Combining Texts

Ideas for 'Thinking About Mathematics', 'Guide to Ground' and 'Leibniz: Guide for the Perplexed'

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2 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

17286	Logical consequence is verification by a possible world within a truth-set [Fine,K]
	Full Idea: Under the possible worlds semantics for logical consequence, each sentence of a language is associated with a truth-set of possible worlds in which it is true, and then something is a consequence if one of these worlds verifies it.
	From: Kit Fine (Guide to Ground [2012], 1.10)
	A reaction: [compressed, and translated into English; see Fine for more symbolic version; I'm more at home in English]

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.