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Ideas for 'Philosophy of Mathematics', 'The Idea of the Brain' and 'Community and Association'

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2 ideas

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

10212	Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro]
	Full Idea: To some extent, every truth-functional connective differs from its counterpart in ordinary language. Classical conjunction, for example, is timeless, whereas the word 'and' often is not. 'Socrates runs and Socrates stops' cannot be reversed.
	From: Stewart Shapiro (Philosophy of Mathematics [1997], 3)
	A reaction: Shapiro suggests two interpretations: either the classical connectives are revealing the deeper structure of ordinary language, or else they are a simplification of it.

5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

10209	A function is just an arbitrary correspondence between collections [Shapiro]
	Full Idea: The modern extensional notion of function is just an arbitrary correspondence between collections.
	From: Stewart Shapiro (Philosophy of Mathematics [1997], 1)
	A reaction: Shapiro links this with the idea that a set is just an arbitrary collection. These minimalist concepts seem like a reaction to a general failure to come up with a more useful and common sense definition.