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Ideas for 'Thinking About Mathematics', 'Frege philosophy of mathematics' and 'Reference and Generality (3rd ed)'

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2 ideas

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

9820	In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
	Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms.
	From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3)

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.