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Full Idea
Every potential infinity seems to suggest an actual infinity - e.g. generating successors suggests they are really all there already; cutting the line suggests that the point where the cut is made is already in place.
Gist of Idea
Infinite cuts and successors seems to suggest an actual infinity there waiting for us
Source
Stephen Read (Thinking About Logic [1995], Ch.8)
Book Ref
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.236
A Reaction
Finding a new gambit in chess suggests it was there waiting for us, but we obviously invented chess. Daft.
| 12489 | If there were real infinities, you could add two together, which is ridiculous [Locke] |
| 19406 | I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz] |
| 13190 | I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz] |
| 10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| 15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |