Timeline for In what ways did Leibniz's philosophy foresee modern mathematics?
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| Nov 10, 2011 at 5:17 | vote | accept | CommunityBot | ||
| Nov 8, 2011 at 19:41 | comment | added | Pete L. Clark | ...Anyway, if nothing else, probably my first comment corroborates this: if you say "infinitesimal" to a mathematician and don't elaborate, she is probably going to think in terms of the infinitesimal calculus, not the related philosophical ideas. It would seem somehow more in the spirit of a question to explain what Leibnizian monads have to do with contemporary mathematics... | |
| Nov 8, 2011 at 19:39 | comment | added | Pete L. Clark | Hmm. Well first of all I agree with Todd: "purely mathematical" is sticky today; it is absolutely anachronistic when applied to 17th century natural philosophers. Still I would say that "infinitesimal" is a mathematical idea which is related to other philosophical ideals of Leibniz. At the risk of oversimplifying something I myself don't understand very well, it seems that monad is the philosophical idea whereas infinitesimal is the mathematical one.... | |
| Nov 8, 2011 at 19:34 | comment | added | Todd Trimble | It should be added that back in those days, there weren't very sharp distinctions made between mathematics, physics, and philosophy of the sort we would recognize today. Indeed, 'natural philosophy' was often what we might call physics today. So it's hard to say that Leibniz himself would have thought of infinitesimals as purely mathematical, and it wouldn't be surprising if they figured in his presumably more philosophical tracts. | |
| Nov 8, 2011 at 19:26 | comment | added | Margaret Friedland | My memory does not serve me very well; Leibniz's idea of infinitesimals precedes his theory of monads. The relation is complicated. See e.g.philosophy.leeds.ac.uk/GMR/articles/infinitesimals.html | |
| Nov 8, 2011 at 19:26 | comment | added | Jacques Carette | @Pete: I have read a lot of Leibniz in the last year, and yes, just about everything he did was done within a philosophical context. While we can discern and extract purely mathematical ideas out of his writings, he did not. | |
| Nov 8, 2011 at 19:14 | comment | added | Margaret Friedland | @Jacques: My pleasure. @Pete: Some would indeed claim philosophical origin of infinitesimals and relate them to monads. This may be a stretch, but at any rate Leibniz commented on them extensively, so they became a part of his philosophy. He may have held different views at different times, though; see e.g. muse.jhu.edu/journals/perspectives_on_science/v006/… | |
| Nov 8, 2011 at 18:53 | comment | added | Pete L. Clark | Are you actually claiming that Leibniz's infinitesimals was a philosophical idea? Without wanting to fully raise the (of course very thorny) question of what exactly constitutes a "philosophical idea", let just express a little skepticism on this point. I would rather say that Leibniz introduced infinitesimals as a purely mathematical idea, albeit one that he could not adequately formalize or justify. Moreover I would summarize Robinson's great (and certainly wholly mathematical!) achievement as demonstrating that Leibniz's tentative mathematical idea was mathematically sound. | |
| Nov 8, 2011 at 18:11 | comment | added | Jacques Carette | +1 for mentioning Candide (and I would +1 as well for the actual content of the answer, but I can't). | |
| Nov 8, 2011 at 17:58 | history | edited | Margaret Friedland | CC BY-SA 3.0 |
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| Nov 8, 2011 at 14:46 | history | edited | Margaret Friedland | CC BY-SA 3.0 |
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| Nov 8, 2011 at 14:36 | history | answered | Margaret Friedland | CC BY-SA 3.0 |