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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.

Evangelion045
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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. http://plato.stanford.edu/entries/aristotle-mathematics/ – user4894 Jun 10 '14 at 18:44
  • I've already done it. But i would appreciate some guidelines from someone with experience in investigation about this problem. – Evangelion045 Jun 10 '14 at 18:48
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    you can try with : AW Moore, [The Infinite](http://www.amazon.com/Infinite-Problems-Philosophy-W-Moore/dp/0415252857/ref=sr_1_1?s=books&ie=UTF8&qid=1402434380&sr=1-1&keywords=AW+Moore+The+Infinite) (1990). – Mauro ALLEGRANZA Jun 10 '14 at 21:06
  • What is actual and potential infinity? I got lost. – Asphir Dom Jun 10 '14 at 23:26
  • @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 ALLEGRANZA Jun 11 '14 at 06:36
  • I'm just looking for bibliography about that topic. Why is it too broad to answer in a few paragraphs? Mauro did. – Evangelion045 Jun 16 '14 at 00:44

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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).

Mauro ALLEGRANZA
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