I'm looking for bibliography about the problem of Actual infinite vs. Potential infinite. I would appreciate information about papers or books treating this problem deeply, philosophical and historical remarks.
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If you're just looking for a bibliography, can't you use Google to find some references? I'd start with SEP and Wikipedia. plato.stanford.edu/entries/aristotle-mathematics– user4894Jun 10, 2014 at 18:44
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I've already done it. But i would appreciate some guidelines from someone with experience in investigation about this problem.– Evangelion045Jun 10, 2014 at 18:48
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1you can try with : AW Moore, The Infinite (1990).– Mauro ALLEGRANZAJun 10, 2014 at 21:06
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What is actual and potential infinity? I got lost.– Asphir DomJun 10, 2014 at 23:26
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@Asphir Dom - The distinction traces back at least to Aristotle : the succession of natural numbers is fr sure potentially infinite, because for every number you can think of or state, you can always add +1 to it getting a bigegr one. Potential infinite means "unlimited possibility of iterating a process". Actual infinity is something (cosmos, God, alef_0) which is infinite and we assume that it is "really" existsing "all together" somewhere : in the real world, in the mind of God, in the platonic heaven ...– Mauro ALLEGRANZAJun 11, 2014 at 6:36
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1 Answer
You can start with Continuity and Infinitesimals with bibliography, both for the mathematical and the philosophical sides of the problem.
From the same author, you can find a book-lenght version of it : John Bell, The Continuous and the Infinitesimal in Mathematics and in Philosophy (2005).
In addition to AW Moore, The Infinite (1990), I suggest also Shaughan Lavine, Understanding the Infinite (1994).
answered Jun 11, 2014 at 7:06
