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.

  • 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 – 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 (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 6:36

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).

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