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2 ideas
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 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. |