The Online Library of Liberty

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• Preface.
• Part I.: Special Analysis.
• Chapter I.: A Datum Wanted.
• Chapter II.: The Universal Postulate.
• Chapter III.: Its Corollaries.
• Chapter IV.: Our Present Position.
• Part II.: Special Analysis.
• Chapter I.: Compound Quantitative Reasoning.
• Chapter II.: Compound Quantitative Reasoning (continued).
• Chapter III.: Imperfect and Simple Quantitative Reasoning.
• Chapter IV.: Quantitative Reasoning In General.
• Chapter V.: Perfect Qualitative Reasoning.
• Chapter VI.: Imperfect Qualitative Reasoning.
• Chapter VII.: Reasoning In General.
• Chapter VIII.: Classification, Naming, and Recognition.
• Chapter IX.: The Perception of Special Objects.
• Chapter X.: The Perception of Body As Presenting Dynamical, Statico-dynamical, and Statical Attributes. ∗
• Chapter XI.: The Perception of Body As Presenting Statico-dynamical and Statical Attributes.
• Chapter XII.: The Perception of Body As Presenting Statical Attributes.
• Chapter XIII.: The Perception of Space.
• Chapter XIV.: The Perception of Time.
• Chapter XV.: The Perception of Motion.
• Chapter XVI.: The Perception of Resistance.
• Chapter XVII.: Perception In General.
• Chapter XVIII.: The Relations of Similarity and Dissimilarity.
• Chapter XIX.: The Relations of Cointension and Non-cointension.
• Chapter XX.: The Relations of Coextension and Non-coextension.
• Chapter XXI.: The Relations of Coexistence and Non-coexistence.
• Chapter XXII.: The Relations of Connature and Non-connature.
• Chapter XXIII.: The Relations of Likeness and Unlikeness.
• Chapter XXIV.: The Relation of Sequence.
• Chapter XXV.: Consciousness In General.
• Chapter XXVI.: Results.
• Part III.: General Synthesis.
• Chapter I.: Method.
• Chapter II.: Connexion of Mind and Life.
• Chapter III.: Proximate Definition of Life.
• Chapter IV.: The Correspondence Between Life and Its Circumstances.
• Chapter V.: The Degree of Life Varies As the Degree of Correspondence.
• Chapter VI.: The Correspondence As Direct and Homogeneous.
• Chapter VII.: The Correspondence As Direct But Heterogeneous.
• Chapter VIII.: The Correspondence As Extending In Space.
• Chapter IX.: The Correspondence As Extending In Time.
• Chapter X.: The Correspondence As Increasing In Speciality.
• Chapter XI.: The Correspondence As Increasing In Generality.
• Chapter XII.: The Correspondence As Increasing In Complexity.
• Chapter XIII.: The Co-ordination of Correspondences.
• Chapter XIV.: The Integration of Correspondences.
• Chapter XV.: The Correspondences In Their Totality.
• Part IV.: Special Synthesis.
• Chapter I.: The Nature of Intelligence.
• Chapter II.: The Law of Intelligence.
• Chapter III.: The Growth of Intelligence.
• Chapter IV.: Reflex Action.
• Chapter V.: Instinct.
• Chapter VI.: Memory.
• Chapter VII.: Reason.
• Chapter VIII.: The Feelings.
• Chapter IX.: The Will.

CHAPTER V.

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,—

• All men are mortal,
• Socrates is a man,
• therefore
• Socrates is mortal,

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.

[∗]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.