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Single Idea 10209

[from 'Philosophy of Mathematics' by Stewart Shapiro, in 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic ]

Full Idea

The modern extensional notion of function is just an arbitrary correspondence between collections.

Gist of Idea

A function is just an arbitrary correspondence between collections

Source

Stewart Shapiro (Philosophy of Mathematics [1997], 1)

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.24


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.