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Full Idea
If a man had a positive idea of infinite, either duration or space, he could add two infinities together; nay, make one Infinite infinity bigger than another, absurdities too gross to be confuted.
Gist of Idea
If there were real infinities, you could add two together, which is ridiculous
Source
John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 2.17.20)
Book Ref
Locke,John: 'Essay Concerning Human Understanding', ed/tr. Nidditch,P.H. [OUP 1979], p.222
A Reaction
A beautifully heartfelt objection to everything Cantor stood for, two hundred years before Cantor got round to it.
| 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] |