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Ideas for 'Thinking About Mathematics', 'Liberal Individualism and Liberal Neutrality' and 'Russell's Metaphysical Logic'

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3 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 / 2. Descriptions / c. Theory of definite descriptions

21727	Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B]
	Full Idea: The theory of definite descriptions may eliminate apparent commitment to such entities as the present King of France, but certainly not to the present Queen of England.
	From: Bernard Linsky (Russell's Metaphysical Logic [1999], 7.3)

5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism

21719	Extensionalism means what is true of a function is true of coextensive functions [Linsky,B]
	Full Idea: With the principle of extensionality anything true of one propositional functions will be true of every coextensive one.
	From: Bernard Linsky (Russell's Metaphysical Logic [1999], 6.3)