IV.—Consistency and Real Inference

IV.—Consistency and Real Inference

It would not be going too far to say that the principal difficulty in the way of a student of Logic at the present day (at any rate in England) consists not so much in the fact that the chief writers upon the subject contradict one another upon many points, for an opportunity for contradiction implies agreement up to a certain stage, as in the fact that over a large region they really hardly get fairly within reach of one another at all. To quarrel upon specific points people must have at any rate some principles in common; where this is not the case, they have little else to do than to make up for the vagueness of their dissent by the vigour with which they give expression to it. Much of the consequent confusion can, we are convinced, be easily allayed by a simple process of intercomparison, provided only the various systems be referred to their leading principles of distinction. In adopting such a plan we need make no apology for confining our attention to the most popular and familiar writers on each side; indeed for such representative purposes they are distinctly the most suitable. But, at the same time, it must be understood that though nominally comparing authors, we are really comparing systems.(4 ¶ 1)

That we have not overrated the magnitude of the divergence between the various systems will be evident from a very few extracts and quotations. Hamilton, by implication rather, and Mansel, formally and explicitly, deny that the subject-matter with which Mill is occupied deserves the name of logic at all; they regard it as being nothing more than a somewhat arbitrary selection from Physical Science. Mill in turn gives equally conclusive indications from his side. He declares, when discussing the import of propositions, that the Conceptualist view is one of the most fatal errors ever introduced into the philosophy of logic. Elsewhere he gives criticisms which amount to the retort that those who adopt that view are making logic nothing more than a somewhat arbitrary selection from Psychology.(4 ¶ 2)

Before proceeding to work out this distinction into some of its details, let us go back, so to say, to the watershed whence the different views as to the nature and province of logic must take their rise. Every one, it is to be presumed, will admit that a proposition is a statement in words of a judgment about things.[8] Without the words it is pretty generally agreed that there could be nothing more than the merest germ of thought, if even that; without the judgment expressed by it, it would clearly not be the appropriate action of a rational being; whilst without the reference to things it would, of course, fail in its main object of communicating knowledge, nor could there be any question raised about its material truth or falsehood.(4 ¶ 3)

Now, each of these three sides of the proposition might conceivably be selected as that which is distinctly characteristic of it, to the exclusion of the others; and since the proposition by analysis leads to terms, and by synthesis to arguments, what holds of the proposition holds equally throughout the entire field of logic. Hence we should apparently be led to three alternative views as to the general nature of logic. One of these views, however—namely, that which lays the stress on the words in which the judgment is couched—need hardly be discussed. It has indeed been maintained by Whately that logic is concerned with language, and with language only. But he does not adhere to this limitation, as indeed no clear thinker could, for the secondary and dependent nature of language as being a medium of thought, or having reference to facts, is far too prominent to be disregarded. Hence it follows that supporters of this view are under such powerful attraction to one or other of the remaining two, that for all practical purposes we need not take any but these into account.(4 ¶ 4)

Beginning then with the Conceptualist view, that is, starting with the judgment as above indicated, we must, of course, take, as the element of the judgment, the concept, for this only belongs to the same, namely, the mental order or stratum of things. The concept and the judgment are, so to say, on the same plane; they are homogeneous and comparable the one with the other, whereas to mingle names or propositions with them would be to mix up disparate things.(4 ¶ 5)

It may be admitted at once that this view has simplicity as a merit; but let us just see to what lengths and sacrifices the determination to adhere to it will lead us. Taking the concept, which may be best defined as the mental[9] counterpart of a general name, we say that this is the real element of the judgment, that the judgment consists of two concepts standing in some sort of relation to each other. So long as we are concerned with general names, this wlil carry us on tolerably well; but how are we to treat singular names? Most people would say that these refer directly to individual objects, that this and nothing else than this is their meaning. But the Conceptualist sometimes hesitates to say this, for to do so would be to make a dangerous approach towards subordinating the form to the matter. Accordingly the consistent thinker (and in a question of consistency it is, of course, to Mansel rather than to Hamilton that we turn) abolishes individual terms altogether. He goes the length of asserting that every proper name is a concept, which is perfectly general in its intrinsic character like all other concepts, and that if it does not happen to fit only one individual in the course of time, this is a mere historical fact, and therefore alien to the logician’s consideration. By so saying, he may be presumed to mean that my mental representation of any given individual, say Socrates, can contain only a limited selection of attributes; that this limited group might possibly be found to recur again elsewhere; that, if it did do so, we should not then be able to discriminate between the two without a fresh resort to the individuals themselves with a view to obtain fresh attributes for the purpose of distinction, and that to do this would be to go outside the concept, in other words, to transgress into the matter instead of keeping to the pure form.(4 ¶ 6)

Again, it must have struck readers that the Conceptualist logicians make little or no reference to belief. The reason of this is not far to seek. For one thing, belief cannot but have some degree of reference to external objects, and with them no communication whatever is to be held, except, of course, as the original materials or data of thought. For another thing, when, as here, we are only occupied with necessary inferences, nothing but full belief, absolute or conditional, can intrude itself, and therefore we really need not attend to it at all. It need not come before us here, any more than before the pure mathematician; for, like him, we are only concerned with what follows from, or is consistent with, something else. Provided the links are necessarily connected together, we do not care how the chain may be fixed at either end. It is only when we deal with Induction and Probability and the delicate questions raised as to whether there is or is not sufficient ground for belief, that this consideration of belief is raised at all. Accordingly any distinction between real and imaginary notions is rejected, the only distinction recognised being that between the possible and the impossible, the former including every notion (whether or not there be things corresponding to it) which does not involve actual self-contradiction, and the latter those which do involve self-contradiction.(4 ¶ 7)

Again, Classification, in any shape deserving that name, disappears, for it cannot be carried on without some observation and comparison of the objects to be classified. What takes its place is Division, for this is really classification confined to purely formal conditions. But even against this objections may be raised. The only way in which we can divide a class is by separating it into those members which do, and those which do not, possess some attribute; but we clearly cannot tell whether things do or do not possess any assignable attributes except by examination of them, and in purely formal logic this is precluded. It is quite true that division by dichotomy is formally valid, for, whatever be the nature of A, a thing must either be A or not-A. But then, as Mansel objects, what makes us think of A rather than of any other attribute in relation to the thing in question? Hence, though dichotomy in general, as a principle of division, is sound enough, it has nevertheless to be abandoned, because every particular application of it is suggested by reference to the objects and consequent knowledge of their properties, and of this the pure logician is jealous to the last extreme.(4 ¶ 8)

The treatment of Induction moreover is simplified. That any process so narrow and unproductive as the so-called Perfect Induction, should have acquired that name, and have been accepted on its own merits, is hard to believe. But when the general theory from which it follows is adopted, the question assumes a very different aspect. Let us resolve to stick to the analysis and composition of concepts, and this perfect induction, poor as it is, is the best we can attempt. It does not demand any resort to external nature, any fresh resort that is, the concepts originally set before us being sufficient for our purpose. It is as near an approach therefore to ordinary Scientific Inductions as can be attained by formulæ which are to hold true whatever be the nature of the particular subject matter to which they are applied.(4 ¶ 9)

The foregoing remarks will serve to indicate the nature and extent of the divergence between the two opposed views, but something must now be said upon the two designations, Formal and Conceptualist, wihch are frequently used as practical synonyms to express them. These terms are obviously distinct in their original significations. Formal has reference to the limits of the subject rather than its actual nature. It reminds us that we are confining ourselves to those mental processes, or parts of processes, which are independent of the particular subject-matter, that is, in other words, which follow from the mere form of expression. Conceptualist, on the other hand, refers rather to the nature of our subject than to its limits; it reminds us that we are occupying ourselves with the consideration of concepts or general notions as distinguished from external phenomena. The two terms are not indeed in strictness synonymous, nor need the principal doctrines implied by them be necessarily held together. Whately, for instance, as a thorough formalist, but he shows no predilection for the conceptualist doctrines.(4 ¶ 10)

It is true, on the other hand, that the consistent Conceptualist is under powerful inducements to adopt the formal view, partly on grounds of rigid sequence, but still more on grounds of psychological sympathy. Those who have for any reasons determined to confine themselves to the manipulation of concepts, will naturally recognise a deep and important distinction between those mental processes which do not, and those which do require us to go outside the concept for fresh matter in order to carry them on; that is, in other words, between those processes which are, and which are not, formal. Add to this the fact that those who occupy the conceptualist standpoint are, as a rule, those who believe in necessary laws of thought as an ultimate fact (a connection arising out of psychological grounds into which we have not space to enter here), and we see an additional reason why they should make a sharp distinction between the two classes of processes, respectively, which are, and which are not, formal. The distinction between formal and material, if admitted, cannot but be of some importance in any case, though it be little more than a distinction of method; but in the case in question it gets taken up by, and resolved into, the far more important distinction between what is à priori and what is merely empirical, and there are therefore additional and far stronger reasons for adhering to it.(4 ¶ 11)

If we now turn to the opposie or Material view of Logic, we find a similar series of mutually connected characteristics. Passing over some of those points which have been sufficiently illustrated already by contrast, let us come to that which admirers of Mill will generally regard as his strongest claim to originality, viz., his peculiar doctrine of the syllogism. We think that we are detracting little, if at all, from his merits by saying that this doctrine seems the natural, simple, and almost necessary outcome of the general view of logic which he has adopted. It is, in fact, upon his consistent following out of this view, rather than upon this or that conclusion in particular, that we should rest his real claims to high distinction.(4 ¶ 12)

His explanation of the syllogism will be arrived at most simply by referring first to what he says about the nature of the so-called immediate inferences. It may have struck some readers as noteworthy that he refuses to allow them the name of inferences at all. But there is surely a meaning in this, and the disputants on each side are quite consistent in adhering to their own views. Take, for instance, the proposition All men are fallible; from this we obtain by a certain series of processes Some infallibles are not men. Now regard these propositions as judgments; that is, stop short at the mental process of framing the judgment instead of going on to the facts about which the judgment is made, and it can hardly be denied that one of them is an inference from the other. They certainly cannot be called one and the same judgment, considering that they have different subjects, different predicates, different quantity, and different quality. And if they are not the same judgment, the latter must surely be an inference from the former. But penetrate to the facts to which these judgments refer, and we see at once that they are identical, or to speak more accurately, the one is a portion of the other. The things are the same, being merely differently grouped, or looked at from a different point of view. The same remarks will apply to another class of immediate judgments which have given some trouble to logicians, for instance, A is greater than B, therefore B is less than A. Here also the judgments are distinct, while the facts judged are identically the same.(4 ¶ 13)

Now let us introduce the above distinction into the controversy whether the syllogism is or is not a petitio principii, and the dispute seems allayed at once, or, at any rate, its origin and existence are accounted for. The conclusion regarded as a judgment is unquestionably distinct from the premisses so regarded, and therefore from that point of view the ordinary theory seems perfectly tenable. But once let a thinker start with the determination that his propositions shall be regarded as, so to say, bottoming upon acts instead of stopping short at concepts, and there is an obvious incompleteness and difficulty about the old explanation. The conclusion, regarded as an objective fact, is the premisses, or rather a portion of them. We are accordingly driven to carry our investigation a step further back, and we then perceive that the only step of reasoning at which new facts were appealed to, instead of merely new judgments about them being made, was in the formation of the major premiss. When, from a limited number of observed instances, we generalise so as to include the whole class to which they belong, we are talking and judging about new facts instead of merely varying our judgments about the old ones. Hence Mill’s view readily follows, viz.: that it is the major premiss which really contains the whole inference, the remaining part of the syllogism consisting merely in identification and interpretation of what has gone before. As an illustration of the fact that this explanation of the syllogism, original and important as it is, is, nevertheless, that to which a consistent supporter of what we may term the Baconian view of logic, would necessarily be led, it may be pointed out that it has received for instance the support of Dr. Whewell. He is in radical opposition to Mill on fundamental philosophical principles, but agreeing with him on the whole as to the nature and province of scientific logic, he agrees with him in consequence on the point in question.(4 ¶ 14)

The foregoing remarks will be sufficient to indicate the nature and extent of the divergence between the two views before us. It would, of course, be far beyond the scope of the present article to attempt to decide between their claims, but something may fairly be said about some of their subordinate merits and deficiencies. For the Conceptualist theory the main recommendation is the extreme simplicity and homogeneity of the resultant system. Whatever is done is completely done. Nothing is admitted as demonstration, but what is (hypothetically) certain. We have none of those results, so dissatisfying to the lover of speculative accuracy, in which no final decision can be obtained by our mere formulæ, but the settlement of the question has to be abandoned to the judgment and skill of the practiced observer. This completeness of rsult is moreover accompanied by a symmetry of treatment which is very fascinating to many minds. These merits are, of course, purchased at a heavy cost. In addition to the philosophical difficulties which the system involves, a large number of detailed objections may be raised against it. After the elaborate exposition of these given in Mill’s Examination of Hamilton’s Philosophy, there is no occasion for us to enter upon them here.(4 ¶ 15)

With regard to the defects of the Material view of Logic, those who accept it on the whole will not of course admit that they amount to serious and insurmountable obstacles. Nevertheless, their existence must be frankly admitted. They may nearly all be summed up in the charge of vagueness of outline, and uncertainty of result. We cannot lay down a precise line for the limit of logic and logical treatment in general, as distinguished from that of the special sciences. In definition we are forced to admit that the connotation of terms does not admit of accurate determination, but varies with usage, and may be almost entirely altered by scientific discoveries. When challenged to state after how many occurrences the repetition of an event may be confidently expected, or how many instances are required to establish an induction, we are obliged to admit that no definite answer can be given, but that it wholly depends upon the nature of the subject-matter. So with classification; this is no process which can be performed by rule, but it imperatively requires that sagacity of observation and judgment which only long practice combined with natural aptitude can secure. These difficulties are inherent in all human experience, and therefore no science which attempts to grapple with the facts of experience can avoid them.(4 ¶ 16)

There is, indeed, a special difficulty occasionally experienced by the student which must be regarded as irrelevant. Those, for instance, who begin with Mill are not unfrequently puzzled by his statement that Logic has to do with facts or things themselves rather than with our ideas about them; and they not unnaturally ask, How can he then be an Idealist? And if so, is he not grossly inconsistent? The answer, of course, is that since the particular opinion which any one entertains as to the nature of the external world does not affect his position when dealing with scientific evidence in detail it need not affect the position of one who deals with such evidence as a whole, viz.: the logician. It is a question of metaphysics which lies behind all evidence, and leaves it for the most part entirely unaffected, at least by any direct contact. The astronomer who infers that the sun is 92,000,000 miles distant from the earth is not called to account and questioned as to how he reconciles this statement with his metaphysics if he be an Idealist; and the logician may fairly claim a like toleration. If he lays it down that names are names of things, not of our ideas of things, that what is the import of a proposition is not the judgment but the facts to which the judgment refers, we have really no more occasion to pry into his metaphysical opinions than into those which he may happen to hold in theology.(4 ¶ 17)

The foundation and ground of Induction is a more serious difficulty; for, though like the last, it cannot by rights claim discussion in logic, it is nevertheless almost impossible so to treat Induction as not to provoke some perplexing inquiries. The Conceptualist, of course, avoids all this, for he is only concerned with that which is strictly necessary, and therefore with such Induction only (or what he gives that name to) as is performed formally and necessarily. But the material logician often finds himself in the position of having raised difficulties, by his mode of treating the subject, which almost compel him to commit himself to opinions which cannot be justified from a logical but only from a psychological point of view. Suppose that he says (as Mill does) that all our knowledge of the uniformity of nature is derived from Induction. He is at once met by some such objection as this: You found that belief upon induction, and yet for every act of induction, even for the very first, you must postulate that belief? So long as we keep strictly to the province of logic, no answer, I think, can fairly be given to this objection. Every conscious act of induction must demand and presuppose a belief in the uniformity of nature, not indeed necessarily throughout its whole extent, but, at any rate, over some area; and therefore the belief cannot have grown up from the beginning by a series of such acts. In other words, if the inductive inference and the conviction of the uniformity of nature are both to be consciously apprehended, it appears to be a paralogism to regard them as mutually dependent on one another.(4 ¶ 18)

Let the logician, however, be permitted to transgress into psychological inquiries, and an answer seems ready to his hand. It may not be a completely satisfactory one, as indeed nothing final can as yet be looked for concerning the nature of belief, but it will serve to turn the edge of the preceding objection. He may fairly reply that we, or our ancestors, have acted upon that uniformity, as the brute creatures do, and that it was only at a later stage that consciousness awakened—that is, that what we call belief ripened out of mere association and habit. Take the case of one of the more intelligent animals. They undoubtedly act upon the uniformity of nature; if they did not, they could not continue to subsist for a day any more than ourselves. Now, suppose a gradual dawn of self-consciousness in one of them, and a consequent desire to give a reason for processes wihch had been so long satisfactorily performed. The fact is that it is assumed that in Logic, though our processes may be sometimes unconsciously performed, they are, nevertheless, always capable of being called out into distinct consciousness when we choose. This need not be the case in Psychology, and indeed on the doctrines of the analytical or association school can seldom be the case with regard to ultimate principles. Hence the logician, when he attempts to give an account and justification of his proceedings in accordance with his own methods, will occasionally be reduced to the alternative of abandoning difficulties as insoluble, or of giving what will be objected against as involving a paralogism. It would avoid perplexity if he were frankly to assume or state his psychological premises, and, if necessary, indicate the kind of justification he would give of them.(4 ¶ 19)

J. Venn

4 n. 1. The reader is reminded that we are confining our attention, not entirely to English logicians, but to those who may be considered as influential here. No Hegelian, I presume, would consider what we have taken as our starting point to be in any way deserving of such a name.

4 n. 2. We are admitting for purposes of discussion the tenability of the Conceptualist doctrine—that is, we are not rejecting the psychological theories or assumptions upon which it rests.