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 given[9] 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".