IDENTITY, CONTRADICTION, AND EXCLUDED MIDDLE. It has been common to look upon some truths as necessary, in opposition to others that, although certain to all intents and purposes, are not necessary, but contingent. Thus, it is considered a necessary truth, that two straight lines cannot inclose a space; that the less cannot include the greater, that a man cannot be in two places at the same time. On the other hand, it is not necessary that gold should be yellow, or water transparent; these facts, we conceive, might have been otherwise arranged. There has been much controversy as to this character of necessity that distinguishes some of our beliefs from others. (See NECESSITY.) The schoohnen laid down three principles, involving what they con sidered the widest generalizations of our necessary beliefs : these are the laws of iden tity, contradiction, and excluded middle.
The law of identity is expressed thus: " Whatever is, is; " a proposition justly con sidered as irresiStib1e. If any objeCtion lies againstit, it is, that nothing appears to be got by affirming it. When we say that "Water freezes at 32"," there is a piece of new information conveyed; by merely knowing water in its liquid state, we should not know that at 32° it became solid; the affirmation is something real. But when we say that " Water is water," there is the form of information, but nothing is conveyed; the proposi tion belongs to the class termed " identical." We merely reaffirm what is already affirmed. The law of identity can only mean that we are to adhere to the meaning of a word as once given; that is to say, we should be consistent in the use of terms. It is a law, not of things, but of the employment of language to denote things.
The law of contradiction is, that " the same attribute cannot be both affirmed and denied of the same subject;" or that a thing cannot be and not be at the same time. In other words, two affirmations that contradict each other cannot be both true. We can not say both that the " Sun has risen," and the "Sun has not risen:" "Gold is heavy," and "Gold is not heavy." Here, also, one might suggest the remark, that the propo sition is an identical one; for the use of the word " not" can only mean that the proposi tion to which it is coupled cannot be held along with the proposition to which it is not coupled. That if the affirmative be true the negative must be false, and if the negative be true the affirmative must be false, are but the same thing differently expressed. The word "not" is an abbreviation for what would otherwise be a more roundabout expression. Instead of saying: "I disbelieve and deny that gold is white," we say: "Gold is not whine." So far, therefore, the principle of contradiction, like that of identity, is not a law of things, but of the use of 'language; implying simply, that when we have affirmed a fact in one form of words, we must, in varying our terms, adhere to the same affirmation.
But this remark does not exhaust the scope of the principle. It has already been observed (see CONDITIONED), that our knowledge can never be confined to one absolute property; in other words to know a thing, we must know something different from it. We cannot even he conscious of one unvarying impression; animals that live in total darkness are not conscious of the darkness, they would become so only in passing into light. It is true that we are constantly in the habit of mentioning a single property, and leaving out of account the related fact but for which the first would have no exist ence; we may talk of light without alluding to darkness. But it is not the less certain that the alternative circumstance, for the time suppressed, is a real part of the case; and there are many occasions, when our meaning cannot• be fully imparted without actually quoting the alternative; and to be logically or formally complete, we ought at all times to state the two.
There are many qualities the very mention of which brings vividly before the mind an opposed couple: as, up, down; straight, crooked; desire; aversion; etc. But beyond these cases, it is a tenable assertion that every fact or property recognized by the human mind must be recognized with relation to some other fact or property, its contrast or opposite, but for which as an alternative, the mind would not have that opportunity of transition essential to consciousness itself. Take redness, which does not suggest to the Mind an opposite in the same manifest form as in the above instances. If all light were red there would be no designation of redness; the only terms would be light and dark. But as there are varieties of light, that is, as we experience mental shocks or impres sions by transitions occurring under the luminous agency, we are made alive to sub ordinate differences, which we mark as so many distinct properties. When white and red are presented to the eye in succession, there is imparted a shock of difference, developing an item of knowledge, which, to be fully expressed, would be "white-red." White would then mean the opposite of red, and red the opposite of white; to the affirmation, "Snow is white," there would correspond as an essential and inseparable part of the same fact, " Snow is not red." But as there are a great many transitions of color that make the mind sensible to difference, the mention of one color is attended with, not one simple denial, but many denials. We have red-green, red-yellow, red blue, etc.; and, moreover, when these couples pass in succession before the view, we are further struck with the fact of agreement in the common effect " redness." Thus, the fact or property. "redness," is the name for the common element in certain couples, which element it affirms, while denying in each case the contrasting element; it is not white, not-green, not-yellow, not-blue, and not every other color, which placed side by side with it made the mind alive to difference. When, by differences and agreements as now described, a class of colors is constituted, the mention of one is the denial of every other member of the class; and the denial of one is the mention of seine other or others, provided we are keeping our attention confined to that class. Prof. de Mor gan introduced into logic the Anise "universe of the proposition," to intimate the class of objects implied when an affirmation, with its corresponding denial, is given forth. Thus, "Such a thing is red," implies as the universe of the proposition the class of colors; "A rose smells sweet " is in the universe "odors." Many other examples might be quoted in illustration of the general principle, and also to show that, in the case of ambiguity or uncertainty in the meaning of a positive term, the proper remedy is to demand an explicit statement of the quality, or qualities, denied. Thus, if a thing is spoken of as "beautiful," which contrast is intended? for there are several implied in the name. Is it "beautiful, not ugly or deformed," "not indifferent or insipid," "not sublime?" etc.• The important function of defining terms is thus, in the last resort, to bring into open what is usually left in the form of a tacit understanding, the denial corresponding to each affirmation. See also CoN D TION ED.