Timeline for In what ways did Leibniz's philosophy foresee modern mathematics?
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| Nov 9, 2011 at 13:08 | history | edited | Charles Matthews | CC BY-SA 3.0 |
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| Nov 8, 2011 at 20:25 | comment | added | Sergey Melikhov | (cont'd) Indeed, while extensionality enters ZF, Leibniz law enters Martin-Lof type theory (mathoverflow.net/questions/28644/the-isomorphism-inference-rule/…) and the original version of Quine's New Foundations (see math.boisestate.edu/~holmes/holmes/define_equality.ps). By the way, results like Yoneda's lemma and the embedding of a vector space in its double dual may be seen as incarnations of Leibniz's law. | |
| Nov 8, 2011 at 20:06 | comment | added | Sergey Melikhov | "Leibniz law" (en.wikipedia.org/wiki/Identity_of_indiscernibles) and extensionality (en.wikipedia.org/wiki/Extensionality) are certainly related, but distinguished by some (ags.uni-sb.de/~cp/p/eq2.html) | |
| Nov 8, 2011 at 19:38 | comment | added | Jacques Carette | Maria Rosa Antognazza made the same point in her recent biography of Leibniz (an excellent read). Thanks for the Garber reference, I'll order that now. I have made several posts on MO regarding extensionality/intensionality, and indeed few people seemed to appreciate the subtle issues involved. | |
| Nov 8, 2011 at 19:10 | history | answered | Charles Matthews | CC BY-SA 3.0 |