Combining Texts

Ideas for 'Thinking About Mathematics', 'Intellectual Autobiography' and 'Outline of a Theory of Truth'

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2 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

8729	Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
	Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements.
	From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2)
	A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle.

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in 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')