Law of identity

Aristotle

The website Importance of Philosophy states concerning Aristotle's Law of Identity:

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Everything that exists has a specific nature. Each entity exists as something in particular and it has characteristics that are a part of what it is. "This leaf is red, solid, dry, rough, and flammable." "This book is white, and has 312 pages." "This coin is round, dense, smooth, and has a picture on it." In all three of these cases we are referring to an entity with a specific identity; the particular type of identity, or the trait discussed, is not important. Their identities include all of their features, not just those mentioned. Identity is the concept that refers to this aspect of existence; the aspect of existing as something in particular, with specific characteristics. An entity without an identity cannot exist because it would be nothing. To exist is to exist as something, and that means to exist with a particular identity.

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Encyclopedia Britannica declares:

"Laws of thought, traditionally, the three fundamental laws of logic: (1) the law of contradiction, (2) the law of excluded middle (or third), and (3) the principle of identity. That is, (1) for all propositions p, it is impossible for both p and not p to be true, or symbolically ∼(p · ∼p), in which ∼ means “not” and · means “and”; (2) either p or ∼p must be true, there being no third or middle true proposition between them, or symbolically p ∨ ∼p, in which ∨ means “or”; and (3) if a propositional function F is true of an individual variable x, then F is indeed true of x, or symbolically F(x) ⊃ F(x), in which ⊃ means “formally implies.” Another formulation of the principle of identity asserts that a thing is identical with itself, or (∀x) (x = x), in which ∀ means “for every”; or simply that x is x."