Yet had we the power of discrimination only, Science could not be created. To know that one feeling differs from another gives purely negative information. It cannot teach us what will happen. In such a state of intellect each sensation would stand out distinct from every other; there would be no tie, no bridge of affinity between them. We want a unifying power by which the present and the future may be linked to the past; and this seems to be accomplished by a different power of mind. Lord Bacon has pointed out that different men possess in very different degrees the powers of discrimination and identification. It may be said indeed that discrimination necessarily implies the action of the opposite process of identification; and so it doubtless does in negative points. But there is a rare property of mind which consists in penetrating the disguise of variety and seizing the common elements of sameness; and it is this property which furnishes the true measure of intellect. The name of “intellect” expresses the interlacing of the general and the single, which is the peculiar province of mind.[25] To cogitate is the Latin coagitare, resting on a like metaphor. Logic, also, is but another name for the same process, the peculiar work of reason; for λογος is derived from λεγειν, which like the Latin legere meant originally to gather. Plato said of this unifying power, that if he met the man who could detect the one in the many, he would follow him as a god.
Laws of Identity and Difference.
At the base of all thought and science must lie the laws which express the very nature and conditions of the discriminating and identifying powers of mind. These are the so-called Fundamental Laws of Thought, usually stated as follows:—
1. The Law of Identity. Whatever is, is.
2. The Law of Contradiction. A thing cannot both be and not be.
3. The Law of Duality. A thing must either be or not be.
The first of these statements may perhaps be regarded as a description of identity itself, if so fundamental a notion can admit of description. A thing at any moment is perfectly identical with itself, and, if any person were unaware of the meaning of the word “identity,” we could not better describe it than by such an example.
The second law points out that contradictory attributes can never be joined together. The same object may vary in its different parts; here it may be black, and there white; at one time it may be hard and at another time soft; but at the same time and place an attribute cannot be both present and absent. Aristotle truly described this law as the first of all axioms—one of which we need not seek for any demonstration. All truths cannot be proved, otherwise there would be an endless chain of demonstration; and it is in self-evident truths like this that we find the simplest foundations.
The third of these laws completes the other two. It asserts that at every step there are two possible alternatives—presence or absence, affirmation or negation. Hence I propose to name this law the Law of Duality, for it gives to all the formulæ of reasoning a dual character. It asserts also that between presence and absence, existence and non-existence, affirmation and negation, there is no third alternative. As Aristotle said, there can be no mean between opposite assertions: we must either affirm or deny. Hence the inconvenient name by which it has been known—The Law of Excluded Middle.
It may be allowed that these laws are not three independent and distinct laws; they rather express three different aspects of the same truth, and each law doubtless presupposes and implies the other two. But it has not hitherto been found possible to state these characters of identity and difference in less than the threefold formula. The reader may perhaps desire some information as to the mode in which these laws have been stated, or the way in which they have been regarded, by philosophers in different ages of the world. Abundant information on this and many other points of logical history will be found in Ueberweg’s System of Logic, of which an excellent translation has been published by Professor T. M. Lindsay (see pp. 228–281).