Timeline for Deleuzian finitism and Spinozian infinitism
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| Jun 17, 2020 at 8:34 | history | edited | CommunityBot |
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| Jun 10, 2015 at 21:54 | vote | accept | Mozibur Ullah | ||
| Dec 14, 2014 at 14:51 | answer | added | Jonathan Basile | timeline score: 2 | |
| Aug 19, 2014 at 23:06 | history | edited | Joseph Weissman♦ |
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| May 29, 2014 at 10:41 | comment | added | Mozibur Ullah | Your description of oega is fine as a defiition, but to find it, one requires the first axiom of infinity. Otherwise, at least formally, one cannot prove that exists. | |
| May 29, 2014 at 10:37 | comment | added | Mozibur Ullah | If by infinite one means only that which is not finite then omega or aleph-0 is surely infinite; but if by infinite one means that which has no greater, then this is untrue - we have omega+1 or aleph-1. One then sees that ZFC has an axiom of infinity, the first one in the large cardinal hierarchy. If one could prove that there is such a thing as a largest large cardinal, I would conjecture that with enough imagination and ingenuity, means would be found to transcend that confinement. | |
| May 29, 2014 at 10:31 | comment | added | Mozibur Ullah | I'm no expert either. But my intuition is to say yes. Actually, it turns out that the ordinals can have a canonical topology, so the notions of 'open' & 'closed' have formal meanings, as do other topological phenomena. But I think this isn't quite the notion of 'open' that you are using. I'd go back to the Aristotelian notions of actual & potential infinite, where he says the potential infinity obtains (open), but the actual infinity (closed) does not. Of course one has to understand infinite in a certain way. | |
| May 29, 2014 at 3:52 | comment | added | senderle | But the on the other hand there is no largest ordinal. Does that mean that the... class of all ordinals is "open"? I don't know the math here well enough to know whether open and closed are applicable concepts up there in the set theory stratosphere. | |
| May 29, 2014 at 3:47 | comment | added | senderle | Well -- perhaps. I definitely feel that recursion is a useful conceptual heuristic for understanding Deleuze's way of thinking, but I'm not sure that's enough. I'll turn this into a question: does the transfinite resist closure? That's vague, but I can't put it any better. If it does, then yes. Well, on first blush, that sounds as if the answer is no, because you could describe ω as the smallest set containing the empty set and closed under succession. | |
| May 29, 2014 at 0:25 | comment | added | Mozibur Ullah | @Senderle:Ok - it does seems like useful intuition. I haven't looked at that text: my understanding of Deleuze is slight, at best. Are you fingering Cantors transinfinite as an exemplar of a true infinite? | |
| May 28, 2014 at 23:57 | comment | added | senderle | @MoziburUllah, I'm afraid it's only a vague intuition, but I am thinking of Difference and Repetition, which I read ages and ages ago and only really half remember. | |
| May 28, 2014 at 23:56 | history | edited | Mozibur Ullah | CC BY-SA 3.0 |
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| May 28, 2014 at 23:49 | comment | added | Mozibur Ullah | @Senderle: that should be - why do you say that? But then Deleuze is the theoretician of la differance. I suppose that ight explain his interest in the differential calculus, except that understanding is analytic; whereas the modern understanding is synthetic - ie differential geometry - aka the tangent bundle and its development. | |
| May 28, 2014 at 23:15 | comment | added | Mozibur Ullah | @senderle: do you say that? I suspect that it is along the right lines - can one have an infinite without differentiation? One could, I think, if one goes back to Parmenides One. | |
| May 28, 2014 at 22:30 | comment | added | senderle | Without knowing half of a single thing about Spinoza, I would draw your attention to the phrases "the false infinite" and "the infinity of religion" -- neither of which necessarily suggests that there is no true infinity. I don't know Deleuze well but I get the sense that he would have condoned a conception of the infinite as (potentially) infinite differentiation. | |
| May 28, 2014 at 9:11 | history | edited | Mozibur Ullah | CC BY-SA 3.0 |
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| May 27, 2014 at 1:38 | history | tweeted | twitter.com/#!/StackPhilosophy/status/471103036329168897 | ||
| May 26, 2014 at 18:35 | history | edited | Mozibur Ullah | CC BY-SA 3.0 |
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| May 26, 2014 at 17:38 | history | asked | Mozibur Ullah | CC BY-SA 3.0 |