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Single Idea 13419

[filed under theme 6. Mathematics / C. Sources of Mathematics / 8. Finitism ]

Full Idea

The finitist may have no conception of function, because functions are transfinite objects.

Gist of Idea

If functions are transfinite objects, finitists can have no conception of them

Source

Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4)

Book Ref

-: 'Philosophia Mathematica' [-], p.237

A Reaction

He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given?

The 3 ideas from 'Review of Tait 'Provenance of Pure Reason''

13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]