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There are certain principles known as the Laws of Thought or the Maxims of Consistency. They are variously expressed, variously demonstrated, and variously interpreted, but in one form or another they are often said to be the foundation of all Logic. It is even said that all the doctrines of Deductive or Syllogistic Logic may be educed from them. Let us take the most abstract expression of them, and see how they originated. Three laws are commonly given, named respectively the Law of Identity, the Law of Contradiction and the Law of Excluded Middle.

1. The Law of Identity. A is A. Socrates is Socrates. Guilt is guilt.

2. The Law of Contradiction. A is not not-A. Socrates is not other than Socrates. Guilt is not other than guilt. Or A is not at once b and not-b. Socrates is not at once good and not-good. Guilt is not at once punishable and not-punishable.

3. The Law of Excluded Middle. Everything is either A or not-A; or, A is either b or not-b. A given thing is either Socrates or not-Socrates, either guilty or not-guilty. It must be one or the other: no middle is possible.

Why lay down principles so obvious, in some interpretations, and so manifestly sophistical in others? The bare forms of modern Logic have been reached by a process of attenuation from a passage in Aristotle's Metaphysics¹ (iii. 3, 4, 1005b–1008). He is there laying down the first principle of demonstration, which he takes to be that "it is impossible that the same predicate can both belong, and not belong, to the same subject, at the same time, and in the same sense".² That Socrates knows grammar, and does not know grammar—these two propositions cannot both be true at the same time, and in the same sense. Two contraries cannot exist together in the same subject. The double answer Yes and No cannot be given to one and the same question understood in the same sense.

But why did Aristotle consider it necessary to lay down a principle so obvious? Simply because among the subtle dialecticians who preceded him the principle had been challenged. The Platonic dialogue Euthydemus shows the farcical lengths to which such quibbling was carried. The two brothers vanquish all opponents, but it is by claiming that the answer No does not preclude the answer Yes. "Is not the honourable honourable, and the base base?" asks Socrates. "That is as I please," replies Dionysodorus. Socrates concludes that there is no arguing with such men: they repudiate the first principles of dialectic.

There were, however, more respectable practitioners who canvassed on more plausible grounds any form into which ultimate doctrines about contraries and contradictions, truth and falsehood, could be put, and therefore Aristotle considered it necessary to put forth and defend at elaborate length a statement of a first principle of demonstration. "Contradictions cannot both be true of the same subject at the same time and in the same sense." This is the original form of the Law of Contradiction.

The words "of the same subject," "at the same time," and "in the same sense," are carefully chosen to guard against possible quibbles. "Socrates knows grammar." By Socrates we must mean the same individual man. And even of the same man the assertion may be true at one time and not at another. There was a time when Socrates did not know grammar, though he knows it now. And the assertion may be true in one sense and not in another. It may be true that Socrates knows grammar, yet not that he knows everything that is to be known about grammar, or that he knows as much as Aristarchus.

Aristotle acknowledges that this first principle cannot itself be demonstrated, that is, deduced from any other. If it is denied, you can only reduce the denier to an absurdity. And in showing how to proceed in so doing, he says you must begin by coming to an agreement about the words used, that they signify the same for one and the other disputant.³ No dialectic is possible without this understanding. This first principle of Dialectic is the original of the Law of Identity. While any question as to the truth or falsehood of a question is pending, from the beginning to the end of any logical process, the words must continue to be accepted in the same sense. Words must have an identical reference to things.

Incidentally in discussing the Axiom of Contradiction (ἀξίωμα τἢς ἀντιφάσεως),⁴ Aristotle lays down what is now known as the Law of Excluded Middle. Of two contradictories one or other must be true: we must either affirm or deny any one thing of any other: no mean or middle is possible.

In their origin, then, these so-called Laws of Thought were simply the first principles of Dialectic and Demonstration. Consecutive argument, coherent ratiocination, is impossible unless they are taken for granted.

If we divorce or abstract them from their original application, and consider them merely as laws of thinking or of being, any abstract expression, or illustration, or designation of them may easily be pushed into antagonism with other plain truths or first principles equally rudimentary. Without entering into the perplexing and voluminous discussion to which these laws have been subjected by logicians within the last hundred years, a little casuistry is necessary to enable the student to understand within what limits they hold good.

Socrates is Socrates. The name Socrates is a name for something to which you and I refer when we use the name. Unless we have the same reference, we cannot hold any argument about the thing, or make any communication one to another about it.

But if we take Socrates is Socrates to mean that, "An object of thought or thing is identical with itself," "An object of thought or thing cannot be other than itself," and call this a law of thought, we are met at once by a difficulty. Thought, properly speaking, does not begin till we pass beyond the identity of an object with itself. Thought begins only when we recognise the likeness between one object and others. To keep within the self-identity of the object is to suspend thought. "Socrates was a native of Attica," "Socrates was a wise man," "Socrates was put to death as a troubler of the commonweal"—whenever we begin to think or say anything about Socrates, to ascribe any attributes to him, we pass out of his self-identity into his relations of likeness with other men, into what he has in common with other men.

Hegelians express this plain truth with paradoxical point when they say: "Of any definite existence or thought, therefore, it may be said with quite as much truth that it is not, as that it is, its own bare self".⁵ Or, "A thing must other itself in order to be itself". Controversialists treat this as a subversion of the laws of Identity and Contradiction. But it is only Hegel's fun—his paradoxical way of putting the plain truth that any object has more in common with other objects than it has peculiar to itself. Till we enter into those aspects of agreement with other objects, we cannot truly be said to think at all. If we say merely that a thing is itself, we may as well say nothing about it. To lay down this is not to subvert the Law of Identity, but to keep it from being pushed to the extreme of appearing to deny the Law of Likeness, which is the foundation of all the characters, attributes, or qualities of things in our thoughts.

That self-same objects are like other self-same objects, is an assumption distinct from the Law of Identity, and any interpretation of it that excludes this assumption is to be repudiated. But does not the law of Identity as well as the law of the likeness of mutually exclusive identities presuppose that there are objects self-same, like others, and different from others? Certainly: this is one of the presuppositions of Logic.⁶ We assume that the world of which we talk and reason is separated into such objects in our thoughts. We assume that such words as Socrates represent individual objects with a self-same being or substance; that such words as wisdom, humour, ugliness, running, sitting, here, there, represent attributes, qualities, characters or predicates of individuals; that such words as man represent groups or classes of individuals.

Some logicians in expressing the Law of Identity have their eye specially upon the objects signified by general names or abstract names, man, education.⁷ "A concept is identical with the sum of its characters," or, "Classes are identical with the sum of the individuals composing them". The assumptions thus expressed in technical language which will hereafter be explained are undoubtedly assumptions that Logic makes: but since they are statements of the internal constitution of some of the identities that words represent, to call them the Law of Identity is to depart confusingly from traditional usage.⁸

That throughout any logical process a word must signify the same object, is one proposition: that the object signified by a general name is identical with the sum of the individuals to each of whom it is applicable, or with the sum of the characters that they bear in common, is another proposition. Logic assumes both: Aristotle assumed both: but it is the first that is historically the original of all expressions of the Law of Identity in modern text-books.

Yet another expression of a Law of Identity which is really distinct from and an addition to Aristotle's original. Socrates was an Athenian, a philosopher, an ugly man, an acute dialectician, etc. Let it be granted that the word Socrates bears the same signification throughout all these and any number more of predicates, we may still ask: "But what is it that Socrates signifies?" The title Law of Identity is sometimes given⁹ to a theory on this point. Socrates is Socrates. "An individual is the identity running through the totality of its attributes." Is this not, it may be asked, to confuse thought and being, to resolve Socrates into a string of words? No: real existence is one of the admissible predicates of Socrates: one of the attributes under which we conceive him. But whether we accept or reject this "Law of Identity," it is an addition to Aristotle's dialectical "law of identity"; it is a theory of the metaphysical nature of the identity signified by a Singular name. And the same may be said of yet another theory of Identity, that, "An individual is identical with the totality of its predicates," or (another way of putting the same theory), "An individual is a conflux of generalities".

To turn next to the Laws of Contradiction and Excluded Middle. These also may be subjected to Casuistry, making clearer what they assert by showing what they do not deny.

They do not deny that things change, and that successive states of the same thing may pass into one another by imperceptible degrees. A thing may be neither here nor there: it may be on the passage from here to there: and, while it is in motion, we may say, with equal truth, that it is neither here nor there, or that it is both here and there. Youth passes gradually into age, day into night: a given man or a given moment may be on the borderland between the two.

Logic does not deny the existence of indeterminate margins: it merely lays down that for purposes of clear communication and coherent reasoning the line must be drawn somewhere between b, and not-b.

A difference, however, must be recognised between logical negation and the negations of common thought and common speech. The latter are definite to a degree with which the mere Logic of Consistency does not concern itself. To realise this is to understand more clearly the limitations of Formal Logic.

In common speech, to deny a quality of anything is by implication to attribute to it some other quality of the same kind. Let any man tell me that "the streets of such and such a town are not paved with wood," I at once conclude that they are paved with some other material. It is the legitimate effect of his negative proposition to convey this impression to my mind. If, proceeding on this, I go on to ask: "Then they are paved with granite or asphalt, or this or that?" and he turns round and says: "I did not say they were paved at all," I should be justified in accusing him of a quibble. In ordinary speech, to deny one kind of pavement is to assert pavement of some kind. Similarly, to deny that So-and-so is not in the Twenty-first Regiment, is to imply that he is in another regiment, that he is in the army in some regiment. To retort upon this inference: "He is not in the army at all," is a quibble: as much so as it would be to retort: "There is no such person in existence".

Now Logic does not take account of this implication, and nothing has contributed more to bring upon it the reproach of quibbling. In Logic, to deny a quality is simply to declare a repugnance between it and the subject; negation is mere sublation, taking away, and implies nothing more. Not-b is entirely indefinite: it may cover anything except b.

Is Logic then really useless, or even misleading, inasmuch as it ignores the definite implication of negatives in ordinary thought and speech? In ignoring this implication, does Logic oppose this implication as erroneous? Does Logic shelter the quibbler who trades upon it? By no means: to jump to this conclusion were a misunderstanding. The fact only is that nothing beyond the logical Law of Contradiction needs to be assumed for any of the processes of Formal Logic. Aristotle required to assume nothing more for his syllogistic formulæ, and Logic has not yet included in its scope any process that requires any further assumption. "If not-b represent everything except b, everything outside b, then that A is b, and that A is not-b, cannot both be true, and one or other of them must be true."

Whether the scope of Logic ought to be extended is another question. It seems to me that the scope of Logic may legitimately be extended so as to take account both of the positive implication of negatives and the negative implication of positives. I therefore deal with this subject in a separate chapter following on the ordinary doctrines of Immediate Inference, where I try to explain the simple Law of Thought involved. When I say that the extension is legitimate, I mean that it may be made without departing from the traditional view of Logic as a practical science, conversant with the nature of thought and its expression only in so far as it can provide practical guidance against erroneous interpretations and inferences. The extension that I propose is in effect an attempt to bring within the fold of Practical Logic some of the results of the dialectic of Hegel and his followers, such as Mr. Bradley and Mr. Bosanquet, Professor Caird and Professor Wallace.¹⁰

The logical processes formulated by Aristotle are merely stages in the movement of thought towards attaining definite conceptions of reality. To treat their conclusions as positions in which thought may dwell and rest, is an error, against which Logic itself as a practical science may fairly be called upon to guard. It may even be conceded that the Aristotelian processes are artificial stages, courses that thought does not take naturally, but into which it has to be forced for a purpose. To concede this is not to concede that the Aristotelian logic is useless, as long as we have reason on our side in holding that thought is benefited and strengthened against certain errors by passing through those artificial stages.

Footnote 1: The first statement of the Law of Identity in the form Ens est ens is ascribed by Hamilton (Lectures, iii. 91) to Antonius Andreas, a fourteenth century commentator on the Metaphysics. But Andreas is merely expounding what Aristotle sets forth in iii. 4, 1006 a, b. Ens est ens does not mean in Andreas what A is A means in Hamilton.

Footnote 2: τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτὸ, … αὕτη δὴ πασῶν ἐστὶ βεβαιοτάτη τῶν ἀρχῶν. iii. 3, 1005b, 19–23.

Footnote 3: Hamilton credits Andreas with maintaining, "against Aristotle," that "the principle of Identity, and not the principle of Contradiction, is the one absolutely first". Which comes first, is a scholastic question on which ingenuity may be exercised. But in fact Aristotle put the principle of Identity first in the above plain sense, and Andreas only expounded more formally what Aristotle had said.

Footnote 4: Μεταξὑ ὰντιφάσεως ἐνδέχεται εἶναι οὐθέν, ἀλλ᾿ ἀνάγκη ἢ φάναι ἢ ὰποφάναι ἒν καθ᾿ ἑνὸς ὁτιοῦν. Metaph. iii. 7, 1011b, 23–4.

Footnote 5: Prof. Caird's Hegel, p. 138.

Footnote 6: See Venn, Empirical Logic, 1–8.

Footnote 7: E.g., Hamilton, lect. v.; Veitch's Institutes of Logic, chaps, xii., xiii.

Footnote 8: The confusion probably arises in this way. First, these "laws" are formulated as laws of thought that Logic assumes. Second, a notion arises that these laws are the only postulates of Logic: that all logical doctrines can be "evolved" from them. Third, when it is felt that more than the identical reference of words or the identity of a thing with itself must be assumed in Logic, the Law of Identity is extended to cover this further assumption.

Footnote 9: E.g., Bosanquet's Logic, ii. 207.

Footnote 10: Bradley, Principles of Logic; Bosanquet, Logic or The Morphology of Knowledge; Caird, Hegel (in Blackwood's Philosophical Classics); Wallace, The Logic of Hegel.