Actual infinite vs. Potential infinite

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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

Posted 2014-06-10T18:36:00.410

Reputation: 41

Question was closed 2014-06-11T21:34:43.443

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 – 2014-06-10T18:44:54.220

I've already done it. But i would appreciate some guidelines from someone with experience in investigation about this problem. – Evangelion045 – 2014-06-10T18:48:18.313

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you can try with : AW Moore, The Infinite (1990).

– Mauro ALLEGRANZA – 2014-06-10T21:06:39.327

What is actual and potential infinity? I got lost. – Asphir Dom – 2014-06-10T23:26:30.620

@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 – 2014-06-11T06:36:13.303

I'm just looking for bibliography about that topic. Why is it too broad to answer in a few paragraphs? Mauro did. – Evangelion045 – 2014-06-16T00:44:54.300

Answers

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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

Posted 2014-06-10T18:36:00.410

Reputation: 33 575