Regarding this law, Aristotle wrote:
First then this at least is obviously true, that the word "be" or "not be" has a definite meaning, so that not everything will be "so and not so". Again, if "man" has one meaning, let this be "two-footed animal"; by having one meaning I understand this:—if "man" means "X", then if A is a man "X" will be what "being a man" means for him. (It makes no difference even if one were to say a word has several meanings, if only they are limited in number; for to each definition there might be assigned a different word. For instance, we might say that "man" has not one meaning but several, one of which would have one definition, viz. "two-footed animal", while there might be also several other definitions if only they were limited in number; for a peculiar name might be assigned to each of the definitions. If, however, they were not limited but one were to say that the word has an infinite number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning our reasoning with one another, and indeed with ourselves, has been annihilated; for it is impossible to think of anything if we do not think of one thing; but if this is possible, one name might be assigned to this thing.)
—Aristotle, Metaphysics, Book IV, Part 4 (translated by W.D. Ross)More than two millennia later, George Boole alluded to the very same principle as did Aristotle when Boole made the following observation with respect to the nature of language and those principles that must inhere naturally within them:
There exist, indeed, certain general principles founded in the very nature of language, by which the use of symbols, which are but the elements of scientific language, is determined. To a certain extent these elements are arbitrary. Their interpretation is purely conventional: we are permitted to employ them in whatever sense we please. But this permission is limited by two indispensable conditions, first, that from the sense once conventionally established we never, in the same process of reasoning, depart; secondly, that the laws by which the process is conducted be founded exclusively upon the above fixed sense or meaning of the symbols employed.
—George Boole, An Investigation of the Laws of ThoughtFurthermore, we cannot think conceptually without making use of some form of language (symbolic communication), for thinking conceptually entails the manipulation and amalgamation of simpler concepts in order to form more complex concepts. Therefore we must have a means of distinguishing these different concepts, namely symbols or signs. It follows then that the first principle of language (law of identity) is also rightfully called the first principle of thought, and by extension, the first principle of reason (rational thought).
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