laws of thought

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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 (symbolically, (p p)); (2) either p or not p must be true, there being no third or middle true proposition between them (symbolically p p); and (3) if a propositional function F is true of an individual variable x, then F is true of x (symbolically, (x) [F(x) F(x)]). Another formulation of the principle of identity asserts that a thing is identical with itself, or (x) (x = x)
laws of thought