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2 ideas
19192 | The truth definition proves semantic contradiction and excluded middle laws (not the logic laws) [Tarski] |
Full Idea: With our definition of truth we can prove the laws of contradiction and excluded middle. These semantic laws should not be identified with the related logical laws, which belong to the sentential calculus, and do not involve 'true' at all. | |
From: Alfred Tarski (The Semantic Conception of Truth [1944], 12) | |
A reaction: Very illuminating. I wish modern thinkers could be so clear about this matter. The logic contains 'P or not-P'. The semantics contains 'P is either true or false'. Critics say Tarski has presupposed 'classical' logic. |
18897 | Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers] |
Full Idea: Because predicate logic contrues identities dyadically, its account of inferences involving identity propositions needs laws or axioms of identity, explicitly asserting that the dyadic realtion in 'x=y' possesses symmetry, reflexivity and transitivity. | |
From: Fred Sommers (Intellectual Autobiography [2005], 'Syllogistic') |