The Online Library of Liberty

A project of Liberty Fund, Inc.

• 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 VI.

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.

[∗]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.