The Relation of Logic to Psychology Part 1

Ritchie, D. G. “The Relation of Logic to Psychology.” The Philosophical Review 5, no. 6 (1896): 585.

It’s easy enough to mark in general terms the distinction between logic and psychology; but in the treatment of many logical questions, even by our most careful writers, there seems to me frequently some want of clearness in the detailed application of this distinction. And, in consequence of this want of clearness, many logical questions seem to be rendered more obscure and doubtful than need be. In any case, an attempt to see how the accepted distinction works out in several of the problems of logic may serve to test the accuracy of this distinction, and, unless I am too sanguine, may even throw some light on these problems themselves.

Every psychologist and every logician would agree that, whereas logic, even in its widest sense, has to do only with knowledge, and not with feeling and will, psychology has to do with all mental phenomena. So far as this goes, however, logic might be simply a branch of psychology, and many psychologists, though professedly recognizing some further distinction between logic and psychology, are in the habit of including a great many logical questions in their treatment of the psychology of cognition. Almost all, however, recognize a distinction between the properly psychological and the properly logical aspects of the problem of knowledge. This distinction may be conveniently marked by saying that psychology has too among other things with knowing while logic haste does with 'knowledge.' In other words, psychology has to do with mental processes as events; logic has to do with the validity of these mental processes. Psychology is therefore called a 'descriptive' science; it deals with facts, with what actually happens in the mind. Logic, on the other hand, is a 'regulative' science; it deals with what ought to be, with rules for the right performance of the mental processes that lead to cognition. And, on this account, as is often pointed out, logic is related to the psychology of cognition in a way analogous to the relation of ethics to the psychology of feeling and volition, and to the relation of aesthetics to the psychology of a certain group of the emotions.

So far, we seem to be on firm ground. No sooner, however, do we begin to apply these generally accepted distinctions than difficulties suggest themselves. They may show themselves even in connection with the definition given of "logic in an elementary text-book. Thus Jevons mentions the common definition of logic as "the science of the laws of thought," and goes on to explain "law of thought" as meaning "a certain uniformity or agreement which exists and must exist in the modes in which all persons think and reason, so long as they do not make what we call mistakes or fall into self-contradiction and fallacy" Now this looks like an acceptance of the view that logic is a "regulative" science, whose "laws" are "rules" or “precepts." But Jevons continues, "the laws of thought are natural laws with which we have no power to interfere, and which are of course not to be in any way confused with the artificial laws of a country, which are invented by men and can be altered by them. "Now if by 'laws of thought' we mean simply general statements of what actually happens in our thinking, or statements of what under certain conditions will happen as a matter of fact, 'laws of thought' are merely the concern of the psychologist. But psychologists are not restricted to those uniformities which exist in our thinking when we do not make mistakes. In seeking to ascertain the 'laws of association of ideas’ which are psychological 'laws of thought,' the psychologist may find the fallacies into which the average human mind is prone to fall an even more instructive study than the rigidly correct intellectual processes of the soundest scientific thinker. 'Laws of thought’ for the psychologist, are certainly 'natural laws' in the sense of the other 'laws of nature'; they are statements of what happens, or at least of what under certain conditions would happen. A statement of the fallacies into which the intellects permit us to fall, would be a statement of laws of thought in this psychological sense. But 'laws of thought,' in the logician’s sense, tell us how we ought to reason, and thus may not seem properly comparable with the 'laws of nature.' We seem to be able to violate the logical laws of thought; we do every time we commit a logical fallacy. Now we cannot, in any strict use of language, be said to ' violate a law of nature, ‘though the phrase is used often enough. What is meant is that we violate some practical precept of prudence based upon knowledge of a law of nature. The man who throws himself from the top of a high cliff does not violate, he illustrates, the law of gravitation; he may be violating the laws of prudence or of morality. And so, the man who commits a fallacy illustrates psychological, but violates logical, laws. Are we, then, to compare the ' laws of thought' in their logical sense with maxims of prudence, or precepts of morality, or even with "the artificial laws of a country?” Are the laws of logic simply precepts of intellectual prudence which are, or should be, based on a study of psychological processes? Warnings against inaccuracy in observation, against hasty generalization, against the tendency to overlook negative instances, if these warnings are called logical 'laws,' are such only in this sense. But this is a kind of logical doctrine which some of the stricter logicians have considered an excrescence rather than an essential part of the science. And, in any case, the term 'laws of thought' has not been applied to describe such maxims for the avoidance of fallacies as we find in the first book of Bacon's Novum Organum, but has always denoted specially the axioms of formal logic, the principles of identity, contradiction, and excluded middle ; and to these the logicians who take a wider view of their science would generally add the principle of sufficient reason(under some name or other). Now can these fundamental axioms be considered practical precepts based on psychological laws. If so, what are these fundamental psychological laws? If they are not distinguishable from the logical axioms, and these last are therefore laws of nature, how are the fallacies which consist in their violation possible? The distinction between nature or things' and our thinking about things, will hardly help us here, for these axioms of logic are at once statements about things and about the necessities of our thought. Here, then, we are face to face with a difficulty which is just one aspect of the problem, how is knowledge possible? with its companion problem, how is error possible?

The 'formal' logicians, who have chiefly favored the definition of logic as 'the science of the laws of thought,' may seem, in limiting the problem of logic to consistency, to have separated logic from epistemology. But here we see that a consideration of the laws of thought themselves brings before us some at least of the fundamental questions about knowledge. In teaching logic to students who are only beginning the study of philosophy, or who are unable, or cannot be induced, to study ultimate philosophical questions, it may be advantageous to put aside the problems of epistemology. For bibliographical purposes, also, it is convenient to mark a distinction between works which deal mainly with the general question of the nature and limits of human knowledge, and those which are mainly or exclusively occupied with a detailed examination of the forms of judgment and inference with a view to testing their validity. But it does not seem to me possible to draw “any really scientific line between logic and epistemology. The attempt to cut off logic from the problem of the validity of knowledge can only lead to that narrow and 'formal' treatment which has brought logic into bad repute with men of science and philosophers alike, and which has made it an easy prey to the sport of the exuberant mathematician. If we seek to limit the province of logic by defining it as 'the science of inference,' we cannot avoid the question about the relation between our self-consistent reasonings on the one side and facts on the other. An attack on the syllogism, or a defense of it, must deal with the question whether its astringit res; and that is surely a question of epistemology. Again, even if we limit logic to inference, we must drag in by a side door those processes 'subservient to inference' which we have just kicked out at the front entrance. To what science does it belong to consider concepts, judgments, definitions, divisions, not the mental processes as such of thinking, judging, defining, classifying, but the products of these processes in their possible relations to the real world to which they profess to refer? And how can we deal with the validity of general concepts, with the distinction between the essential and accidental, with the difference between 'real kinds' and artificial classes, without being compelled to face the very problems with which 'theory of knowledge' professes to deal? Nay, how can we discuss the meaning of affirmation and negation without considering the relation of thought to reality? Traditionally, such topics as I have just named belong to the province of logic. As a matter of historical propriety, the science of logic might be expected to denote those subjects which are treated in Aristotle's Organon and specially in the Analytics. To separate logic from epistemology is to ignore the most important of Aristotle's logical writings, the Posterior Analytics; and the habit of ignoring this work is doubtless responsible for a good deal of that contempt for the Aristotelian logic which some logicians seem still to imagine to be the beginning of wisdom. Not merely, however, as a matter of historical sentiment and convenience, but on the ground of philosophical accuracy, we must include the question about the validity of knowledge in logic. Only for provisional pedagogic reasons can we afford to leave it out. I shall assume, then, that our 'general logic,' if taken seriously, must carry us up into ‘transcendental logic'; and I have just been showing how Jevons, in his first 'elementary' lesson, raises (unwittingly, perhaps) the fundamental question about knowledge and error.

In Mill's Logic we have perhaps the most striking instances of a confusion between logic and psychology, or rather of a tendency to merge logic in psychology, a tendency which gradually becomes explicit and acknowledged. In his “Introduction” Mill speaks, indeed, as if his logic were independent of metaphysics; and by ' metaphysics' it is clear from the context that he understands principally psychology, "the analysis of mental processes." But, by this independence of logic, he only means that logic, being chiefly practical in its aims, need not carry the analysis of mental processes very far. "The extension of logic as a science," he says, "is determined by its necessities as an art." That the "analysis of mental processes," which need not be carried very far in logic, is nevertheless psychological analysis, comes out clearly in the course of the treatise. Thus, in the chapter on " The Functions and Logical Value of the Syllogism," he speaks of those against whom he argues as representing the syllogism" as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths, whether of science or of daily life, which we believe." "Larger half," it may be remarked in passing, is a phrase which may seem ominous to foreshadow Mill's skepticism about the certainty of mathematical truths. Further on in the same chapter (8, p. 235) he speaks distinctly of “the psychological process," "false psychology," -taking for granted that the psychological analysis of itself decides theological question. It is in strict accordance with this that Mill, in treating the whole problem of necessary truths, deals with it solely as one of psychology. He rejects the inconceivability of the opposite as a test of truth, on the ground that as a matter of fact many persons have been incapable i.e., psychologically incapable of conceiving or believing what has afterwards turned out to be true. Now, if 'inconceivability' be taken in a purely psychological sense, it is impossible to defend the 'ultimate postulate' as an infallible test of truth. The psychological question about belief has indeed a very important connection with the logical test of truth ; but, unless the logical question is distinguishable from the psychological, Mill’s position is assailable only by showing that it is completely skeptical and destructive of other parts of his logical theory, such as his admission of the validity of the proof per impossibile. As a logical principle, the inconceivability of the opposite is nothing but the principles of Identity, Contradiction, and Excluded Middle taken together; and it is best to take them together, for in their separation they are only partial and one sided expressions of the basis on which all our knowledge rests. I am most certainly not prepared to defend the principle of the inconceivability of the opposite as the ultimate test of truth on any interpretation which would make of it a separate and distinct principle from that which is universally admitted as the basis of formal logic the logic of mere consistency and which is everywhere taken for granted in mathematical proofs. If A is B, it is impossible that in precisely the same sense of the terms, and the same relations of time, place, etc., A can also be Not B; and, conversely, if A cannot be Not-B, it must be B. This is the principle of Contradiction combined with the principle of Excluded Middle; and this is also, expressed in its most abstract form, the principle of the inconceivability of the opposite, as a logical principle.

In the application of the principle, two considerations are of primary importance; and, if they are sufficiently kept in view, a great many of the objections commonly made to the principle fall to the ground. In the first place, it should be stated in a hypothetical form: "If A is B." That is to say, the principle cannot by itself furnish us with any positive knowledge whatsoever. We must start with some assertion; and this assertion may be itself a mere assumption which may turn out to be quite untenable. But, in the testing of the truth of this assumption, the principle of contradiction renders indispensable service. When we test a hypothesis by comparing it with facts, we must assume the validity of the logical processes by which we deduce from our hypothesis the consequences which would follow if its truth were provisionally admitted. And the validity of logical processes involves the validity of the principle of contradiction. Even when a merely psychological interpretation is given to the principle of the inconceivability of the opposite, its validity as a logical principle is tacitly assumed. We know, for instance, that a sincere and undoubting Catholic, or Calvinist, or Mohammedan cannot, as a matter of fact, consciously and knowingly accept propositions as true which are inconsistent with the fundamental articles of the creed which has come to be a real part of his mind. He will, as a matter of psychological necessity, reject such propositions, although they may be accepted as certainly true by persons who have been differently brought up, or who do not hold their professed religious beliefs with the same thorough-going earnestness of conviction. And, it must be added, though the thesis is not always so clearly recognized, he ought, as a matter of logical necessity, to reject such propositions. To profess to believe propositions which are strictly inconsistent with one another, is proof that there is a want of thoroughness somewhere, a want of clearness in thinking, or a want of sincerity, or both. Of course, there are various well-known devices for forgetting over the difficulty, notably the distinction between two (or more) kinds of truth. There are undoubtedly real and important differences between what is scientifically true,' on the one hand (and that means, of course, true according to the phraseology, and subject to the limitations and conventions of this or that particular science), and, on the other hand, what is morally true or 'aesthetically true,' in the sense of being more satisfactory to the moral or aesthetic emotions. But there is here an ambiguity in the word 'true.' The artist in color or in words may produce a higher artistic effect by deviating from the exact proportions of nature, and we may call such deviation a preference of artistic over scientific 'truth.’ An analogous distinction may reasonably be admitted in matters of religion: that is to say, religious emotion, like aesthetic, may struggle to find expression for itself in utterances which, taken as judgments and literally interpreted, are not accepted by the intellect. But it is only with the truth or falsehood of judgments, construed strictly, that logic can concern itself ;and no distinctions between the 'truth' of poetry and the ‘truth' of fact entitle us to say that in precisely the same sense of the terms the two propositions 'the world was made in six days,' and 'the world was not made in six days’ can both be true. In ordinary phraseology, for our practical convenience, we still use pre-Copernican astronomy; but we do not seriously assert that the sun goes round the earth, and that the sun does not go round the earth, in precisely the same sense of the words. When, therefore, any one holding a system of beliefs finds that a strict application of the logical consequences of that system obliges him to contradict a proposition which, apart from that system, seems to him sufficiently proved, he ought logically either to deny that proposition or to be prepared to revise his system of beliefs. What any one face to face with such a contradiction, will actually do depends on the kind of person he is. Most people's system of beliefs is not very much of a system: they can accommodate in their minds a number of inconsistent beliefs by holding many of them very languidly, by not thinking much about them, and by keeping them for use on different occasions, just as Sunday clothes and ordinary apparel can be stowed away in separate drawers. There are a number of interesting psychological problems as to the nature and degrees of belief. But with this logic as such has nothing to do, for logic' should be made of sterner stuff.' Beliefs which are still dimly outlined in a realm of dreams and hazy twilight are not yet subject matter for logic. They must be brought up into the full light of ' clear and distinct Thinking ' before they can be logically analyzed and compared and tested.

But this is as much as to say that the principle of Contradiction must be taken in a perfectly strict sense; and this is the second consideration to be attended to in applying it. The principle of Excluded Middle applies to logical contradictories only and not to contraries. It is only in the case of contradictory opposition that we can infer from the falsehood of a proposition to the truth of its opposite. A and Not-A divide the universe or 'the universe of discourse' between them, but Not-A must not be turned without further proof into some positive B or C, nor must A alter its meaning in the very least. These limitations to the applicability of the principles of Contradiction and Excluded Middle are generally admitted in words; but I do not think they are sufficiently recognized in the discussion about the inconceivability of the opposite as the test of truth. In other words, 'inconceivability' is treated as a matter of psychology, and the purely logical character of the 'ultimate postulate' and its identity with the axioms of formal logic are overlooked. Let me take the familiar example by which Mill seems so easily and plausibly to prove the untrustworthiness of the alleged test of truth. The antipodes were rejected as inconceivable by the ancients: we know that they exist. Not many persons may have rejected the notion of antipodes simply because it was unfamiliar to them, or because it was rejected by others on whose authority they relied. But those who rejected the notion thoughtfully did so in the belief that gravitation was a force acting in the direction of an absolute down and they were quite right to reject the alleged existence of the antipodes, if their system of belief about gravitation was correct. They could not consistently think of human beings, constituted as wearers, walking on the other side of the earth, and not falling down. Can we consistently think of such an idea? What we can picture, or image is irrelevant to the question. Can we think it, i.e., think it out? No more than we can consistently think of human beings at the antipodes falling off now that we know that 'falling off would mean to them 'falling up/ which Isa self-contradictory notion.

This example brings out very clearly the risks which may attend the application of an infallible principle to concrete problems. It can only be safely applied where we are certain that there is no ambiguity in the terms and when we are distinctly aware of the conditions under which we are making our assertions. We are very apt to take that which is true (or false) secundum quid, as if it were true (or false) simpliciter ;in other words, we are apt to make statements roughly and vaguely without 'clearly and distinctly realizing all that wearer really meaning by the terms we use. The infallible logical principle is always infallible; there is no doubt as to it when it speaks ex cathedra. But we are apt to apply it without detention to the fluctuating meaning of ordinary words and the vague outline of most of our conceptions. It is not a test which is valid in formal logic and in mathematics, and not elsewhere for every assertion about anything implies its validity. The difference is only that in abstract matters, where the conditions are fully stated and easily kept in mind, the principle can be applied with a certainty to which we can only approximate in the case of more complex and concrete subjects.

It may be here objected that the principle of inconceivability of the opposite, so interpreted, is a principle of consistency only and not of truth; truth, it may be said, is the agreement of thought with things, of theory with facts. But what do we mean by 'facts'? Everything that in ordinary language, ordinary scientific language, is called a 'fact' is, if we are to use words with philosophical precision, a theory.' Even the simplest perceptive judgment (e.g., it is hot, it hurts) involves some element of interpretation. In becoming aware of a sensation as 'hot' or 'painful,' we have applied thought to what is given in sense. Nothing is mere datum mere fact (if 'fact' is to be opposed to 'theory') except (1) the uninterpreted sensation (and even in calling it a sensation we are making it something more definite and individual than a careful psychology warrants), and (2) the ultimate fact of consciousness itself. The uninterpreted sensation, moreover, is really an abstraction from what we actually know, and therefore is not in any full sense of the term an existing reality. Consciousness itself, on the other hand, cannot very well be opposed to 'thought,' unless we restrict the term ' thought’ to the operation of the discursive understanding. Beyond these ultimate facts the data of outer and inner sense all so called facts are theories, thoughts about these data. Thus the question of truth cannot be separated from that of consistency. The only distinction we can draw, if we are speaking accurately, is that 'mere consistency' means consistency within any system of thought or belief, however narrow, however incongruous with other 'systems' or with the data of sense or consciousness; whereas 'truth' means ultimately consistency within a complete and perfect system of knowledge which embraces the whole universe. Such truth is, of course, to us an ideal merely; and we are in the habit of dignifying with the name of truth anything that is consistent with whatever system of beliefs is the best and most coherent that we have yet been able to reach. Truth is consistency on a large scale, where the 'universe of discourse' includes potentially, or analogically at least, a reference to the ultimate data of sense and consciousness. I insert the qualification 'potentially or analogically', because otherwise we might seem obliged to deny the truth of abstract mathematical propositions. We can verify such propositions as 2 + 2 = 4 by touching fingers or counting heartbeats, but we cannot draw a hard and fast line between such propositions and those in which an appeal to perception is impossible. The square root of 2 divided by the square root of 2 equals 1, is quite as true, but is not equally well adapted for the methods of the Kindergarten.

A different kind of objection to the character here assigned to the principle of Contradiction, might seem to be suggested by the philosophical doctrine that truth is to be found in the unity of contradictions. Such an objection would, however, rest solely on an ambiguity in language. The unity of contradictions does not mean a unity of logical contradictories as explained above. As Mr. McTaggart has very clearly put it in his Studies in the Hegelian Dialectic: "So far is the dialectic from denying the law of contradiction, that it is specially based on it. The contradictions are the cause of the dialectic process". The dialectic movement of thought is, in fact, just the process I have been describing, by which systems of belief are tested and corrected. Contradictions in the strict logical sense can never be reconciled. One or other must be true. But the true proposition may be so very abstract that it gives us very little to satisfy our desire for positive knowledge. On the other hand, when we are dealing with contraries, which are what people generally mean when they speak of opposites or contradictories, the principle of contradiction forbids us accepting both as true; but both may be false, and if, nevertheless, both have some plausibility or reasonableness, we are driven logically to look for some deeper and fuller truth which lies beyond and of which they may be partial and inadequate expressions, false because one-sided and incomplete. The laws of ‘formal logic,' if carefully interpreted, are by no means useless, even in metaphysics. To take an example: that 'Time is finite' and that 'it is infinite' are often spoken of as contradictory judgments. They are not; and they are not even contrary judgments, though they have contrary (or, if 'infinite' means merely' not finite,' contradictory) predicates 'Time is finite' and 'Time is not finite' are contrary propositions (A and E), which may both be false. 'Time is in every respect finite (or infinite)' and 'time is in some respects not finite (or infinite)' are contradictories (A and O), one or other of which must be true. The application of the principle of contradiction in all its sharpness sets us free from the incompleteness of the oppositions in which the inaccuracy of ordinary language leaves us entangled. How much popular argumentation turns on the assumption that between Freedom and Necessity, between Law and Liberty, between Authority and Reason, between the Ideal and the Real there is an absolute antithesis!

The 'wonder' which makes science and philosophy begin and advance, is just the feeling of a contradiction; it is theological law of thought making us uncomfortable by setting up standard of rigid coherence over and against the scrappy, incongruous, ill-fitting bits of belief we have got hold of. The progress of the sciences is often spoken of as if it consisted in a continuous accumulation of facts; but, if facts are merely accumulated, that is not yet science, but only materials for science to work upon. When an alleged new fact is presented to us, we inevitably, i.e., by psychological necessity, test it by our existing system of beliefs; and, as already said, we are logically bound to do so. If the alleged fact turns out to be really a fact and does not cohere with our existing system of beliefs, that system ought to be modified so as to become coherent with it. In this process of modification, it may happen that many supposed facts will have to disappear. The progress of science is the continually more and more complete adjustment of our system, or rather systems, of belief; they are made more coherent in themselves and with one another, and so enable us to fit isolated facts into their places. Now such a progress may be more correctly represented as a dialectic movement of thought than as a continuous aggregation of facts. The ideal of a completely harmonious whole of knowledge is always before us, however unconsciously, leading us to destroy and reject incomplete and incoherent systems, or, in the more advanced stages of the process, to fit them into their places as partial and yet complementary fragments of the truth. Such scientific revolutions as the substitution of the Copernican for the Ptolemaic astronomy, of the Newtonian for the older account of gravitation, of the undulatory for the corpuscular theory of light, of the Lamarckian theory of species for the traditional theory, and of the Darwinian for the Lamarckian explanation of biological evolution, cannot be described correctly as additions to our stock of facts; they are the displacement of less adequate by more adequate theories. This 'dialectic' character of intellectual progress becomes still more conspicuous in the case of metaphysical systems. The substitution of new 'categories' for old, in the sciences, in politics, in art, in religion, in any department of human life, leads to a readjustment of the metaphysical system in which the old categories had been held together in what seemed a coherent system. What a new 'fact' or a new 'law' is for each of the special sciences, that a new 'category' is for metaphysics.

In the mathematical sciences we have, indeed, an example of what seems a steady and continuous advance; but it is an advance simply by the application of the Cartesian method of 'clear and distinct thinking,' i.e., by the continual application of the logical laws of thought to the data of space and number. And even in the progress of mathematics there have been periods of revolution, like that in which Descartes was a leader, when, if old categories have not been rejected, they have been absorbed in wider conceptions. There have, indeed, in recent times been suggestions which, if true, have been thought fatal to the supposed absolute truth of mathematics. I refer, of course, to the non-Euclidean systems of geometry; and perhaps to some persons even heretical systems of arithmetic may seem conceivable, such as would have to prevail in John Stuart Mill's planet where 2 + 2 = 5. Now, so far as I am able to understand a matter in which I have no special knowledge, such hypotheses as those of spherical space, of space of more than three dimensions, etc., are altogether meaningless, except on the previous assumption of our tri-dimensional space, i.e., of our actual space, which for convenience of thinking we analyze into three dimensions, finding that we require at least three determinations to fix the position of any point, but that three are quite sufficient. If it is said that in spherical space parallel straight lines meet, that can only mean that on the surface of a globe lines which on a flat projection of this surface would be parallel must converge; or else it is nonsense. If it has any meaning, it assumes the truth of Euclidean geometry. Similarly, if any one likes to amuse himself by talking of 2 and 2 making 5, he can only mean either to use the symbol 5 where we now use 4, or else he means that when (e.g.] two pounds weight of a certain kind of substance are placed alongside of other two pounds of the same substance, the resulting heap is found to weigh five pounds, a statement which if true would reveal some hitherto unsuspected physical or chemical change, but which is meaningless except on the assumption of the absolute truth of our arithmetic; for the assertion of the mysterious appearance of the extra pound implies that 2 + 2 = 4, and that 4 + 1 = 5.We find 4 + 1, where we expected.

Even supposing the contention of the neo-geometers to be admitted I mean, of course, their metaphysical contention with which alone I am concerned the truth of geometry would still be absolute within the conditions as to the nature of space taken for granted in any particular system of geometry. The dispute is as to whether Euclidean geometry is only a system parallel to other possible systems, or whether it occupies a position of primacy, being presupposed in all of them. Within the limits of any fantastic 'meta-geometry' or 'metarithmetic' the logical laws of thought would have to hold good or there would be no system.

The main purpose of the foregoing discussion has been to show the connection or I should rather say, the identity between the ultimate test of truth in every department of knowledge, viz., coherence within a system, and those 'laws of thought' which are the basis of formal logic in its narrowest interpretation. Leaving these more general problems, which would usually be classed as epistemological, I shall in a future article deal with some of the special problems which are usually discussed under the head of logic.

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