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Ideas for 'Thinking About Mathematics', 'Protrepticus (frags)' and 'First-Order Modal Logic'

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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 / F. Referring in Logic / 3. Property (λ-) Abstraction

9725	'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
	Full Idea: 'Predicate abstraction' is a key idea. It is a syntactic mechanism for abstracting a predicate from a formula, providing a scoping mechanism for constants and function symbols similar to that provided for variables by quantifiers.
	From: M Fitting/R Mendelsohn (First-Order Modal Logic [1998], Pref)