Talk:Potential infinity

This article sorely lacks a lead paragraph, as well as sources. Katzmik (talk) 14:43, 21 September 2008 (UTC)

Ohmygod. This is just dreadful. Perhaps it should be merged with Completed infinity, as these are complementary notions. If it is to be retained at all, his will have to be majorly redone. First reference to be consulted is
 * Anglin 1994, Mathematics: A Concise History and Philosophy, Springer-Verlag, NY, ISBN: 0-387-94280-7.

Here are two pertainent quotes:
 * "Throughout the history of philosophy, there has been a dbate as to whether there is anything 'actually' infinite in some respect. Everyone agress that the set of natural numbers is at least 'potentially' infinite, in the sense that, no matter how far you count, you might count further. Howeever, thinkers divide on the question of whether the set of natural numbers exists as a completed totality, asn an 'atually' infinite object. ¶ Anaximander [610-540 B.C.] opened this discussion by coming out in favor of the infinite ..." (Anglin 1994:14)


 * "Aristotle and the Infinite. ¶ Aristotle was a staunch finitist. He rejected infinite sets and infinite lines (Physics 206b, 266b, 207; Metaphysics 1084a). He rejected infinitesimals (Physics 266b)" [etc -- this goes on for a page and a half]. "As a replacement for the infinie, Aristotle put forward the idea of the potentially infinite [etc -- for another paragraph]. (Anglin 1994:64-65)

BillWvbailey (talk) 21:02, 24 September 2008 (UTC)