousness is produced—a change that is incisive in its commencement, and, when the hand is removed, equally incisive in its termination. In the midst of the continuous feeling of muscular tension, vaguely rising and falling in intensity, there all at once occurs a distinct feeling of another kind. This feeling, beginning and ending abruptly, constitutes a definite state of consciousness; and becomes, as it were, a mark in consciousness. By similar experiences other such marks are produced; and in proportion as they are multiplied, there arises a possibility of comparing them, both in respect to their degrees and their relative psitions: while at the same time, the feelings of muscular tension being, as it were, divided out into lengths by these superposed marks, become similarly comparable; and so there are acquired materials for a simple order of thought. Observe, also, that while these tactual sensations may, when several things are touched in succession, produce successive marks in consciousness, separated by intervening muscular sensations, they may also become continually coexistent with these muscular sensations; as when the finger is drawn along a surface. And observe further, that when the surface over which the finger is drawn is not a foreign body, but some part of the subject's body, these muscular sensations, and the continuous tactual sensation joined with them, are accompanied by a series of tactual sensations proceeding from that part of the skin over which the finger is drawn. Thus, then, when the infant moves its finger along the surface of its body from A to Z, there are simultaneously impressed upon consciousness three sets of sensations—the varying series of sensations proceeding from the muscles in action; the series of tactual sensations proceeding from the points of the skin successively touched between A and Z; and the continuous sensation of touch from the finger-end. Now it might be argued that some progress is made towards the idea of space, in the simultaneous reception of these sensations—in the contemplation of them as coexistent: seeing that the notion of coexistence and the notion of space have a common root; or in other words—seeing that to be conscious of a duality or multiplicity of sensations, is the first step towards being conscious of that duality or multiplicity of points in space which they imply. It might also be argued that as, when the finger is moved back from Z to A, these serial sensations are experienced in a reverse order, there is thus achieved a further step in the genesis of the idea: seeing that coexistent things are alone capable of impressing consciousness in any order with equal vividness. But passing over these points, let us go on to notice, that as subsequent motions of the finger over the surface from A to Z, always result in the like simultaneous sets of sensations, these, in course of time, become indissolubly associated. Though the series of tactual sensations, A to Z, being producible by a foreign body moving over the same surface, can be dissociated from the others; and though, if the cheek be withdrawn by a movement of the head, the same motion of the hand, with its accompanying muscular sensations, may occur without any sensation of touch; yet, when these two series are linked by the tactual sensation proceeding from the finger-end, they necessarily proceed together; and become inseparably connected in thought. Whence, it obviously results that the series of tactual sensations A to Z, and the series of muscular sensations which invariably accompanies it when self-produced, serve as mutual equivalents; and being two sides of the same experience, suggest each other in consciousness. Due attention having been paid to this fact, let us go on to consider what must happen when something touches, at the same moment, the entire surface between A and Z. This surface is supplied by a series of independent nerve-fibres, each of which at its peripheral termination becomes fused into, or continuous with, the surrounding tissue; each of which is affected by impressions falling within a specific area of the skin; and each of which produces a separate state of consciousness. When the finger is drawn along this surface, these nerve-fibres A, B, C, D,…Z, are excited in succession; that is—produce successive states of consciousness. And when something covers, at the same moment, the whole surface between A and Z, they are excited simultaneously; and produce what tends to become a single state of consciousness. Already I have endeavoured to show in a parallel case (§ 58), how, when impressions first known as having sequent positions in consciousness are afterwards simultaneously presented to consciousness, the sequent positions are transformed into coexistent positions, which, when consolidated by frequent presentation, are used in thought as equivalent to the sequent positions: and it is needless here to repeat the explanation. What it now concerns us to notice is this:—that as the series of tactual impressions A to Z, known as having sequent positions in consciousness, are, on the one hand, found to be equivalent to the accompanying series of muscular impressions; and on the other hand, to the simultaneous tactual impressions A to Z, which, as presented together are necessarily presented in coexistent positions; it follows that these two last are found to be the equivalents of each other. A series of muscular sensations becomes known as equivalent to a series of coexistent positions; and being habitually joined with it, becomes at last unthinkable without it. Thus, the relation of coexistent positions between the points A and Z (and by implication all intermediate points), is necessarily disclosed by a comparison of experiences: the ideas of Space, Time, and Motion, are evolved together. When the successive states of consciousness A to Z, are thought of as having relative positions, the notion of Time becomes nascent. When these states of consciousness, instead of occurring serially, occur simultaneously, their relative positions, which were before sequent, necessarily become coexistent; and there arises a nascent consciousness of Space. And when these two relations of coexistent and sequent positions are both presented to consciousness along with a series of sensations of muscular tension, a nascent idea of Motion results.
The development of these nascent ideas, arising as it does from a still further accumulation and comparison of experiences, will be readily understood. What has been above described as taking place with respect to one relation of coexistent positions upon the surface of the skin—or rather, one linear series of such coexistent positions, is, during the same period, taking place, with respect to endless other such linear series, in all directions over the body. The like equivalence between a series of coexistent impressions of touch, a series of successive impressions of touch, and series of successive muscular impressions, is being established between every pair of points that can readily be brought into relation by movement of the hands. Let us glance at the chief consequences that must ultimately arise from this organization of experiences.
Not only must there gradually be established a connection in thought between each particular muscular series, and the particular tactual series, both successive and simultaneous, with which it is associated; and not only must there, by implication, arise a knowledge of the special muscular adjustments required to touch each special part; but, by the same experiences, there must be established an indissoluble connection between muscular series in general and series of sequent and coexistent positions in general: seeing that this connection is repeated in every one of the particular experiences. And when we consider the infinite repetition of these experiences, we shall have no difficulty in understanding how their components become so consolidated, that even when the hand is moved through empty space, it is impossible to become conscious of the muscular sensations, without becoming conscious of the sequent and coexistent positions—the Time and Space, in which it has moved.
Observe again, that as, by this continuous exploration of the surface of the body, each point is put in relation not only with points in some directions around it, but with points in all directions—becomes, as it were, a centre from which radiate lines of points known first in their serial positions before consciousness, and afterwards in their coexistent positions—it follows, that when an object of some size, as the hand, is placed upon the skin, the impressions from all parts of the area covered being simultaneously presented to consciousness, are placed in coexistent positions before consciousness: whence results an idea of the superficial extension of that part of the body. The idea of this extension is really nothing more than a simultaneous presentation of all the impressions proceeding from the various points it includes, which have previously had their several relative positions measured by means of the series of impressions separating them. Any one who hesitates respecting this conclusion, will, I think, adopt it, on critically considering the perception he has when placing his open hand against his cheek—on observing that the perception is by no means single, but is made up of many elements which he cannot think of all together—on observing that there is always one particular part of the whole surface touched, of which he is more distinctly conscious than of any other—and on observing that to become distinctly conscious of any other part, he has to traverse in thought the intervening parts; that is, he has to think of the relative positions of these parts by vaguely recalling the series of states of consciousness which a motion over the skin from one to the other would involve.
It is needless now to dwell upon that further development of these fundamental ideas which results when the visual experiences are united with the tactual and muscular ones. Being merely a further complication of the same process, it may readily be traced out by joining with the above explanations, those given when treating of visible extension and space. It will suffice here to say that, by serving clearly to establish in our minds the identity of subjective and objective motion, sight finally enables us more or less completely to dissociate Motion in the abstract, from those muscular sensations through which it is primarily known to us; and that by doing this, and by so reducing our idea of Motion to that of coexistent positions in Space occupied in successive positions in Time, it produces the apparently necessary connection between these three ideas.
§ 72. Thus then, we find that Motion, originally present to consciousness under a far simpler form than that in which we know it, serves by its union with tactual experiences to disclose Time and Space to us; and that, in the act of disclosing them, it itself becomes clothed with the ideas of them; and ultimately becomes inconceivable without these ideas.
It remains to add that the perception of Motion, as we know it, consists in the establishment in consciousness of a relation of simultaneity between two relations—a relation of coexistent positions in Space, and a relation of sequent positions in Time. In other words, the consciousness of Motion is produced by a simultaneous presentation of these relations—a united cognition of them. And it is scarcely needful to say that in the act of perception, these jointly-presented relations are severally assimilated to the like relations before known—that the perception of great velocity, for example, is possible only by simultaneously thinking of two coexistent positions as remote, and two sequent positions as near: which words remote and near, imply the classing of the two relations with previously experienced ones. And similarly with perceptions of the kind of motion, and the direction of motion.
THE PERCEPTION OF RESISTANCE.
§ 73. We may conclude, à priori, that of the various impressions received by consciousness, there must be some most general impression. The building up of our experiences into a complex structure, implies a fundamental experience on which the structure may rest. The great mass of our sensations, and of the perceptions we form out of them, being merely signs, there must be something which they are signs of; and this something, whatever be its special modifications, must have an essential element. By successive decompositions of our knowledge into simpler and simpler components, we must come at last to the simplest—to the ultimate material—to the substratum. What is this substratum? It is the impression of resistance. This is the primordial, the universal, the ever-present constituent of consciousness.
It is primordial, alike in the sense that it is an impression of which the lowest orders of living beings show themselves susceptible, and in the sense that it is the first species of impression received by the infant—alike in the sense that it is appreciated by the nerveless tissue of the zoophyte, and in the sense that it is presented in a vague manner, even to the nascent consciousness of the unborn child.
It is universal, both as being cognizable (using that word not in the human but in a wider sense) by every creature possessing any sensitiveness, and usually as being cognizable by all parts of the body of each—both as being common to all sensitive organisms, and in most cases as being common to their entire surfaces.
It is ever present, inasmuch as every creature, or at any rate every terrestrial creature, is subject to it during the whole of its existence. Excluding those lowest animals which make no visible response to external stimuli, and those which float passively suspended in the water, there are none but what have, at every moment of their lives, some impressions of resistance; proceeding either from the surfaces on which they rest, or the reaction of their members during locomotion, or both.
Thus, impressions of resistance, as being the earliest that are appreciated by the sensitive creation regarded as a progressive whole, and by every higher creature in the course of its evolutions; and as being appreciated by almost all parts of the body in the great majority of creatures; are necessarily the first materials put together in the genesis of intelligence. And as being the impressions continuously present in one form or other throughout life, they necessarily constitute that thread of consciousness on which all other impressions are strung—form, as it were, the weft of that tissue of thought which we are ever weaving.
But leaving general statements, let us go on to consider these truths somewhat in detail.
§ 74. That our perception of Body has for its ultimate elements impressions of resistance, is a conclusion to which all the foregoing analyses point. In the order of thought (and of any other order we can know nothing) resistance is the primary attribute of body; and extension is a secondary attribute. We know extension only through a combination of resistances: we know resistance immediately by itself. All space-attributes of body are unknowable save by synthesis; while this primordial attribute is knowable without synthesis. Again, a thing cannot be thought of as occupying space, except as offering resistance. Even though but a point in space, if it be conceived to offer absolutely no resistance, it ceases to be anything—becomes no-thing. Resistance is that by which occupied extension (body) and empty extension (space) are differentiated. And the primary property of body, considered as a different thing from not-body, must be that by which it is universally distinguished from not-body: namely resistance. Moreover, it is by resistance we determine whether any appearance is body or not. Resistance without appearance, we decide to be body; as when striking against any object in the dark. Appearance without resistance, we decide not to be body; as in the case of optical illusions. Once more there is a thing which we know to be body only by its resistance; namely, air. We should be ignorant that there was such a thing as air, were it not for its resistance. And we endow it with extension by an act of pure inference. Thus, not only is it that body is primarily known as resistant, and that subsequently, through a combination of resistances, it is known as occupying space, but it is that there is one kind of body which presents to our senses no other attribute than that of resistance.
That our cognition of Space can arise only through an interpretation of resistances, is an obvious corollary from preceding chapters. As was shown, the ultimate element into which our notion of Space is resolvable, is that of the relation between two coexistent positions. And that such two coexistent positions may be presented to our consciousness, it is necessary that they should be occupied by something capable of impressing our organism; that is—by something resistant. As admitted on all hands, Space, in itself, having no sensible properties, would be for ever unknowable to us did it not contain objects. Even Kantists do not contend that it is knowable by itself; but say that our experiences of things are the occasions of its presentation to us. And as all our experiences of things are ultimately resolvable into experiences of resistance—are all either resistances or the signs of resistances; it follows that on any hypothesis, Space is cognizable only through experience of resistances.
Similarly with Motion. As was shown in the last chapter, subjective motion is primarily known to us as a varying series of states of muscular tension; that is—sensations of resistance. The series of tactual sensations through which it is otherwise known, are sensations produced by something that resists. And when, ultimately, objective motion comes to be recognized by sight, it is recognized as a phenomenon equivalent to those previously known through the muscular and visual sensations conjoined; as when we move our own limbs within view of the eyes. So that, abstracting all the elements we afterwards add to it, motion is originally the generalization of a certain order of resistances.
Our notion of Force, also, has a parallel genesis. It is not simply that in science and the arts, resistance, as ascribed by us to objects, is used to measure motive force, and is therefore conceived by us as an equivalent force; but it is that resistance, as known subjectively in our sensations of muscular tension, forms the substance of our conception of force. That we have such a conception, is a fact that no metaphysical quibbling can set aside. That we must necessarily think of force in terms of our experience—must construct our conception of it out of the sensations we have received, is also beyond question. That we have never had, and never can have, any experience of the force by which objects produce changes in other objects, but that we can never immediately know these changes as anything more than antecedent and consequent phenomena, is equally indisputable. And that therefore, our notion of force is a generalization of those muscular sensations which we have when we are ourselves the producers of change in outward things, is an unavoidable corollary. How we are necessarily led to ascribe force, as thus conceived, to all external workers of change, is readily shown. We find that the same sensible effects are produced when body strikes against us, as when we strike against body. Hence we are obliged to represent to ourselves the action of body upon us as like our action upon it. And the sensible antecedent of our action upon body being the feeling of muscular tension, we cannot conceive its action upon us as of like nature, without vaguely thinking of this muscular tension, that is, of force, as the antecedent of its action.
Thus, Matter, Space, Motion, Force—all our fundamental ideas, arise by generalization and abstraction from our experiences of resistance. Nor shall we see in this anything strange, if we do but contemplate, under its simplest aspect, the relation between the organism and its environment. Here is a subject placed in the midst of objects. It can learn nothing of them without being affected by them. Being affected by them implies some action produced by them upon its surface. Their action must be either action by direct contact, or by the contact of something emanating from them. In virtue of the law of gravitation, their primary and most continuous action is by direct contact. In the nature of things, also, their all-important actions, both destructive and preservative—through enemies and through food—are by direct contact. Hence, action by direct contact, being the primary action, the ever-present action, the all-important action, and at the same time the simplest and most definite action, becomes the action of which all other kinds of action are representative. And the sensation of resistance, through which this fundamental action is known, becomes, as it were, the mother-tongue of thought, in which all the first cognitions are registered, and into which all symbols afterwards learnt are interpretable.
§ 75. The matter will be further elucidated, and this last position especially confirmed, on observing that all the sensations through which the external world becomes known to us, are explicable by us only as resulting from certain forms of force. As already shown (§ 50) the so-called secondary attributes of body are dynamical. Science determines them to be the manifestations of certain energies possessed by matter; and even when not scientifically analyzed, they are spoken of as implying the actions of things upon us. But we cannot think of the actions of things upon us, except by ascribing to them powers or forces. These powers or forces must be presented to our minds in terms of our experience. And, as above shown, our only experience of force is the muscular tension which we feel when overcoming force: this constitutes our consciousness of force, and our measure of force. Hence, not only is it that our experiences of resistance form the elementary material of thought, alike as being earliest, as being ever present, and as underlying our fundamental ideas; not only is it that our other experiences are employed by us as the representatives of these elementary experiences; but it is that we cannot understand these other experiences except by translating them into terms derived from the elementary experiences.
An extremely important fact to be here noticed, as further illustrating the same truth, is, that resistance, as disclosed to us by opposition to our own energies, is the only species of external activity which we are obliged to think of as subjectively and objectively the same. We are disabled from conceiving mechanical force in itself, as differing from mechanical force as presented to our consciousness. The axiom—“Action and reaction are equal, and in opposite directions,” applied as it is not only to the action of objects upon each other, but to our action upon them and their action upon us, implies a conception of the two forces as equivalent, both in quantity and nature; seeing that we cannot conceive a relation of equality between magnitudes that are not connatural. How happens it, then, that in this case alone we are compelled to think of the objective force as like the force which we feel? Sound, we can very well conceive as consisting in itself of vibrations, having no likeness whatever to the sensation they produce in us. The impressions we have of colour, can, without much difficulty, be understood as purely subjective effects resulting from an objective activity to which they have not even a distant analogy. And similarly with the phenomena of heat, smell, and taste. Why, then, can we not represent to ourselves the force with which a body resists our efforts to move it, as a something quite unlike the feeling of muscular tension which its resistance gives us? There is an all-sufficient reason. It is not simply that whether we strike or are struck, the sound, the indentation, the sensations of touch, pressure, and pain, are of the same kind; nor is it that we can make the force which is known to our consciousness as muscular tension, produce an effect like that produced by an external body—as when, taking one of the weights out of a pair of scales in equilibrium, we raise the antagonist weight by pressing down the empty scale with the hand; nor is it that we can store up our own force in objects, and make them afterwards expend it in producing results such as it would have directly produced—as when we strain a bow and let its recoil propel the arrow; but it is that there exists no alternative mode of representing this force to consciousness—no other experience, or combination of experiences, by which we can figure it to our minds. Saying nothing of the various facts which, like those just instanced, strengthen the idea of sameness between muscular effort in the subject and mechanical power in the object; our inability to conceive this mechanical power as being in itself different from what we feel it to be in our muscular efforts, is primarily due to the circumstance that there is no feeling, no impression, no mode of consciousness, which we can substitute for this primordial mode. The liberty which we have to think of light, heat, sound, &c., as in themselves different from our sensations of them, arises solely from this; that we possess other sensations by which to symbolize them—namely, those of mechanical force: and it needs but to glance at any theory of objective light, heat, sound, &c., to see that we do think of them in terms of mechanical force; that is, in terms of our muscular sensations. But if we attempt to think of mechanical force as in itself different from our impression of it, there arises the insurmountable difficulty that there is no remaining species of impression to represent it. All other experiences being expressed to the mind in terms of this experience, this experience cannot be expressed to the mind in any terms but its own. To be conceived at all, mechanical force must be represented in some state of consciousness. This state of consciousness must be one directly or indirectly resulting from the action of things upon us. The states of consciousness produced by all other actions than mechanical action, we already represent to our minds in states such as those produced by mechanical action. There remains, therefore, no available state of consciousness save that produced by mechanical action. And hence it is impossible for us to represent mechanical action to ourselves, in any other state of consciousness than that which it produces in us—it is impossible for us to think of objective force as different from our subjective experience of it. Though the proposition that they do differ is verbally intelligible, it is absolutely inconceivable, and must ever remain so.
§ 76. Having thus seen that the perception of resistance is fundamental, alike in respect of genesis, in respect of universality, and in respect of continuity; and that as a consequence it is also fundamental in the sense of being the perception into which all other perceptions are interpretable, while itself interpretable into none; we may proceed to consider it analytically.
As shown when treating of the statico-dynamical attributes of body, the sensations concerned in our various perceptions of resistance, are those of touch proper, pressure, and muscular tension, either uniform or changing. The sensation of touch proper cannot be considered as in itself giving an immediate knowledge of resistance; but is simply the sign of something capable of resisting. When the contact is so gentle as to produce no feeling of pressure, it cannot be said whether the object is soft or hard, large or small. It is simply inferred that there is something: just as it would have been had a sensation of sound or colour been received. Hence the sensation of touch proper may be left out of the inquiry.
Our knowledge of resistance, then, is gained through the sensations of pressure and muscular tension. These may occur separately. When our bodies are inactive, save in the sense of being gravitative and resistant masses of matter, we have the sensation of pressure only—either from the reaction of the surface on which we rest; or from the action of a weight placed upon us; or from both. When, as a consequence of some volition, we bring our forces to bear upon outward objects—when our bodies are active and objects are reactive—we have coexistent sensations of pressure and muscular tension. And when, as on raising the arm into a horizontal position, the bodily action is such as to call forth no direct reaction from objects, we experience the sensation of muscular tension alone. Now the fact to be here more particularly noticed, is, that whenever the sensations of pressure and muscular tension coexist, they always, other things equal, vary together. Now that I am holding my pen gently between the fore-finger and thumb, I have a very slight sensation of pressure and a very slight sensation of muscular tension. If I grasp the pen hard, both sensations increase in intensity; and I find that I cannot change one without changing the other. The like relation is observable on raising light and heavy weights; or on thrusting against small and large objects. Hence it results that these sensations become known to consciousness as equivalents. A given sensation of pressure, is thinkable as tantamount to a certain sensation of muscular tension; and vice versâ. And now there arises the inquiry—which of these two is habitually used in thought as the sign, and which as the thing signified?
In point of time the two are co-ordinate. Not only from the very first, does the infant experience the reaction upon consciousness accompanying the action of its own muscles; but from the very first, it has sensations of pressure from the surfaces on which it rests, and from the hands that lay hold of it. But though equally early, and as it would seem, equally fundamental, it may be readily proved that in the order of constructive thought, the sensation of muscular tension is primary, and that of pressure secondary. This will be made tolerably manifest by the simple consideration, that these sensations of pressure caused by the weight of the body and the actions of the nurse, can at first give no notions of what we understand as resistance or force; seeing that before they can give such notions, there must exist ideas of weight and of objective action. Originally these sensations of pressure which the infant passively receives, being unconnected in experience with definite antecedents and consequents, are as isolated and meaningless as sensations of sound or odour. Not to dwell upon this fact however, further than to point out that the involuntarily-produced sensations of pressure may be left out of the question, let us, in the first place, go on to observe that the voluntarily-produced sensations of pressure are second in order of time to the sensations of muscular tension. Before the infant can experience the feelings which neighbouring objects give to its moving limbs and fingers, it must first experience the feelings that accompany the motion of its limbs and fingers. In the second place let it be observed, that the muscular sensations are more general than the voluntarily-produced sensations of pressure; seeing that while these last occur only when the energies are employed upon external bodies, the first occur both when the energies are thus employed, and when they are employed in moving and holding up the limbs themselves. Let it be observed in the third place, that while only some of the sensations of pressure are voluntarily produced, all the sensations of muscular tension are voluntarily produced. And let it once more be observed, that when both are voluntarily-produced—as when some object is grasped, or lifted, or thrust against—the muscular sensation is always present to consciousness as the antecedent, and the sensation of pressure as the consequent; and that any variation in the last, is known as resulting from a variation in the first. Among the intelligible experiences of the infant, therefore, the sensation of muscular tension, being alike the earliest, the most general, and that which stands in the position of immediate antecedent to the sensation of pressure, whenever the origin of that sensation is known, is necessarily the sensation in which all experiences of resistance are registered and thought of. Hence the reason why, when anything pushes against us, we do not represent its force to our minds in terms of the pressure experienced; but in terms of the effort which that pressure signifies. Hence the fact that when the weight of an object is spoken of, we do not think of the intensity of the tactile impression which results on lifting it; but of the intensity of the accompanying muscular strain.
That the cognition of resistance is finally resolvable into that of muscular tension, and that this forms the raw material of thought in its earliest forms, will be most clearly seen on considering that at first it forms the only available measure of external phenomena. The acquisition of knowledge is from the beginning experimental. Were the infant to remain passive in the midst of surrounding objects, it could never arrive at a comprehension of them. It can arrive at a comprehension of them, only by active exploration. But what is the condition under which alone such an exploration will answer its end? How can the properties of things be compared, and estimated, and classified? By means of some common measure already possessed. The infant's only mode of determining the amounts of external activities, is, by ascertaining how much of its own activity they are severally equivalent to. As inanimate objects cannot act upon it in such way as to disclose their properties, it must call out their reactions by acting upon them: and to become cognizant of these reactions, implies some scale of action in itself. This scale of action must underlie the whole structure of its experiences—must be the substratum of its thoughts—must be that mode of consciousness to which all other modes are ultimately reducible. Thus then, the sense of muscular tension, of which this scale is constituted, forms, in the nature of things, the primitive element in our intelligence.
§ 77. Respecting the perception of resistance, that is of muscular tension, it has still to be pointed out that it consists in the establishment of a relation of coexistence between the muscular sensation itself and that particular state of consciousness which we call will. That the muscular sensation alone, does not constitute a perception of resistance, will be seen on remembering that we receive from a tired muscle, a feeling nearly allied to, if not identical with, that which we receive from a muscle in action; and that yet this feeling, being unconnected with any act of volition, does not give any notion of resistance.
To which there is only to add, that in the act of perception, this relation is classed with the like foreknown relations; and that in so classing it, consists the knowledge of the special muscular combination, adjustment, and degree of force exercised.
PERCEPTION IN GENERAL.
§ 78. As foregoing chapters have made sufficiently manifest, the term Perception, is commonly applied to states of consciousness infinitely varied, and even widely different in nature. Between the consciousness of a vast landscape, and the consciousness of a minute dot on the surface of this paper, there exist countless gradations which pass insensibly one into another; and which yet unite extremes almost too strongly contrasted to be classed together. A perception may vary indefinitely in complexity, in degree of directness, and in degree of continuity. As in one of the primitive cognitions of resistance lately treated of, it may rise but a step above simple sensation. On the other hand, when watching the evolutions of a ballet, there is a consciousness not only of the multiplied relations of coexistent positions which constitute our notions of the distance, size, figure, and attitude of each dancer—not only of the various like relations between each and the several colours of her dress—not only of the relations of position among the respective dancers; but also, of the numerous relations of sequence which the body and limbs of every dancer exhibit in their movements with respect to each other; and of those yet more involved relations of sequence exhibited in the movements of every dancer with respect to the rest. In degree of directness, again, there is a similarly marked contrast between the perception that some surface touched by the finger is hard, and the perception that a building under whose walls we stand is a particular cathedral. The one piece of knowledge is almost immediate: the other is mediate in a double, a triple, a quadruple, and even in a still higher degree—mediate inasmuch as the solidity of the building is inferential; inasmuch as its proximity is inferential; inasmuch as its position, its size, its shape, are inferential; inasmuch as its artificial origin, its material, its hollowness, are inferential; inasmuch as its ecclesiastical purpose is an inference from these inferences; and inasmuch as the identification of it as a particular cathedral, is yet a still more remote inference resulting from the union of these inferences with those various others through which the locality is recognised. In like antithesis stand the degrees of continuity, in our respective perceptions of an electric spark, and the rush of a cataract which attracts our gaze. And when to these various facts, we add the further fact, that our perceptions, or at any rate our visual perceptions, are continuous in Space as well as in Time—that when looking at a landscape and turning our eyes to different parts of it, we cannot say how much is contained in each perception, or how many perceptions take in the panorama—that while only one particular point in the whole field of view is perceived with perfect distinctness, innumerable other points are perceived with degrees of distinctness imperceptibly decreasing as they recede from the central point, so that it is impossible to say where the perception ends—when we remember this, it will be abundantly manifest that the state of consciousness which we call a perception, cannot be rigorously marked out and separated; but that it merges insensibly into others of its own kind, both synchronous and successive, and into others which we class as of different kinds, both superior and inferior. It passes at the one extreme into reasoning; and at the other borders upon sensation. It may include innumerable relations simultaneously co-ordinated; or but a single relation. It cannot be demarcated from the nascent perceptions that coexist with it; nor (where the thing perceived is in motion) from the perceptions which follow it. So that, however convenient a term Perception may be for common purposes, it must not be understood as signifying any truly scientific division.
§ 79. The only valid distinction to be drawn, is that between Perception and Sensation. Though from time to time referred to with more or less distinctness by early philosophers, it is only in later times that this distinction has been currently acknowledged; and it is but recently that the relation between the two has been specifically formulated in the doctrine of Sir William Hamilton, “that, above a certain point, the stronger the Sensation, the weaker the Perception; and the distincter the perception the less obtrusive the sensation; in other words—though Perception proper and Sensation proper exist only as they coexist, in the degree or intensity of their existence they are always found in an inverse ratio to each other.” Before making any criticisms upon this doctrine, which seems to me rather an adumbration of the truth than the truth itself, it will be needful to state the exact meanings of Sensation proper and Perception proper.
Manifestly, every sensation, to be known as such, must be perceived—must become an object of perception; and hence, as thus considered, all sensations are perceptions. The mere physical affection of the organism does not constitute a sensation proper. While absorbed in thought, I may be subject to undue heat from the fire, uncomfortable pressure from a hard seat, or a continual noise from the street; and though my sentient organs are very decidedly affected, I may yet remain unconscious of the affections—may become conscious of them only when they pass a certain degree of intensity; and only then can be said to experience them as sensations. Moreover, not only in sensation proper, do I contemplate the organic affection as an affection of myself—as a state of consciousness standing in a certain relation to other states; but I also contemplate it as existing in a certain part of my body—as standing in certain relations of position. I perceive where it is. But though, under both these aspects, sensation must be regarded as one species of perception, it will readily be seen to differ widely from perception proper—from the cognition of an external object. In the one case, that which occupies consciousness is something contemplated as belonging to the ego: in the other, it is something contemplated as belonging to the non-ego. And these it is, which, as sensation proper and perception proper, are asserted to coexist in degrees of intensity that vary inversely.
That this is not altogether a correct assertion, will, I think, become apparent on carefully examining the facts as determined by experiment. Let the finger be brought against some hard rough body—say a broken stone, the back of a ribbed sea-shell, or anything capable of giving a tactile impression of some complexity. Between that degree of pressure used in ordinary touch, and the pressure that is painful from its intensity, there are many gradations; and Sir William Hamilton's doctrine implies that, beginning with the degree of pressure needful for distinct perception, and gradually increasing it until the pain becomes unbearable, the perception, step by step decreases in vividness, while the sensation, step by step increases in vividness; but that neither at the beginning nor the end, does the one exclude the other. Do the facts correspond with this statement? I think not. During the ordinary gentle pressure, it will be found that consciousness is occupied entirely about the surface and its irregularities; that no thought is taken of the sensations through which the surface and its irregularities are known; that to attend to these sensations rather than to the objective phenomenon implied by them, requires a decided effort; and that when they are thought of, it is in another state of consciousness quite distinct from the previous one. If the pressure be gradually increased, there is not a gradual decrease in the vividness of the perception and an increase in the vividness of the sensation, but the consciousness remains, as before, occupied about the surface; the hardness and roughness of which, become the peculiarities most contemplated as the pressure becomes greater: and though the sensation may be more easily thought of than before, and is more distinctly realized when it is thought of, still, it can be thought of only in a second state of consciousness not included in the original one. But now, if the pressure be increased so far as to produce decided pain, there will occur quite a different state of consciousness, in which the thing contemplated is the subjective affection and not its objective cause. When the pain reaches any considerable intensity, it will be found that the perception has not only altogether ceased, but that it can be recalled into consciousness only by an effort. And it will be very clearly perceived that were the nature of the object producing the painful pressure, not already known, it would be entirely unknowable. Generalizing the facts then, it would seem, not so much that Sensation and Perception vary inversely, as that they exclude each other with varying degrees of stringency. When the sensations (considered simply as physical changes in the organism) are weak, the objective phenomenon signified by them is alone contemplated: the sensations are altogether excluded from consciousness, and cannot be brought into it without a decided effort. When the sensations are rendered somewhat more intense, the perception still remains equally vivid—still remains the sole occupant of consciousness; but as, by their increasing intensity, the sensations tend to force themselves into consciousness, it requires less effort than before to make them the subject of thought. Gradually as the intensity of the sensations is further increased, a point is approached at which consciousness is as likely to be occupied by them, as by the external fact they imply—a point at which either can be thought of with equal facility, and at which each tends in the greatest degree to draw attention from the other. If the intensity of the sensations be yet further increased, they begin to occupy consciousness to the exclusion of the perception, which, however, can still be brought into consciousness by a slight effort. But, finally, if the sensations rise to extreme intensity, consciousness becomes so absorbed by them, that it is impossible without great effort, if at all, to think of the thing causing them.∗
What now is the real nature of this mutual exclusion? Is it not an instance of the general fact that consciousness cannot be in two distinct states at the same time? I cannot know that I have a sensation, without, for the moment, having my attention occupied solely with that sensation: I cannot know the external thing causing it, without, for the moment, having my attention occupied solely with that external thing: and as either cognition rises, the other ceases. If, as Sir William Hamilton asserts, the two cognitions always coexist, though in inverse intensities, then it must happen, that if, beginning at either extreme, the conditions be slowly changed, so that while the cognition most distinctly present to the mind becomes gradually less distinct, the other becomes gradually more distinct; there must arrive a time when they will be equally distinct—when the subjective and objective phenomena will be thought of together with equal clearness; which is impossible. It is very true, as shown above, that under such change of conditions, there arrives a time when the subjective and objective phenomena attract the attention in equal degrees, and are thought of alternately with equal facility. And it may even be admitted that while either is being thought of, the other is nascent in thought. But this is quite a different thing from saying that they occupy consciousness together.
Perception proper and sensation proper, will however be best understood, and the purpose of the present chapter most furthered, by considering their antagonism under the light of preceding analyses. In all cases it has been found that perception is an establishment of specific relations among states of consciousness; and is so distinguished from the establishment of the primary states of consciousness themselves. While in apprehending a sensation, the mind is occupied with a single subjective affection; in apprehending the external something producing it, the mind is occupied with the relation or relations between that affection and others, either past or present. The sensation cannot be known save as an undecomposable state of consciousness. The outward object cannot be known save as a decomposable state of consciousness; which is recognized as such or such, in virtue of the special manner in which the component states are united. Now the contemplation on the one hand of a special state of consciousness, and on the other of the special relations among states of consciousness, are quite different mental acts—acts which may be performed in immediate succession, but not together. To know a relation is not simply to know the terms between which it subsists. Though when the relation is perceived, the terms are nascently perceived, and conversely, yet introspection will show that there is a distinct transition in thought from the terms to the relation, and from the relation to the terms. That the whole matter centres in the question—How do we think of a relation as distinguished from the terms between which it subsists? will be plain from the fact that Sir William Hamilton, while implying that it is something more, himself says that in one respect, “perception proper is an apprehension of the relations of sensations to each other.” Joining which doctrine with the one contended against, we see that, according to his hypothesis, the sensations and the relations between them, can be simultaneously thought of with equal degrees of distinctness, or with any other relative degrees of distinctness—a manifestly untenable proposition.
The only further remark here called for, is, that perception cannot be correctly defined as “an apprehension of the relations of sensations to each other”; for that in most perceptions some of the elements are not presented but represented in consciousness. When passing the finger over a rough surface, the perception contains very much more than the co-ordinated sensations immediately experienced. Besides these it contains the remembered visual impressions produced by such a surface; which cannot be kept out of the mind; and in the suggestion of which the perception largely consists. Again, when gazing at some one object, it will be found that objects on the outskirts of the field of view, are recognized more by representation than by presentation. If, without moving his eyes, the observer asks himself what he actually perceives of these outlying objects, he will find that they impress him simply as ill-defined patches of colour; that were it not for his previous experiences, he would not know the meanings of these patches; and that in perceiving what the objects are, he ekes out the vaguely presented impressions with some comparatively distinct represented ones. And what thus manifestly happens with perceptions of this order, happens in one form or other with all perceptions. In fact, when analyzed to the bottom, all perceptions prove to be acquired perceptions. From its simplest to its most complex forms, perception is essentially a diagnosis.
§ 80. Finally, to express in its most general form the truth that has been variously illustrated in detail—Perception is a discerning of the relation or relations between states of consciousness, partly presentative and partly representative; which states of consciousness are themselves known only to the extent involved in the knowledge of their relations.
Under its simplest form—a form however of which the adult mind has few if any examples—perception is the consciousness of a single relation. More commonly, a number of relations are simultaneously presented and represented; and the relations between these relations are cognized. Most frequently, the relations of relations of relations are the objects of perception: as when any neighbouring solid body is regarded. And very often—as when observing the motions of an animal, which are known to us as the relations between certain highly complex relations of position now present, and certain others just past—a still more abstract relativity is contemplated.
Further it is to be noticed, that in the ascending grades of perception, there is an increase not only in the number and abstractness of the relations grasped together, but also in the variety of their kinds. Numerous relations of position, of extension, of coexistence, of sequence, of degree in all sensible qualities, are co-ordinated in one thought; or what appears to us such.
Add to which that, as heretofore pointed out in each special case, the act of perception is the establishment of a relation of likeness between the particular relation or group of relations contemplated, and some past relations or groups of relations—the assimilation of it to such past relations or groups of relations—the classing of it with them.
§ 81. And now it remains only to apply the analysis thus far pursued, to the relations themselves. By a continued process of decomposition we have found that our intellectual operations severally consist in the establishment of relations, and groups of relations, among the primitive undecomposable states of consciousness, produced in us by our own actions and the actions of surrounding things. But what are these relations? They can be nothing more than certain secondary states of consciousness, produced by the union of the primary states. Unable as we are to transcend consciousness, we can know a relation only as some modification of consciousness. The original modifications of consciousness are the feelings produced in us by subjective and objective activities; and any further modifications of consciousness must be such as result from combinations of these original ones. In all their various kinds and compounds, what we call relations, can be to us nothing more than the modes in which we are affected by the comparison of sensations, or remembered sensations, or both. Hence what we have next to do, is, first to resolve the special kinds of relations into the more general kinds; and then to ascertain what are the ultimate phenomena of consciousness which the primordial relations express.
THE RELATIONS OF SIMILARITY AND DISSIMILARITY.
§ 82. Of all relations the most complex is that of Similarity—that in virtue of which we range together objects of the same species, notwithstanding their differences of magnitude; and in virtue of which we put into the same class, phenomena of causation that are widely contrasted in degree. Already, in treating of Reasoning and of Classification, much has been said of this relation which forms their common basis. Here it needs only to state what it is when considered under its most general aspect.
The similarity which we predicate of natural objects belonging to the same class, is made up of many component similarities. Two animals identical in kind but unlike in size, are similar not only as wholes, but are also similar in their parts. The head of one is similar to the head of the other; the leg to the leg; the hoof to the hoof; the eye to the eye. Even the parts of the parts will be found more or less similar; as, on comparing two teeth, the crown to the crown, and the fangs to the fangs. And even such minute components as the hairs, show in their structure this same parallelism. One of these ordinary similarities therefore, consisting of an intricate plexus of similarities held together in similar ways, and resolvable as it consequently is into simple similarities, will, by implication, be analyzed in analyzing one of these simple similarities.
Though similarities of sequence do not admit of a complication parallel to that which similarities of coexistence admit of—seeing that, as known by us, a sequence is in its nature single—yet, they admit of another species of complication: namely, that arising from composition of causes and composition of effects. While, by the gravitation of a weight, the string to which it hangs may be elongated, and no other appreciable result be produced; by the joint action of a certain temperature, a certain amount of moisture, and a certain miasm, upon an individual of a particular diathesis, who happens to be in a particular state, there may be produced the immense complication of effects constituting a disease. Each of these sequences is classed with others which we call similar; and in conjunction with them may form a premiss for future conclusions. And though, in the first case, there is a single antecedent and a single consequent, while, in the second case, there is a group of antecedents and a group of consequents—though in this second case the antecedent is not a force, but a variety of forces united in a special plexus of relations, and the consequent is not an effect, but a variety of effects united in a special plexus of relations; yet, we so obviously think of a composite cause and a composite effect, as related in the same way that a simple cause and a simple effect are related, that in treating of similar sequences we may confine our attention to the simple ones, as those out of which the othersarise by complication of the terms.
Thus, then, choosing some primitive type of each, we have to consider what there is in common between similar coexistences and similar sequences.
§ 83. Of the one class, similar triangles furnish the most convenient example: and as an example of the other, we may take the uniform sequence of heat upon compression.
After all that was before said, it is needless to do more than remind the reader, that in both of these cases the similarity resolves itself into either equality or likeness of relations—that triangles are similar when any two sides of the one bear to each other a relation like that which the homologous sides of the other bear to each other; and that when classing as similar, the various cases in which compression produces heat, the likeness of the relations between compression and heat in those various cases, is the sole thing meant. Here it concerns us, not to dwell upon the fact that similarity is likeness of relations, but to consider what this likeness of relations implies.
In the first place, it is to be observed, that while it implies likeness in nature between the two antecedents and between the two consequents, it does not imply likeness in their amounts; but that, in nearly all cases, though not necessarily, the two antecedents are quantitatively unlike, and the two consequents are quantitatively unlike. Two triangles may be similar, though the sides of the one are severally a score times as great as the homologous sides of the other; and though in one case a small evolution of heat results from the pressure of a hundred pounds, and in another case a greater evolution from the pressure of a hundred tons, the cases are classed as similar. So that thus regarded, similarity may be described as the likeness of relations whose antecedents are like in kind, but mostly unlike in degree, and whose consequents are like in kind, but mostly unlike in degree.
This likeness of relations has itself two phases. It may be both qualitative and quantitative; or it may be qualitative only. It may be a likeness both in the kind of the relations and their degree; or it may be a likeness in kind only. And hence arise the two orders of similarity—perfect and imperfect: the similarity on which mathematical reasoning proceeds; and the similarity on which the reasoning of daily life proceeds. Thus, in the case of the triangles, the intuition of similarity implies, first, that the relations of extension between the sides of the one, are compared in thought with the like kind of relations between the sides of the other. There can be no idea of similarity if a relation of coexistence between two sides of one triangle, is presented in consciousness along with some relation of extension between two sides of the other. Evidently, therefore, the primary element in the intuition of perfect similarity, is—likeness of nature between relations. And then, joined to this, is the secondary element—likeness of degree between these connatural relations. The relations must be of the same order; and each antecedent must bear to its consequent a contrast of the same strength. In imperfect similarity however, the only implication is, likeness of nature in the relations. When, in any new case, we predicate heat as a result of compression, the implied similarity between such new case and previous cases, is simply a consciousness of connate relations, of which the two antecedents are connate and the two consequents are connate. Nothing is said of degree. The new relation between compression and heat, is simply thought of as a sequence like in kind to certain foreknown sequences; and though there may be a vague idea of the quantity of heat as varying with the quantity of compression, this is not included in the predication. Hence then, while imperfect similarity involves the connature of relations whose antecedents are connatural and whose consequents are connatural; perfect similarity involves the cointension of such connatural relations.
§ 84. So much for the elements into which the relation of similarity is resolvable, objectively considered. Subjectively considered, it may be defined as a consciousness that two successive states of consciousness are severally composed of like states of consciousness arranged in like ways: or more specifically—it is a consciousness of the cointension of two connatural relations between states of consciousness, which are themselves like in kind but commonly unlike in degree. And this being the consciousness of similarity in its simplest form, it results that when, as in ordinary cases, the similarity consists of many component similarities, each of the compared states of consciousness contains many relations that are severally connatural and cointense with the corresponding relations in the other.
Respecting dissimilarity it needs only to be said that—neglecting all those ordinary applications or rather misapplications of the word in which it is used to describe any kind of unlikeness, and confining our attention to dissimilarity proper, as existing between two geometrical figures—it is a consciousness of the non-cointension of two connatural relations between states of consciousness which are themselves like in kind, but commonly unlike in degree.
The relations of similarity and dissimilarity being thus proximately decomposed into certain more general relations, the further analysis of them is involved in the analysis of these more general relations: to which let us now proceed.
THE RELATIONS OF COINTENSION AND NON-COINTENSION.
§ 85. Keeping to the subjective point of view, and regarding every relation as some state of consciousness holding together other states of consciousness; it is first to be remarked that relations of cointension are of two kinds, according as the states of consciousness between which they subsist are primary or secondary—are simple states, or the relations among simple states. Of these, the kind exemplified in the last chapter, and the kind which we must here first deal with, is that subsisting between states of consciousness which are themselves relations.
Every relation between states of consciousness of necessity implies a change in consciousness. That there may be a relation, there must be two states between which it subsists; and before there can be two states there must be some change of state. On the one hand, there can be no change in the state of consciousness without there resulting two states standing in some relation; and on the other hand, there can be no relation until consciousness undergoes some change of state. These are two sides of the same necessary truth.
Now changes in consciousness differ widely in kind. The mental transition from a flash to an explosion, is totally unlike that from a touch to a burn. Between an impression produced by the colour of a rose and one produced by its odour, there is a contrast wholly different from the contrast between the impressions of hardness and transparency which a crystal gives. Differences of kind among the changes in the states of consciousness—even the undecomposable states—have indeed two orders: each of them extensive. There are the changes experienced when, from a sensation of one class, we pass to a sensation of a totally unrelated class—changes that are various in kind; and there are the changes experienced when, from a sensation of one class, we pass to a sensation of the same class but of another species—changes that are also various in kind; though less widely unlike than the others. To speak more specifically:—We have on the one hand, such extremely different changes as those experienced on passing from a colour to touch, from a taste to a sound, from a burn to a smell, from a sense of pressure to one of cold, from a feeling of roughness to one of dazzling, &c., &c.: and on the other hand, we have the less different changes experienced on passing from one colour to another—as red to green, yellow to blue, pink to grey; or on passing from one taste to another—as bitter to sour, sour to sweet, sweet to bitter; or on passing from one sound to another, or one smell to another. Add to which, that when the transitions, instead of being from sensation to sensation, are from precept to precept, or from concept to concept, there arise other orders of changes still more varied in their kinds.
Not only, however, do changes in consciousness differ widely in kind, but they differ widely in degree. The differences in degree are divisible into two classes—those which subsist when the successive states of consciousness are unlike in nature; and those which subsist when the states of consciousness are like in nature. Thus, when some loose gunpowder is exploded, the transition from the impression of light to that of a faint sound, is not the same as the transition from the impression of light to that of a loud sound, which results when the powder is fired out of a pistol. Nor is the transition from the sensation of touch to that of temperature the same when grasping wood as when grasping iron. And evidently throughout all the various orders of changes above indicated, the like contrasts subsist. Equally multiplied and familiar are those other contrasts, subsisting between changes in consciousness that do not alter the nature of its state, but only the intensity. Thus when, of two doors intervening between his ear and some continuous sound, one is suddenly opened, the change in a listener's consciousness is not so great as when both doors are suddenly opened. Nor, when contemplating in succession two allied shades of bright purple placed side by side, is the change in consciousness so great as on transferring the gaze from either of them to an adjacent shade of lilac. Those changes in consciousness which do not affect the nature of its state, are much more measurable than the others. Two changes of intensity in the same kind of feeling, may be known as like or unlike in degree, far more completely than two changes from one kind of feeling to another. And, indeed, it is doubtful whether these last can be considered measurable at all—whether the change from a light to a sound, being, as it were, total, must not be held as the same in degree with all other changes from light to sound; however much the relative amounts of light or sound may vary. But be this as it may, it is clear that in such cases all minor differences must be dwarfed by the greatness of the contrast; and that consequently no accurate discrimination between the changes can be made.
Now changes in consciousness, which we thus find to be various not only in kind but in degree, are themselves cognizable as states of consciousness: not indeed as simple states; but as states in which the transition between two states is the thing contemplated. That the change, the link uniting the two states, is nothing separate from, and nothing additional to, the states themselves, seems manifest. That consequently, it cannot be thought of without thinking of the states themselves, seems also manifest. And that to be conscious of it, is simply to be conscious of the two states in succession, seems equally manifest. But at the same time it is unquestionable that we have the power of thinking of the change itself, as something more than the two states individually considered. Possibly there may be a physiological reason for this. Certain facts point to the conclusion that the change itself constitutes a fleeting state of feeling, separate from the less fleeting states which it links together. Every one knows that a violent change in the sensations is accompanied by a species of shock. Even though expecting it, a bright flash of light will cause the eyes to wink; and yet light of the same brilliancy, if continuous, can be steadily looked at without difficulty. The sudden application of cold water to the skin produces a start, notwithstanding a previous determination to bear it unmoved; and yet the sensation of cold, when once established, can be borne with equanimity. Nay, extremely marked transitions among the ideas will occasionally produce an analogous effect. Probably many can call to mind cases in which, from the sudden remembrance that something important had been forgotten, or from the reception of unexpected good news, a sensible shock was experienced. And indeed the serious injuries sometimes resulting from violent changes of mental state, sufficiently imply that such changes must be accompanied by a decided feeling. Whence it may be inferred, that as the violence of changes in the state of consciousness is altogether a thing of degree, all such changes are accompanied by some feeling however slight.
But whether a change in consciousness be or be not knowable as something more than the juxtaposition of a preceding and a succeeding state, it is undeniable that we can so think of changes in consciousness as to distinguish their various kinds and degrees. In whatever way I cognize the transition from a sensation of touch to one of sound, it is beyond question that I can think of it as unlike in kind to the transition from a sensation of touch to one of cold. Whether, in thinking of a change, I think of the two successive states, or of the contrast between them, it remains alike true, that in passing from an impression of the brightest green to one of bright green, and from one of bright green to one of pale green, I am conscious of two changes which are the same in kind but different in degree. And to say that I am conscious of these changes as such or such, is to say that they are states of my consciousness.
Thus then, having the ability to think, not only of the original simple states of consciousness, but also of the changes among them—being conscious, of differences in kind and degree, not only between successive sensations, but also between successive changes in sensations—it results that these changes are classifiable as the original sensations are. As two sensations can be known as like or unlike in kind; so can two changes among them be known as like or unlike in kind: and as two sensations that are like in kind can be known as like or unlike in intensity; so can two changes among them that are like in kind, be known as like or unlike in intensity. We can recognize changes as connatural; or the reverse: and connatural changes we can recognize as cointense; or the reverse.
But, as above pointed out, these that we have been treating of as changes in consciousness, are nothing else than what we call relations. There can be no phenomena of consciousness beyond its successive states, and the modes of succession of its states—the states themselves, and the changes from one state to another. And seeing that what we are conscious of as relations, are not the primitive states themselves, they can be nothing else than the changes from state to state. The two answer in all respects. We can think neither of a change nor of a relation, without thinking of the two terms forming its antecedent and consequent. As we cannot think a relation without a change in consciousness from one of its terms to the other; so we cannot think a change without establishing a relation between a preceding phenomenon and a succeeding one. Though some of them are eventually so transformed as to appear of another nature, yet, primarily, all that we class as different orders of relations, are nothing but different kinds and complications of changes among the states of consciousness.
In subsequent chapters sundry developments of this doctrine will be found. Here, we have merely to observe its bearing on the inquiry before us. Relations, subjectively considered, being nothing but changes in the state of consciousness, it follows that the cointension of relations is the cointension of such changes; or in other words—likeness in degree between changes like in kind.
§ 86. After what has been said, not much need be added respecting the simpler species of the relation of cointension: that, namely, of which the terms are not relations among states of consciousness, but the primary states of consciousness themselves. This is of course definable as—likeness in degree between sensations like in kind.
Nor, respecting the relation of non-cointension is it requisite to say more than that it is unlikeness in degree between either changes like in kind or sensations like in kind.
The only further remark that may here fitly be made, is one concerning the use of the words cointension and non-cointension to denote these orders of relationship. All our ideas of intensity, when traced to their origin, manifestly refer to the degrees of our sensations. Intensity is a word that connotes some species of force—a force that is violent, vehement, severe, keen, ardent; and all our ideas of force ultimately refer to sensations. We speak of intense heat and cold, intense pressure, intense pleasure and pain, intense passion, intense bitterness and sourness, intense irritation, restlessness, itching: in all of which cases we speak of feelings in respect to their degree. Hence then, in comparing simple states of consciousness that are alike in kind, we observe their relative intensities. If their intensities are equal, they must be called cointense: and the equality of their intensities is cointension. Add to which, that as the changes in consciousness are also different in respect of their violence, and are seemingly accompanied by some species of sensation, they also are comparable in respect to their intensity: whence it follows that cointension is predicable of such changes, that is relations, when they are alike in kind and degree.
THE RELATIONS OF COEXTENSION AND NON-COEXTENSION.
§ 87. As was shown when treating of Space and of the statical attributes of Body, all modes of extension are resolvable into relations of coexistent positions. Space is known to us as an infinitude of coexistent positions that do not resist: Body as a congeries of coexistent positions that do resist. The simplest extension therefore, as that of a line, must be regarded as a certain series of coexistent positions; equal lines, as equal series of coexistent positions; and coextension, as the equality of separate series of coexistent positions—that is, the sameness in the number of coexistent positions they include.
It was explained at considerable length, that a series of coexistent positions is known to the adult mind, through the simultaneous excitation of some series of independent sensitive agents distributed over the surface of the body: either those extremely minute and closely packed ones of which the retina consists, or those more sparingly dispersed and less individualized ones supplied to the skin. And it was also explained, that the simultaneous excitation of any series of such agents becomes known as the equivalent of their serial excitation; or rather—is a transformation of a series of states of consciousness known as having successive positions, into a quasi single state of consciousness in which these component states are presented in synchronous positions, or coexistent positions: and that these coexistent positions can become known as such, only through the previous establishment of the serial positions to which they correspond—only though those serial excitations of consciousness that result from the motion of images over the retina and objects over the skin. Whence it follows that while, eventually, extension is known in a quasi single state of consciousness produced by the synchronous excitation of a number of independent nerves, either tactual or visual; it is originally known through a series of states produced by the successive excitation of such nerves. Add to which that these synchronous excitations being simply the equivalents and symbols of the successive ones, on which they are based, and to which they are always reducible, the successive ones are those in which all phenomena of extension, subjectively considered, must ultimately be expressed.
Reduced to its lowest terms then, extension is knowable as some series of states of consciousness. But what series? Consciousness is ever passing through a series of states; but is not ever occupied about extension. In the first place then, the series is to be distinguished as more or less homogeneous. The successive states of which it consists must not be of many kinds, but of one kind—must be connatural. But this is not enough; for there are various successions of connatural states—as those produced by heat, odour, or continuous sound—which are not constituents in the idea of extension. Hence then, extension, as originally known, must be some series of connatural states of consciousness of a special order; and as before shown (§ 71) it must, in its primary form, be that order of states produced by the united sensations of motion and touch. Two equal extensions then, are originally known to us as two equal series of sensations of motion and touch. And coextension, when reduced to its lowest terms, means—equality in the lengths of such series; that is—equality in the numbers of the states they severally include.
Two objections to this definition should be noticed. It may be remarked, with apparent truth, that it is a misuse of language to call that which we feel when drawing a finger over the skin, a series of states of consciousness; seeing that the sensations of motion and touch are continuous—are not divided into successive sensations. But saying nothing of the fact that the nerves that are one after another excited by the moving finger are really independent, and must therefore be supposed actually to send successive feelings to the sensorium; it will suffice to reply, that though, in cases of this kind, the state of consciousness is apt to seem unbroken and homogeneous, it is in fact, marked out into a great number of separate portions. For it must be remembered that the very condition on which only consciousness exists, is, perpetual change. If, while a continuous sensation like the one in question were being received, consciousness could be solely occupied with it, there would—if the hibernicism may pass—be no consciousness.∗ A little consideration will show, that during one of these seemingly homogeneous states of consciousness, produced by a persistent sensation, the attention is transitorily occupied with various other things—with surrounding objects, with sounds, with the idea of self, &c. &c.—none of which are wholly absent from the mind. Whence it is clear that what we are liable to take for an unbroken state of consciousness, is really a state broken by numerous incidental states—by fleeting thoughts, which, passing through it, serve to divide it out into portions, and reduce it to a series of states. The second objection is, that coextension, as ordinarily determined by the juxtaposition of the coextensive objects, involves no comparison between two series of states of consciousness; but merely an observation that the ends of the objects coincide: and this is true. But it is clear that this mode of ascertaining coextension is nothing but an artifice, based upon the experience that extensions separately known to us through the equal series of states they produce, always manifest this coincidence of their ends when placed side by side. And as we are here dealing, not with the artificial test of coextension, but with the notion of coextension as it naturally arises, the objection is invalid: more especially as we have thus far considered, not the developed consciousness of coextension, but that primary consciousness out of which it is developed.
§ 88. After what has been said, the nature of our developed consciousness of coextension will readily be understood. The successive impressions through which extension is originally presented, having, by a process repeatedly described, been transformed into synchronous impressions—the whole chain of connatural states, at first known in their serial positions, having become known in their coexistent positions; it follows that the consolidated states of consciousness thus resulting, can be compared, and their likeness or unlikeness recognized, just as the chains of states to which they are equivalent can: or rather, they can be known as like or unlike, because the chains to which they are equivalent are known as like or unlike. When two equal lines cast their images upon the retina, the range of sensitive elements excited by each, having been primarily known as a series of states of consciousness; and the two series having been known as equal series; the equality manifestly becomes as predicable of the consolidated states as it was of the serial states. Each of these consolidated states is produced by the simultaneous stimulation of a certain number of independent nerves of a particular kind; and, physiologically considered, that likeness in the two states which constitutes the intuition in question, results from a likeness in the number and combination of the independent nerves simultaneously affected.
As implied by much that has gone before, it is this simultaneity in the excitation of independent nerves, which gives the notion of coexistence, underlying that of extension, and therefore that of coextension. Though, as will presently be shown, the relation of coexistence is not originally disclosed to consciousness by this simultaneity of excitation; but can only be so disclosed after experience has proved the independence of the simultaneously excited nerves; yet, it is only when it has come to be thus disclosed, that extension and coextension, as we comprehend them, can be conceived: seeing that extension implies coexistence in the parts of the thing extended; and, conversely, coexistence implies a duality which is impossible without space. Extension, therefore, as known by the developed mind, being made up of many elementary consciousnesses of coexistence; the relation of coextension cannot be exhaustively analyzed without analyzing the relation of coexistence. But in so far as the nature of our consciousness of coexistence has been incidentally explained, the relation of coextension, as subjectively considered, may be understood—may be defined as the likeness of two composite states of consciousness, visual or tactual, in respect of the number and order of the elementary relations of coexistence which they severally include: such composite states of consciousness being severally produced by the consolidation of what were originally known as serial states.
To which, for form's sake, it may be added, that the relation of non-coextension is definable as the unlikeness of such two composite states of consciousness.
THE RELATIONS OF COEXISTENCE AND NON-COEXISTENCE.
§ 89. It is tolerably evident, even à priori, that, simple as it seems, the relation of coexistence is in reality compound. Though, in the adult mind, apparently undecomposable, yet it is a corollary from very obvious truths, that this relation is originally synthetic. For as coexistence implies two things; as, further, the two things which coexist, cannot occupy consciousness at the same instant; and as they cannot pass through consciousness in simple succession—seeing that they would then be known as sequent and not coexistent—it follows that coexistence can be disclosed only by some duplex act of thought. It is true that the two terms of a relation of coexistence—as the ends of a line at which we look, or the opposite sides of a stick which we grasp—ordinarily appear to be known, not in two states of consciousness, but in one. But it needs only to call to mind the extremely complex process by which our perceptions of objects are built up; and to remember that what in the infant is an elaborate synthesis, afterwards becomes an instantaneous and, as it would seem, direct cognition; to see that no apparent simultaneity in the consciousness of the two things between which there is a relation of coexistence, can be taken as disproving their original seriality. Leaving general considerations however, let us look at the matter more nearly.
If the eyes be directed to two small dots placed close together upon a sheet of paper, the facts that there are two, that they coexist, and that there is a certain space between them, certainly appear to be given in the same immediate intuition: and it seems a scarcely credible proposition that by a nascent intelligence they can neither be known as two, nor as coexistent, nor as having relative positions. But on re-reading § 58 it will, I think, become clear that at first, any two such dots can produce nothing but an indefinite visual sensation, as simple as one of sound or smell. For as was shown, the possibility of distinguishing the image upon the retina as consisting of not one impression, but of two, implies in the first place, that the retina consists of parts capable of being separately excited; seeing that were it but the expansion of one nerve, the stimulation of any part would produce the same effect upon consciousness, while the stimulation of two or more parts could do nothing but increase the intensity of the sensation. And it implies in the second place, that the separate stimulations of these separate parts are distinguishable from one another by consciousness; seeing that did they all produce one effect on consciousness, the result would be the same as though they were one. But before the separate stimulations of these separate parts can be distinguished from one another by consciousness, there must be some experiences. For the two parts of the retina simultaneously affected by the images of two points, to be known as yielding two sensations and not one sensation, implies a knowledge of the parts as separate; and to suppose that this can exist anterior to experience is absurd. Or to state the case more conclusively:—Coexistence being unthinkable without a space in which the things may coexist, it follows that the two points described, cannot be known as coexistent without being also known as out of each other—as at some distance from each other. But, as before explained, to suppose that when two sentient points on the surface of the organism are first simultaneously stimulated, some particular distance is thereby suggested, is to fall into the absurdity of supposing that an idea of some particular distance already exists in the mind (§ 58). Evidently then, as by a nascent intelligence, the space between the two coexistent points is incognizable; and as their coexistence cannot be otherwise conceived, it follows that at first they cannot be known as coexistent.
From all which it is an obvious corollary, that the relation of coexistence is disclosed by the same experiences that disclose extension. But now we have to observe concerning these experiences, a fact not before noticed. The repeatedly described consolidation of serial states of consciousness into quasi single states, is not the whole of the process by which the ideas of coexistence and extension are evolved. It is the peculiarity alike of every tactual and visual series which enters into the genesis of these ideas, that not only does it admit of being transformed into a composite state, in which the successive positions become simultaneous positions, but it admits of being reversed. The chain of states of consciousness, A to Z, produced by the motion of a limb, or of something over the skin, or of the eye along the outline of an object, may with equal facility be gone through from Z to A. Unlike those states of consciousness constituting our perception of sequence, which do not admit of an unresisted change in their order, those which constitute our perception of coexistence admit of their order being inverted—occur as readily in one direction as the other. And this is the especial experience by which the relation of coexistence is disclosed. Let us glance at the chief phases of this experience.
Recurring to the adjacent dots, it will be observed on experiment, that though very close and very small, they can never be both perfectly present to consciousness at the same time. The one on which, at any moment, the visual axes converge, is alone perceived with complete distinctness. The other, though, as it would at first seem, very clearly before the mind, cannot be perceived with the highest degree of definiteness until the visual axes converge upon it; and when the gaze is thus transferred, the dot first contemplated ceases to be so definitely perceived. Moreover, if, while the eyes are fixed upon one of the dots, the thoughts are directed to the other, it will be found that in proportion as the other is distinctly thought of, the one to which the eyes are directed tends to lapse out of consciousness. Both which facts go to show, alike that the serial experiences which originally gave the knowledge of coexistent positions, never wholly cease to be used; and that, even under the most favourable circumstances, the two terms of a relation of coexistence are not present to the mind with equal distinctness; but that while the one is clearly before consciousness, the other is nascent in a higher or lower degree. Let us now observe what happens when the dots are further apart. If they are extremely minute, it will be found that even at the distance of an inch apart, the one is invisible when the eyes are directed to the other, and cannot be known as coexistent with it except by a definite transfer of the attention. If they are dots of moderate size, the consciousness of one will be accompanied by some consciousness of the other until they are separated by a space of six or eight inches; beyond which, this nascent consciousness wholly ceases. With still larger objects, there must be a still larger interval—or, more strictly speaking, a still greater subtended angle—to produce the same result. But however large the objects, it will be found that there is a distance at which either ceases to be in any degree presented to the mind, when the eyes are directed to the other. The unregarded object, when gradually removed to the outskirts of the field of view, does not disappear suddenly; but fades into nothingness so gradually that it is impossible to say when the nascent consciousness of it wholly ceases. And as, between those relative positions in which the coexistence of two objects can be known only by a slight turn of the head, and those in which it can be known only by turning the head half round, there is also a series of imperceptible transitions; it follows that the coexistence of two dots lying close together, and that of two objects lying respectively behind and before the observer, are known in modes which, however apparently different, are united by insensible gradations, and must be primordially the same. In both cases, the terms of the relation of coexistence cannot be perfectly present to consciousness at the same moment. In both cases, motion is required to bring that term of the relation of which there is either no consciousness or but imperfect consciousness, distinctly before the mind. And the differences are simply between the degrees of motion, and between the degrees in which the consciousness is nascent.
This being understood, let us consider in what way we can know the coexistence of two things not visible together. When an adult, having just seen some object A, immediately after sees another object B, he usually asserts their coexistence on the strength of this single observation. He is manifestly enabled to do this by an accumulation of previous experiences; from which he has drawn the induction that certain groups of phenomena are persistent. But what does he mean by persistent? He means that the phenomena are of a kind which he can again become conscious of with the same vividness as before. He means that on turning round his head, the object A, will again impress him as it did at first. The entire contents of his assertion that A and B coexist, is, that the states of consciousness which they severally produce in him, can be alternated as often as he pleases. Leaving, however, the coexistence that is known inferentially, we must here concern ourselves with those primordial experiences which first disclose it. By an incipient intelligence, the impressions produced by the two things A and B, seen in succession, cannot be known to differ in their persistence from two sounds heard one after the other. In either case, there is nothing but a sequence of states of consciousness. How then, does the one relation come to be distinguished from the other? Simply by finding that whereas the terms of the second sequence cannot be known in the reverse order with equal vividness, those of the other can. It is perpetually found that while certain states of consciousness follow one another with as much facility and clearness in one direction as in the opposite (A, B—B, A) others do not; and hence results a differentiation of the relation of coexistence from that of sequence. And not only is it that coexistence is originally thus known; but, as just pointed out, it is that, subjectively considered, our whole knowledge of the relation of coexistence consists in recognizing the equal facility with which the terms of the relation will pass through consciousness in either order.
Still more manifest will this become, when it is observed that there are coexistences which even the adult never knows otherwise than through this test. Now that I am writing, I feel in my foot the warmth of the fire; I am further aware of the pressure of my arm upon the desk, and my back against the chair; I see the paper on which I write; and I hear a rumble in the street. I find it quite impossible, however, to think of all these things at the same instant: I cannot unite the heat, the sound, the pressure, and the whiteness, in the same state of consciousness. How then do I know that I am receiving these various impressions at one time? How do I know that the external objects producing them are coexistent? Simply from the fact that I can be successively conscious of these various feelings in any order with equal facility. And could I not do this, I should not know the corresponding phenomena as coexistent.
§ 90. The equal facility with which the terms of a relation of coexistence can be thought of in either order, is evidently knowable by us simply through an internal feeling. That we habitually notice the feelings accompanying changes in consciousness, is proved by the fact that we distinguish them by words. When we speak of a thing as hard to think, or easy to believe, we express by these adverbs the presence or absence of a certain mental tension. In the one case, the antecedent and consequent of the thought can be made to follow only by a great effort; in the other, by little or no effort. When attempting to remember a name we have forgotten; or when forcing ourselves to reflect on some subject to which we are averse, or of which we are tired; or when trying to form an unusually complex conception; we are distinctly conscious of an inward strain. Whence it is clear, that the states of consciousness constituting a thought, may follow one another either with facility or with any degree of difficulty; and that the facility or difficulty of a transition is known to us by its accompanying sensation.
Hence then, when it is said that the relation of coexistence is one of which the terms will follow one another through consciousness in either order with equal facility, the thing asserted is, a likeness or equality of the two feelings which accompany respectively, the change from antecedent to consequent, and the change from consequent to antecedent. Not a likeness or equality of the two feelings produced by the contrasts of the terms; for these must differ according to the order in which the terms are contemplated; but a likeness or equality of the two feelings of resistance—or rather in this case, non-resistance—which occur at the moments of transition.
So that the relation of coexistence is to be defined as a union of two relations of sequence, such that while the terms of the one are exactly like those of the other in kind and degree, and exactly the reverse in their order of succession, they are exactly like them in the feeling which accompanies that succession. Or otherwise, it may be defined as consisting of two changes in consciousness, which, though absolutely opposite in other respects, are perfectly alike in the absence of strain. And of course the relation of non-coexistence differs in this, that though one of the two changes occurs without any feeling of tension, the other does not.
§ 91. It may be worth while just to point out, that these conclusions are indicated even by à priori considerations. For if, on the one hand, the great mass of outward things are statical, are persistent, are not manifesting any active change; and if, on the other hand, perpetual change is the law of the inner world—is the primary condition under which only consciousness can continue; there arises the question—How can the outer statical phenomena, be ever represented by the inner dynamical phenomena? How can the no-changes outside, ever be symbolized by the changes inside? That changes in the non-ego may be expressed by changes in the ego, is comprehensible enough; but how is it possible that objective rest, can be signified by subjective motion? Evidently there is only one possibility. A consciousness ever in a state of change, can represent to itself a no-change, only by an inversion of one of its changes—by a duplication of consciousness equivalent to an arrest—by a regress which undoes a previous progress—by two changes which exactly neutralize each other.
Finally, the reader should be reminded that this analysis of the relation of coexistence, resulting as it does in the conclusion that it is a relation disclosed by experience, supplies the ultimate disproof of the hypothesis that Space is a form of thought; seeing that the cognition of coexistence is the primitive element out of which the cognition of space is built—is the element without which even the germ of that cognition is impossible.
THE RELATIONS OF CONNATURE AND NON-CONNATURE.
§ 92. After what has already been said concerning it (§ 85), but little need here be added respecting the relation of connature. It is of two kinds. In the one kind, the terms between which it subsists are themselves relations, or changes in consciousness: in the other, they are the primitive states of consciousness between which such changes occur. Let us first glance at the more complex of these.
When treating of the relation of cointension, it was pointed out that changes in consciousness are of several classes. There are those in which the antecedent and consequent states are of different orders—as when the transition is from a sound to a smell; those in which they are of the same order, but of different species—as when the transition is from a sound of low pitch to one of high; and those in which they are of the same species, but of different degrees—as when the transition is from a faint sound to a loud one. And these being the different kinds of change between states of consciousness produced by simple sensations, it is manifest that when the states of consciousness become composite, a great multiplicity of kinds of changes arise—changes from greater to less in magnitude, from slow to quick in velocity, from ascent to descent, &c. Hence those various orders of change implied by the negations of the relations already treated of—the changes indicated by the terms dissimilarity, non-cointension, non-coextension, non-coexistence. And hence also those processes of consciousness in virtue of which we class lines with lines, areas with areas, bulks with bulks—all of them distinguished by us as different orders of relations; that is, different orders of changes among the states of consciousness.
Nothing is to be said respecting the connature of relations in its various modes, beyond describing it; for it is clearly a relation that is not decomposable into other relations. That two changes in consciousness are of like kind, is a fact of which we can give no account further than that we perceive it to be so. Simple or complex as the states of consciousness themselves may be, it is manifest that the transition from state to state is in all cases simple; and when two of these transitions produce in us two like feelings, we know nothing more than that we have the like feelings. It is true, as will be shown in a subsequent chapter, that it is possible to say specifically what we mean by asserting the likeness of these feelings. But beyond this it is impossible to go.
As subsisting between relations, therefore, the relation of connature must be defined as—likeness of kind between two changes in consciousness.
§ 93. Respecting the relation of connature as subsisting, not between relations, but between primary states of consciousness—sensations or the representations of them—still less is to be said. What is the nature of the feelings which we have of warmth, of blueness, of pressure, of sweetness, no one can say. They are undecomposable elements of thought with which analysis can do nothing. And when we predicate the connature of any two such sensations—their likeness in kind—we express an intuition of which we can say nothing further than that we have it. Though, as will by and by be seen, the intuition may be otherwise expressed, it cannot be decomposed.
Save to justify the title of the chapter, it is scarcely needful to add, that the relation of non-connature is—unlikeness in kind between either changes in consciousness or the states which they connect.
THE RELATIONS OF LIKENESS AND UNLIKENESS.
§ 94. At length continued analysis has brought us down to the relations underlying not only all preceding relations, but all processes of thought whatever. From the most complex and most abstract inferences of the developed man, down to the most rudimentary intuitions of the infant, all intelligence proceeds by the establishment of relations of likeness and unlikeness. Duly to realize this fact, we must glance at the successive conclusions arrived at in preceding chapters.
In the most perfect kinds of compound quantitative reasoning, we found that each of the several intuitions through which any conclusion is reached, not only involves the relation of likeness under its highest form—that of equality—but involves it in the most various ways. We found that in descending step by step to the lower kinds of reasoning, the intuitions of likeness included in each ratiocinative act, become less numerous and less perfect; but that to the last, likeness of relations is necessarily involved. The classification of objects, we found to imply a perception of the likeness of a new group of relations to a before-known group, joined with more or less unlikeness of the individual attributes; while recognition implies exact likeness, both of the individual attributes and their relations, to those of groups before known. And we further saw that the perception of a special object is impossible save by thinking of it as like some before-known class or individual. The perception of Body, as presenting its three yorders of attributes, we found to imply a classing of the several attributes, their relations to each other, and the conditions under which they are disclosed, with like attributes, relations, and conditions. It was shown that our ideas of Space, Time, and Motion, arise by a discovery of the equivalence of certain states of consciousness, serial and simultaneous; and further, that no particular space, time, or motion can be thought of, without the relation of likeness being involved. More recently, we have seen that the higher orders of relations are severally resolvable into relations of likeness and unlikeness whose terms have certain specialities and complexities. Similarity, was defined as the cointension of two connatural relations between states of consciousness which are themselves like in kind but commonly unlike in degree. Cointension, we found to be, likeness in degree between either changes in consciousness that are like in kind, or states of consciousness that are like in kind. It was shown that coextension is the likeness of two composite states of consciousness, in respect of the number and order of the elementary relations of coexistence which they severally include. Coexistence, was resolved into two sequences whose terms are exactly alike in kind and degree, exactly unlike, or opposite, in their order of succession, and exactly alike in the feeling which accompanies that succession. Connature was defined as likeness in kind between either two changes in consciousness, or two states of consciousness. And each of these relations we found to have its negative, in which unlikeness is the thing predicated.
Seeing thus, that the knowing of successive states and changes of consciousness as like or unlike, is that in which thinking essentially consists, we have next to inquire what is the essential nature of those phenomena in consciousness which we signify by the words likeness and unlikeness. Are the relations of likeness and unlikeness definable? And if so, what are they?
§ 95. Things cannot be truly defined except in terms more general than themselves: and hence, unless there is some relation underlying the relations of likeness and unlikeness, they must be indefinable. Strictly speaking, no such more general relation exists. The only relation yet remaining to be dealt with, is one that is co-ordinate with them—one that lies upon the same plane with them—one that is in fact another side of the same mental phenomena. All that is possible for us, is, to describe likeness and unlikeness in terms of this remaining relation; and to describe this remaining relation, when we come to it, in terms of likeness and unlikeness—to exhibit them as the necessary complements of each other.
This premised, the question above asked will be most readily answered by comparing the relations of likeness and unlikeness together. The essential nature of each will best be shown by contrast with the other. In what then consist the difference between the two mental processes by which these relations are disclosed?
If I cut in two a sheet of coloured paper—say blue—and place the pieces at some distance apart; and if I also place at some distance apart, two other pieces which are of different colours—say red and green; I have in the first pair a relation of likeness, and in the second pair a relation of unlikeness. In what consists the knowledge of each of these relations? On glancing from one of the blue pieces to the other, I am conscious of passing from one state to another state, which is new in so far as it is separate from, and subsequent to, the first, but which is not new in any other respect. On glancing from the red to the green, I am conscious of passing from one state to another state, which is new not only as being subsequent, but which is otherwise new. Suppose now that I place the blue pieces quite close together, joining the two edges that were cut; and that I also place the red and green pieces close together. What happens? The two blue pieces are not now known in two distinct states of consciousness: the two states of consciousness practically merge into one. The red and green pieces however, placed no matter how close, still produce two states when contemplated. Similarly again with odours. A flower when smelt at, produces a certain continuous state of consciousness. If another flower of the same kind be joined with it, and the two are moved about under the nostrils, the successive scents may be made to seem as continuous as the scent of one. But if the flowers are of different kinds, they will, when successively smelt at, produce different states of consciousness. The like is true of sounds. A sustained note from a wind or stringed instrument, may be perfectly homogeneous, or it may be interrupted by some scarcely appreciable flaw, serving nominally to divide it into two notes that are exactly alike. But while, when we listen to such a note, consciousness may with almost equal propriety be considered in one state or two states; when we listen to any musical interval, we very decidedly experience two states. And this antithesis between the relations of likeness and unlikeness, will be yet further elucidated, when it is remarked that not only do the states of consciousness which we call like, lapse insensibly into one state, but that any one state of consciousness having an appreciable continuity, may be conceived as divided out into a series of like states.
From all which it will be sufficiently manifest, that by the words unlike and like, we signify the occurrence or non-occurrence of change in consciousness. Leaving out of sight for a moment that fleeting state of consciousness which marks a transfer of the attention, and which strictly considered is a change, we may say that by unlikeness and likeness we mean respectively, change and no change in consciousness. The two terms of a relation of unlikeness, are two states of consciousness forming the antecedent and consequent of a change in consciousness: the two terms of a relation of likeness, are the antecedent and consequent of what, in one sense, is no change; seeing that it leaves consciousness in the same condition as before.
As implied however, this is but an approximate statement—an adumbration, which, if interpreted strictly, describes an impossibility. For, as the relation of likeness implies two terms, two states of consciousness; and as two states of consciousness, if not themselves different, cannot exist as separate states unless they are divided from each other by some state that is different; it follows that a relation of likeness implies a change, or rather changes, in consciousness. Accurately speaking, therefore, a relation of likeness consists of two relations of unlikeness which neutralize each other. It is a change from some state A to another state B (which represents the feeling we have while passing from one of the like things to the other), and a change from the state B to a second state A; which second state A would be indistinguishable from the first state were it not divided from it by the state B, and which merges into such first state when the state B disappears, from the approximation of the two like stimuli in space or time.
Very many relations of unlikeness similarly consist of two relations of unlikeness, which, however, do not neutralize each other. In all cases where the two terms of the relation do not follow through consciousness in juxtaposition—as when the unlike things looked at are some distance apart, or when between unlike sounds or odours a brief interval of time elapses—there are three states of consciousness involved; the original state A, the transition state B, and that state of which we predicate unlikeness, C. But the primordial relation of unlikeness is one consisting of two states only. When two notes differing in pitch, strike the ear in rapid succession, so as to leave no time for any intervening thought or sensation—when a flash of lightning for a moment dispels the darkness—when any one state of consciousness is supplanted by another state, there is established a relation of unlikeness.
Thus, then, the relation of unlikeness is the primordial one—is the relation involved in every other relation; and can itself be described in no other way than as a change in consciousness.
THE RELATION OF SEQUENCE.
§ 96. As was said in the last chapter, this remaining relation is but another side of the fundamental one there treated of. Sequence is change; and change, as known by us, is the unlikeness of a present state of consciousness to a past state. While on the one hand, the two terms of a relation of unlikeness cannot be known without a change in consciousness; on the other hand, there can be no change in consciousness without there being two states standing in a relation of unlikeness. The fundamental, the undecomposable relation must have two terms—two adjacent states of consciousness. If these are thought of in themselves, they must be thought of as unlike; otherwise they will constitute not two states but one. If they are thought of as states of consciousness, they must be thought of as constituting a sequence; seeing that consciousness cannot be in two states at one time. The ultimate relation, therefore, is nothing more than a change in the state of consciousness: and we call it either a relation of unlikeness or a relation of sequence, according as we think of the contrast between the antecedent and consequent states, or of their order.
Beyond thus describing each aspect of this relation in terms of the other, no account can be given of it. Like every primordial experience—like the sensation of redness or that of warmth, it transcends analysis. All that can be done is to divide the relations of sequence into their respective classes; and to inquire in what manner these are distinguished from one another in consciousness. To do this completely, is by no means easy; and would moreover occupy more space than can here be afforded. It must suffice to describe the leading distinctions, so far as is requisite to show their harmony with the general results of the analysis.
§ 97. It is tolerably manifest that these distinctions cannot be originally given in the consciousness of the sequences themselves. By a nascent intelligence, the relation between two sensations that severally answer to some external cause and effect, cannot be known as different in nature from that between two sensations that follow one another fortuitously. In so far as its incipient experience is concerned, there is no difference. The two relations are two changes in consciousness, and nothing more. If then, some changes, some sequences, are afterwards found to be of a different quality from others, it must be in virtue of a collateral property additional to the succession itself—a collateral property disclosed by further experience. What is that property?
The comparison of a few cases will indicate the answer to this question. After hearing in immediate succession two notes of different pitch, not the least difficulty is found in making those notes—or rather, the ideas of them—pass through consciousness in the reverse order. After an ascending fifth has been struck upon the piano, it is easy so to represent the sounds to the mind as to make a descending fifth. That is to say, the two states of consciousness produced may readily be re-thought in inverted sequence. Not that the two states thus voluntarily changed in their order, are entirely like the original states. Though they are like in nature, they are widely unlike in intensity. While the original states, which we know as two sensations of sound, are vivid, the two ideas which we find may be reversed in succession, are but very faint repetitions of them. And this it is which distinguishes one of these reversable sequences from a coexistence. If the successive states of consciousness A, B, will occur in the opposite order B, A, without any diminution of vividness, the relation between them is that which we know as coexistence. But if the states A, B, when they occur in opposite order, do so only as the weak states B, A, the relation between them is that of reversable sequence. Thus much to prevent misapprehension. What it now concerns us to observe, is, that there are sequences whose terms having been presented to consciousness in one order, admit of being represented to consciousness in the opposite order with great facility. Not that they occur in this opposite order with as much facility as in the original order. Two impressions that were experienced in a certain succession, tend, when recalled, to pass through consciousness in a like succession; and it is in virtue of their tendency to do this, that we know them to have occurred in that succession; or rather, it is their recurrence in this succession which constitutes our knowledge of their original succession. But though, when uninterfered with by the will, the represented impressions follow one another in an order like that in which the presented ones followed; yet, in cases such as the one instanced, the slightest effort of volition suffices to reverse the order—an effort so slight as to be unaccompanied by any sense of tension. That some effort is required, is to be inferred from the fact that while the represented impressions involuntarily follow one another in the original order, they do not follow in the opposite one, unless voluntarily. But this is the sole appreciable distinction. Thus, then, we find that there is a certain order of sequences which have the peculiarity, that they may be represented to consciousness in reverse order with but a nominal effort. And these are the sequences which, objectively considered, we class as accidental.
But if, instead of two phenomena that have occurred in a merely fortuitous succession, or in a succession whose genesis is so complex as to seem fortuitous to us, we take two phenomena which occur in a certain order with considerable regularity, and examine the relation subsisting between the states of consciousness severally answering to them, we shall find it to be of a somewhat different quality. Take, for example, the shouting to any one, and the turning of his head. Frequently as these two phenomena have been known to us in this order, the occurrence of the one almost inevitably suggests the other. If the first be presented to consciousness, it is only by an effort that the other can be prevented from following it. Moreover, the impressions have no tendency to pass through consciousness in the opposite order. The turning of another person's head, does not make us think of a shout. Nevertheless, there is little or no difficulty in reversing the order of these states. The thought of a person turning his head, may be instantly followed in consciousness by the thought of a shout. Sequences of this kind then, are distinguished by the peculiarity that though, when the antecedent is presented or represented in consciousness, a representation of the consequent cannot without difficulty be prevented from rising; yet these two states can readily have their order of succession changed. And this is the character of the sequences which, objectively considered, we class as probable.
When, however, we pass from non-necessary sequences to necessary sequences, we not only find that the states of consciousness are so connected that when the antecedent is presented, it is next to impossible, if not impossible, to prevent the consequent following it; but we find that the antecedent and consequent do not admit of transposition. As an illustration of the first peculiarity, may be taken our inability to think of a heavy weight as breaking the string by which it is suspended, without thinking of the weight as falling. And the last peculiarity is illustrated in the fact, that the relation between a blow and an antecedent motion, cannot be represented to the mind in the reverse order.
§ 98. Thus then, the relation of sequence, considered subjectively as simply a change in consciousness, is of three general kinds. The fortuitous, in which the two terms are as nearly as may be alike in their tendency, or want of tendency, subsequently to suggest each other; and in which the change may be reversed in thought, with a feeling of non-resistance like that with which it originally occurred. The probable, in which the terms are unlike in their tendency to suggest each other; but in which the usual order of the terms may readily be inverted. And the necessary, in which the antecedent being presented or represented to consciousness, the consequent cannot be prevented from following; and in which the direction of the change cannot be changed.
This statement, imperfect as it is, and requiring though it does much to be said in explanation of difficulties that may be suggested, will serve to show, what it here chiefly concerns us to note, that the classification of sequences is itself effected through other sequences. The classification, depending as it does upon the different modes in which the sequences comport themselves when tested, involves, in the outset, the ideas of like and unlike; while the process of testing them, is itself an observing of the degrees of likeness or unlikeness between certain feelings which they severally yield under experiment. And as the relations of likeness and unlikeness are the one a double, and the other a single sequence, it results that the classing of sequences implies the making them the terms of secondary sequences. As all the relations are finally reducible to one, which is nothing else than a change in consciousness, it follows, even à priori, that all relations among the changes in consciousness must themselves be other changes.
CONSCIOUSNESS IN GENERAL.
§ 99. Thus we have arrived at the result that consciousness consists of changes combined in special ways. Successive decompositions of the more complex phenomena of intelligence into simpler ones, and these again into still simpler ones, have at length brought us down to the simplest; which we find to be nothing else than a change in the state of consciousness. This is the ultimate element out of which alone are built the most involved cognitions. Difficult as it seems to realize the fact, yet analysis leaves us no alternative but to hold that the perception of a vast landscape consists in a multitude of co-ordinated changes; and that of co-ordinated changes also, consists the most abstract conception of the philosopher.
This result, reached by taking to pieces our cognitions, is, indeed, the one indicated by à priori considerations. To be conscious is to think; to think is to form conceptions—to put together impressions and ideas; and to do this, is to be the subject of internal changes. It is admitted on all hands that without change, consciousness is impossible. A uniform state of consciousness is in reality no consciousness. When the changes in consciousness cease, consciousness ceases. If then, incessant change is the very condition on which only consciousness can continue, it would seem necessarily to follow that the various phenomena of consciousness are all resolvable into changes; that changes are the constituent elements of every thought; that every intuition, every conception, every conclusion, is made up of changes arranged in a particular manner, and is decomposable into changes. So that even from a general view of the facts, may be prophesied the issue to which a detailed analysis has led us.
Still more clearly may this same issue be foreseen, when it is remembered that we cannot become conscious save through the changes produced in us by surrounding things. Here is an organism placed in the midst of objects. If it is totally uninfluenced by them, it can know nothing of them, think nothing of them. The only way in which it can be rendered cognizant of their existence, is by the effects they produce on it—the changes they work in it; and then it can proximately know nothing but these changes. Only through changes can it be made conscious of objects; and only out of changes can be constructed its knowledge of them.
However we regard the facts, therefore, we see that they confirm the conclusion come to, that the primordial element of all intelligence is simply a change; and that every complex mental phenomenon is a co-ordinated group of changes. But a complete realization of this truth will best be gained by arranging synthetically a few of the results lately reached by analysis. By contemplating in their order of genesis, a few of the primitive cognitions treated of in recent chapters, both the particular conclusions there reached, and the general conclusion based upon them, will be clearly understood.
§ 100. As already sufficiently explained, a continuous or homogeneous state of consciousness is an impossibility—is a no-consciousness. A being that is totally quiescent, that is undergoing absolutely no change, is dead: and a consciousness that has become stationary is a consciousness that has ceased. To constitute a consciousness, however, incessant change is not the sole thing needed. That sentient something whose affections we call consciousness, may readily be conceived as the subject of perpetual and infinitely varied changes, without anything like consciousness, in our sense of the word, being evolved. If the changes are altogether at random—if sensations of different kinds and intensities succeed one another in entire disorder; no consciousness, properly so called, can exist. Consciousness is not simply a succession of changes, but an orderly succession of changes—a succession of changes combined and arranged in special ways. The changes form the raw material of consciousness; and the development of consciousness is the organization of them. This premised, let us consider under what conditions consciousness becomes nascent.
The lowest form of consciousness that can be conceived, is that resulting from the alternation of two states. While some state A, of the sentient subject, persists, there is no consciousness. While some other state B, persists, there is no consciousness. But when there is a change from state A to state B, or from state B to state A, the change itself constitutes a phenomenon in consciousness, that is—a consciousness. Not that such a consciousness is one which we can in any sense realize to ourselves; or one which would in ordinary language be termed consciousness. We must regard it simply as the first step towards the evolution of a consciousness, properly so called—a step such as we may imagine to have been taken in the lowest animals that manifest sensibility. But now let us inquire what is given in this first step. By the hypothesis, the second state B differs from the first state A—constitutes a second state only in virtue of being different; that is to say, A and B are unlike. Not that there can yet, or for a long time to come, exist any cognition of them as unlike. Such a cognition implies a complicated mental act, that becomes possible only after a considerable development. All which it now concerns us to note, is, that this first phenomenon is one of the experiences out of which are ultimately elaborated the ideas of change, of sequence, of unlikeness. Suppose now that there occurs the change B to A. Here are the materials for a second relation of sequence—a second relation of unlikeness. But this is not all. There has now arisen a second state A, like the first state A. Data have been presented, which, in an advanced consciousness, would constitute a relation of likeness. At present, however, even supposing a latent capacity for thinking such a relation, it cannot be thought, from lack of experiences to class it with. Let there now occur another change, A to B. This constitutes a second relation of unlikeness, of the same nature as the one first established—a change or relation like the before-experienced relation. There are now given the materials which, did there exist a power of co-ordinating them, might compose a thought. There have arisen two relations of likeness between primitive states of consciousness, or sensations—between A and A, and between B and B; and also a relation of likeness between two changes—between two relations of unlikeness. By a practised consciousness, this second change or relation would be thinkable as like the first—might be classified with it, or assimilated to it. Let another change B to A arise. A further relation of unlikeness becomes known as like a foregoing one. And by a perpetual repetition of these changes A—B, B—A, the two states and their two relations tend to become more and more cognizable. Thus, even in a consciousness of the lowest imaginable type, there are foreshadowed the relation of sequence, the relation of unlikeness among the sensations, the relation of likeness among the sensations, the relation of unlikeness among the changes, and the relation of likeness among the changes. The earliest possible experiences are those supplying the raw material from which these cognitions are developed.
Suppose now that a third species of state, C—a third order of sensation, is joined to the others. Further relations of likeness and unlikeness between states and between changes, are the consequence. But it is not simply that there can occur a greater variety of phenomena of the same kind: new kinds of phenomena become possible. The two states A, B, we have assumed to alternate with equal facility in each direction A—B, B—A. If however the new state C, frequently follows B, but never precedes it; there results an experience of two orders of change, which become known by mutual contrast: the duplex change A—B, B—A, answering to the relation of co-existence; and the single change B—C, answering to the relation of sequence proper. Moreover, instead of there being, as at first, no possibility beyond that of perpetual alternation between two states, the introduction of a third state not only renders several combinations possible, but it becomes possible for some particular combination to be established as one of more frequent recurrence than the others; and the recurrence of such particular combination, B—A—C for example, supplies the material for a relation of likeness, not between one single change in consciousness and previous changes, but between a group of changes and previous groups. And yet further, the more varied experiences that now arise of the relations of likeness and unlikeness, which subsist between several kinds of primitive states, several kinds of single changes, and several kinds of compound changes, afford data for the consciousness of likeness and unlikeness in general, apart from the particular terms between which they were first established.
Supposing this introduction of new sensations, new changes, and new combinations among them, to be carried on, step by step; let us mark what must result from that universal law of all mental changes, that the more frequently they have occurred in a certain order, the more easily and rapidly do they follow one another in that order. In proportion as the specially-combined changesD—B—A—C, have been repeated, in the same proportion does the time occupied in the transition from the first to the last become abbreviated; and ultimately, the result is, that this succession of changes takes little or no more time than one of the constituent changes originally did. One consequence of this is, that these compound changes tend to become more and more clearly thinkable as single phenomena in consciousness—more and more readily classable with the like previous phenomena, and distinguishable from others. But now observe further, the important fact, that in proportion as a chain of such changes is consolidated into a single change, in the same proportion do the several sensations which form the antecedents and consequentsof the changes, become present to consciousness together. When the compound change D—B—A—C, takes place, as it ultimately does, almost instantaneously, it results that before the first sensation or idea D, has ceased, the others B, A, C, have severally arisen. Hence there is produced a consolidated consciousness, in which many sensations appear to be simultaneously presented—a consolidated consciousness which answers to some outward object that habitually gives this group of sensations. And we have but to conceive an endless progress in this consolidation of changes, to comprehend how there can arise the consciousness of complex things—how the objects with which human intelligence deals become thinkable as like and unlike—how the highest acts of perception and reason become possible.
§ 101. Of course the actual genesis of intelligence is incomparably more complex than it is here represented to be. This description is intended simply to shadow forth the nature of the process—to exhibit the fundamental principles of it. The successive complications above suggested in rapid succession, cannot in reality arise save by insensible degrees. Each order of experiences must be organized by long-continued habit, before any higher order can be dealt with. Each constantly-united group of states of consciousness, must be more or less completely fused into one state, before any further complexity can be reached by the combination of such groups. In respect of its progress, this organization of experiences must conform to the laws of organization in general; and must therefore be extremely slow.
Taking the above description, however, simply as exhibiting the method of the process in its most general outlines, it will serve to show that at the very outset, in the very first phenomena of a nascent consciousness, there are involved the materials of those fundamental relations to which analysis has, from the very beginning, pointed. It will serve to make more comprehensible, how, out of change, kind of change, degree of change, facility of change, arrangement of change, &c., the infinitely varied states of consciousness may be elaborated. And it will serve to suggest how, by the ever-progressing consolidation of changes—the running together of larger and larger groups and series of them—there can arise, out of a linear succession of internal phenomena, the means of representing those extremely complicated phenomena of coexistence which constitute the external world.
§ 102. Among the general truths to be gathered from the foregoing chapters, considered in their ensemble, one of the most significant, is, that there exists a unity of composition throughout all the phenomena of intelligence. We saw at the outset, that the most complex processes of reasoning are resolvable into intuitions of likeness and unlikeness between terms more or less involved. We saw that under various modes, forms, complications and degrees of perfection, these intuitions are traceable not only throughout every species of reasoning, but throughout every species of perception; forming in all cases the general substance of the cognition, whatever its particular modifications. And we have recently seen, both analytically and synthetically, that these intuitions are foreshadowed in the very first steps of an incipient consciousness—that the very earliest and simplest experiences are those which furnish the raw material of these intuitions.
Standing even alone, this consistency in its particular results and their subordination to one general result, supply strong confirmation of the analysis; both as a whole, and in its several parts. But it will be seen to supply yet stronger confirmation, if we reflect that it is inferable, even à priori, that analysis must disclose some such universal law. For if there are, as there must be, certain conditions under which alone consciousness can exist, those conditions must be common to all forms, modes, and degrees of consciousness. They must be disclosed along with the initial phenomena of consciousness; and must underlie each of the more complex phenomena built out of these initial phenomena. In other words:—there must be some form of thought, exhibited alike in the very lowest and the very highest manifestations of intelligence—a form which must therefore be traceable in a nascent consciousness. Hence, when we find, as we do, that simultaneously with the first changes by which consciousness begins, there are of necessity given, data for the relations of likeness and unlikeness—that these relations form but another side of the very changes which constitute consciousness; we may conclude that these relations must be the foundation of our entire intelligence. And this being the conclusion reached at every successive stage of an analysis pursued quite independently of any such à priori consideration, there cannot be a doubt that the conclusion is correct.
The various divisions, therefore, which we ordinarily make among our mental operations, and which psychologists have mostly sought to explain and establish, as marking out distinct faculties, have merely a superficial truth. They are to be understood as indicating modifications of detail which distinguish phenomena that are essentially similar—modifications which do but mask that fundamental unity of composition possessed by all cognitions whatever.
§ 103. Contemplating the facts from another point of view, we may see that not only the form of thought, but the process of thought, is the same throughout. Not only is it that the mode in which the elements of a compound quantitative argument are dealt with by the mind, is essentially similar to the mode in which the elements of every other human thought are dealt with; but it is, that the impressions received by inferior intelligences, even down to the very lowest, are dealt with after a like fashion.
We saw that all reasoning is definable as the classification of relations. We saw that the perception of an object, is possible only by the classing of a present group of attributes and relations with a past group. We saw that the constituents of any complex perception, must be severally classed with previously known constituents of the same order, before the perception in its totality can arise. And we saw that not even the simplest attribute or relation can be known, until there exist others with which it can be ranged; seeing that the knowing it, is the thinking of it as one with certain others—the classing it with those others. Nay, the relation of unlikeness itself, is cognizable only as like previously experienced relations of unlikeness—is incognizable unless there exist other relations with which it may be classed. But as above hinted, this law applies not to human thought alone: it applies to all processes of intelligence whatever; using the word in its most extended sense. The life of the lowest sentient being is made possible only by an organic classification of impressions. The condition on which every creature exists, is, that it shall act in special ways under special stimuli—that contact with nutritive matter shall modify its actions in a manner different from that in which contact with innutritive matter modifies them—that one impression shall lead it to attack, another to hide, and so on. Manifestly, if there is an entire absence of adaptation between its acts and surrounding circumstances, it must quickly cease to live. And if it exhibits any adaptation, it can do so only in virtue of the fact, that certain impressions made upon it call forth one kind of action, while others call forth another kind. There must exist in the organism some means whereby these impressions are distinguished as such or such, or are classified—some organic registry of external differences and similarities. Not, of course, that there is any consciousness of external differences and similarities; but that there is, in the organism, an innate capability of acting thus, or thus, according to the nature of the stimulus; and that in so far, the organism has a power of appreciating differences and similarities—a power of automatic classification.
Hence it becomes clear that the law is the same throughout. When regarded under its fundamental aspect, not only is the highest reasoning seen to be one with all the lower forms of human thought; but it is seen to come under the same generalization with instinct and reflex action, even in their simplest manifestations. The universal process of intelligence is the assimilation of impressions. And the differences displayed in the ascending grades of intelligence are consequent solely upon the increasing complexity of the impressions assimilated.
§ 104. A yet further change in our stand-point, will introduce us to a still more complete view of mental phenomena—will in fact disclose an exhaustive definition of them, whether considered separately or in their totality.
We have seen that the condition on which only consciousness can begin to exist, is the occurrence of a change of state; and that this change of state necessarily generates the terms of a relation of unlikeness. We have seen that not simply does consciousness become nascent only by virtue of a change—by the occurrence of a state unlike the previous state; but that consciousness can continue only so long as changes continue—only so long as relations of unlikeness are being established. Hence then, consciousness can neither arise nor be maintained without the occurrence of differences in its state. It must be ever passing from some one state into a different state. In other words—there must be a continuous differentiation of its states.
But we have also seen that the states of consciousness successively arising, can become elements of thought, only by being known as like certain before-experienced states. If no note be taken of the different states as they occur—if they pass through consciousness simply as images pass over a mirror; there can be no intelligence, however long the process be continued. Intelligence can arise only by the organization, by the arrangement, by the classification of these states. If they are severally taken note of, it can only be as more or less like certain previous ones. They are thinkable only as such or such; that is, as like such or such before-experienced states. The act of knowing them is impossible except by classing them with others of the same nature—assimilating them to those others. Hence then, in being known, each state must become one with certain previous states—must be integrated with those previous states. Each successive act of knowing must be an act of integrating. That is to say, there must be a continuous integration of states of consciousness.
These, then, are the two antagonist processes by which consciousness subsists—the centrifugal and centripetal actions by which its balance is maintained. That there may be the material for thought, consciousness must every moment have its state differentiated. And for the new state hence resulting to become a thought, it must be integrated with before-experienced states. This perpetual alternation is the characteristic of all consciousness from the very lowest to the very highest. It is distinctly typified in that oscillation between two states, constituting the simplest conceivable form of consciousness; and it is illustrated in the most complex thinkings of the advanced man of science.
Nor is it only in every passing process of thought that this law is displayed: it is traceable also in the general progress of thought. These minor differentiations and integrations that are going on from moment to moment, result in those greater differentiations and integrations which constitute mental development. Every case in which an advancing intelligence distinguishes between objects, or phenomena, or laws, that were previously confounded together as of like kind, implies a differentiation of states of consciousness. And every case in which such advancing intelligence recognizes, as of the same essential nature, objects, or phenomena, or laws, that were previously thought distinct, implies an integration of states of consciousness.
Under its most general aspect therefore, all mental action whatever is definable as the continuous differentiation and integration of states of consciousness.
§ 105. The only further fact of importance here needing to be pointed out, is, the harmony which subsists between this final result and that reached by a kindred science. The widest truth disclosed by the inquiries of physiologists, is parallel to the one at which we have just arrived.
As there are two antagonist processes by which consciousness is maintained, so there are two antagonist processes by which bodily life is maintained: and the same two antagonist processes are common to both. By the action of oxygen every tissue is being differentiated; and every tissue is integrating the materials supplied by the blood. No function can be performed without the differentiation of the tissue performing it; and no tissue is enabled to perform its function save by the integration of nutriment. In the balance of these two actions the organic life consists. By each new integration, an organ is fitted for being again differentiated: each new differentiation enables the organ again to integrate. And as with the psychical life, so with the physical—the stopping of either process is the stopping of both.
Moreover the parallel equally holds under the second aspect. Not only does this law apply to the vital processes going on throughout the body from moment to moment; it also applies to organic progress in general. Commencing, as every organism does, as a uniform mass of matter, every step in its evolution consists in the differentiation and integration of parts. On contemplating the phenomena of organization in general, as exhibited throughout creation, it will be seen that the integration of elements which perform the same function, goes on pari passu with the differentiation of elements which perform unlike functions. That advance from homogeneity to heterogeneity, in which all organization consists, is wholly effected by this duplex action.
Thus, in two senses, there is a continuous differentiation and integration of tissues; as, in two senses, there is a continuous differentiation and integration of states of consciousness.
When it is remembered that the laws of structure and function must necessarily harmonize; and that the structure and functions of the nervous system must conform to the laws of structure and function in general; it will be seen that the parallelism here roughly indicated, is such as might be expected to hold. It will be seen that the ultimate generalizations of Psychology and Physiology, must be, as they here appear, different sides of the same primordial truth. It will be seen that they are both expressions of the same fundamental principle of Life.
[∗]In some editions the enunciation runs,—“Ratios which are the same to the same ratio are the same to each other;” but the above is much the better.
[†]For the aid of those who have not lately looked into Euclid, it will be well to append the definition of proportionals, which is as follows:—“If there be four magnitudes, and if any equimultiples whatsoever be taken of the first and third, an any equimultiples whatsoever of the second and fourth, and if, according as the multiple of the first is greater than the multiple of the second, equal to it, or less, the multiple of the third is also greater than the multiple of the fourth, equal to it or less; then, the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth.“
[∗]Here, and throughout, I use this word in its ordinary acceptation as meaning any cognition reached by an undecomposable mental act; whether the terms of that cognition be presented or represented to consciousness. Sir William Hamilton, in classing knowledge as representative and presentative or intuitive, restricts the meaning of intuition to that which is known by external perception. If, when a dog and a horse are looked at it is seen that one is less than the other, the cognition is intuitive; but if a dog and a horse are imagined, and the inferior size of the dog perceived in thought, the cognition is not intuitive in Sir William Hamilton's sense of the word. As, however, the act by which the relation of inferiority is established in consciousness, is alike in the two cases, the same term may properly be applied to it. And I draw further reason for using the word in its common acceptation, from the fact that the line of demarcation between presentative and representative knowledge cannot be maintained. Though there is much knowledge that is purely representative, there is none that is purely presentative. Every perception whatever involves more or less of representation. And this is asserted by Sir William Hamilton himself, when, in opposition to Royer Collard's doctrine, that perception excludes memory, he writes, “On the contrary, I hold, that as memory, or a certain continuous representation, is a condition of consciousness, it is a condition of perception.”
[∗]The sign (:) used in mathematics to express a ratio, is, in this formula, as in many that follow, placed somewhat unusually in respect to the letters it connects, with a view to convenience of reading. And it may here be explained in preparation for subsequent chapters, that this sign, though here marking, as it commonly does, a ratio, or quantitative relation, will hereafter be employed to mark any relation.
[∗]I coin this word partly to avoid an awkward periphrasis; and partly to indicate the kinship of the idea signified, to the ideas of coexistence and coextension. As we have already in use the words connate and connatural, the innovation is but small; and will, I think, be sufficiently justified by the requirement.
[∗]The words tense, tension, intense, intension, are already in use. Intension being synonymous with intensity, cointension will be synonymous with cointensity; and is here used instead of it to express the parallelism with coextension. The propriety of calling relations more or less intense, according to the contrast between their terms, will perhaps not be at first sight apparent. All quantitative relations, however, save those of equality, involving the idea of contrast—the relation of 5 : 1 being called greater than the relation of 2 : 1, because the contrast between 5 and 1 is greater than the contrast between 2 and 1—and contrast being habitually spoken of as strong or weak; as forcible, as intense; the word intension seems the only available one to express the degree of any relation as distinguished from its kind. And cointension is consequently here chosen, to indicate the equality of relations in respect of the contrast between their terms.
[∗]The choice of letters in this formula may need explanation. By using capitals in the first relation and small letters in the second, I intend to signify, on the one hand, the general or class relation, and, on the other, the particular relation contemplated. Letters of the same names are used, to match the fact that the antecedents are homogeneous with the antecedents, and the consequents with the consequents. And the use of roman letters for the antecedents and italic letters for the consequents, conversely implies that the antecedents differ in nature from the consequents—that the two are heterogeneous.
[∗]The foregoing analysis, in which it is incidentally pointed out that every act of specifically quantitative reasoning is preceded by a provisional act of qualitative reasoning (which is only potentially quantitative), suggests an interesting analogy between these particular processes of reasoning, and the general evolution of reasoning. For, not only is it true that, in the course of civilization, qualitative reasoning precedes quantitative reasoning; not only is it true that, in the growth of the individual mind, the progress must be through the qualitative to the quantitative; but it is also true, as we here find, that every act of quantitative reasoning is qualitative in its initial stage.
[∗]I ought here to mention that some year and a half since, in the course of a conversation in which the axiom—“Things that coexist with the same thing coexist with each other,” was referred to; it was remarked by a distinguished lady—the translator of Strauss and Feuerbach—that perhaps a better axiom would be—“Things that have a constant relation to the same thing have a constant relation to each other.” Not having at that time reached the conclusion that a formula having but three terms could not express our ordinary ratiocinations, which involve four; I was greatly inclined to think this the most general truth to which the propositions known by reason are reducible: the more so as, being expressed in terms of relations, it assimilated with many results at which I had already arrived in the course of analyzing the lower intellectual processes. As will appear, however, from the preceding chapters, subsequent inquiry led me to other conclusions. Nevertheless, this suggestion was of much service in directing my thoughts into a track which they might not else have followed. Respecting this axiom itself, it may be remarked that as the word constant, implies time and uniformity, the application of the axiom is limited to necessary time-relations of the conjunctive class. But if, changing the word constant for a more general one, we say—Things which have a definite relation to the same thing have a definite relation to each other; we get an axiom which expresses the most general truth known by conjunctive reasoning—positive and negative, quantitative and qualitative.
[∗]A brief statement of the theory of Reasoning here elaborated in detail, will be found in an essay on “The Genesis of Science,” published in the British Quarterly Review, for July, 1854. In that essay I have sought to show, that scientific progress conforms to the laws of thought disclosed by the foregoing analysis. It contains accumulated illustrations of the fact, that the discoveries of exact science, from the earliest to the latest, severally consist in the establishment of the equality of certain relations whose equality had not been before perceived. That the progress of human reason, as viewed in its concrete results, should throughout exemplify this generalization, as it does in the clearest manner, affords further confirmation of the foregoing analysis: if further confirmation be needed.
[∗]The divisions thus designated, answer to those which Sir William Hamilton, in his valuable dissertation, classes as Secondary, Secundo-primary, and Primary. Whilst coinciding in the general distinctions drawn in that dissertation, I do so on other grounds than those assigned; and adopt another nomenclature for several reasons: partly because the names Primary, Secundo-primary, and Secondary, implying, as they in some degree do, a serial genesis in time, do not, as it seems to me, correspond with the true order of that genesis, subjectively considered, whilst, objectively considered, we cannot assign priority to any; partly because, as used by Sir William Hamilton, these terms have direct reference to the Kantian doctrine of Space and Time, from which I dissent; and partly because the terms above proposed are descriptive of the real distinctions between these three orders of attributes.
[∗]I use this awkward circumlocution to avoid an inaccuracy. Among the sources, physically considered, of the secundo-primary attributes, Sir William Hamilton enumerates inertia. But inertia is not a force: it is simply the negation of activity. It is not a positive attribute: it is a purely negative one. There is a very general belief that matter offers some absolute opposition to anything tending to displace it. This is not the fact. Take away all extrinsic hindrance—all friction, all resisting medium—and an infinitesimal force will produce motion; only the motion will be infinitesimal, in consequence of the law that the velocity varies as the momentum (or force impressed) divided by the mass. Were inertia a force, all the calculations of astronomers respecting planetary perturbations and the like, would be erroneous. The term vis inertiœ is a misnomer.
[∗]With some exceptions this is Sir William Hamilton's classification. I do not, however, separate, as he attempts to do, the atributes which (physically considered) imply atomic attraction (as the Retractile) from those which imply atomic repulsion (as the Resilient); because, in reality, all of them imply both. As there is a balance of the molecular attractions and repulsions in an undisturbed body, so, a body cannot have any of its atoms disturbed by an external force, without both the attractive and repulsive forces coming into active opposition. On examining the fracture of a piece of wood broken transversely, part of the area will be seen to exhibit marks of tension, and part of compression (in wood about 3/8 and 5/8 respectively); and the line dividing these areas is called the “neutral axis.” A body cannot exhibit ductility or retractility without being partially thrown into a state of compression; seeing that, until parts are compressed, the extending force cannot be applied to the body.
[∗]Those who wish to test this statement experimentally, should remember that the mere act of observing the current phenomena of consciousness, itself introduces a new element into consciousness, which tends more or less to disturb the processes going on. The observations should be made obliquely rather than directly—should if possible be made, not during, but immediately after, the appropriate experiences.
[∗]A truth illustrated by the fact, that when, as under intense agony, the sensation ultimately becomes strong enough totally to exclude all thoughts—totally to absorb consciousness—consciousness ceases: the patient faints.