Classical Logic is composed of three fundamental laws: the law of identity, non-contradiction, and the "excluded middle." Bertrand Russell (1912) described these laws in 1912 as follows:

The law of identity.

The law of identity: 'Whatever is, is.' For all a: a = a.

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)

The law of non-contradiction

'Nothing can both be and not be.' In other words: "two or more contradictory statements cannot both be true in the same sense at the same time": ¬(A∧¬A).

In the words of Aristotle, that "one cannot say of something that it is and that it is not in the same respect and at the same time". As an illustration of this law, he wrote: It is impossible, then, that "being a man" should mean precisely not being a man, if "man" not only signifies something about one subject but also has one significance ... And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call "man", and others were to call "not-man"; but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be in fact. — Aristotle, Metaphysics, Book IV, Part 4

The law of excluded middle

'Everything must either be or not be." In accordance with the law of excluded middle or excluded third, for every proposition, either its positive or negative form is true: A∨¬A.

Regarding the law of excluded middle, Aristotle wrote: "But on the other hand there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate. This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false. (Aristotle, Metaphysics, Book IV, Part 7)