more from this thinker | more from this text
Full Idea
I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author.
Gist of Idea
I strongly believe in the actual infinite, which indicates the perfections of its author
Source
Gottfried Leibniz (Reply to Foucher [1693], p.99)
Book Ref
Leibniz,Gottfried: 'Leibniz Selections', ed/tr. Wiener,Philip P. [Scribners 1951], p.99
A Reaction
I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities.
| 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] |