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18518 | Infinite numbers are qualitatively different - they are not just very large numbers [Heil] |
Full Idea: It is a mistake to think of an infinite number as a very large number. Infinite numbers differ qualitatively from finite numbers. | |
From: John Heil (The Universe as We Find It [2012], 03.5) | |
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. |