more from Hilary Putnam

Single Idea 18200

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit.


The continuum is aleph-0

Gist of Idea

Very large sets should be studied in an 'if-then' spirit


Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics

Book Reference

Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.105

A Reaction

Quine says the large sets should be regarded as 'uninterpreted'.

Related Idea

Idea 18198 Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]