more from John Heil

Single Idea 18518

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite]

Full Idea

It is a mistake to think of an infinite number as a very large number. Infinite numbers differ qualitatively from finite numbers.

Gist of Idea

Infinite numbers are qualitatively different - they are not just very large numbers


John Heil (The Universe as We Find It [2012], 03.5)

Book Reference

Heil,John: 'The Universe as We Find It' [OUP 2012], p.43

A Reaction

He cites Dedekind's idea that a proper subset of an infinite number can match one-one with the number. Respectable numbers don't behave in this disgraceful fashion. This should be on the wall of every seminar on philosophy of mathematics.