tag:blogger.com,1999:blog-2492055523235356445.post1352563965335578832..comments2021-01-25T04:04:14.374-08:00Comments on - the dance of reason: Aristotle and the infiniteSac State Philosophyhttp://www.blogger.com/profile/17963066908030437925noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2492055523235356445.post-44476192253034271602015-04-05T22:55:39.532-07:002015-04-05T22:55:39.532-07:00Randy, that’s an interesting thought about Aristot...Randy, that’s an interesting thought about Aristotle. He was a great genius, but it is difficult to know what he’d say if he were to read my post that is based upon 2,200 years of subsequent analysis of his ideas and progress beyond them. If I had to pick two ancient Greeks who would have been most likely to appreciate the need to change their minds due to subsequent progress over the next two millennia, I would pick Aristotle and Archimedes. Aristotle would have been attracted to the constructivist feature of Cantor’s diagonalization proof that some infinite sets are smaller than others, but Archimedes probably would have been more likely than Aristotle to accept Cantor’s actual infinite sets and the calculus of Leibniz and Newton. Aristotle lived at a time when there was no coherent concept of zero or decimal. It took until the beginning of the 20th century to achieve a solid foundation to these or other notions we now believe are needed for fruitful mathematical physics--such as instantaneous speed, convergence of an infinite series, and continuity of a path. If Aristotle were to hold on to his preference for avoiding new technical terms and making do with common sense terms, then he would find today’s mathematics and physics to be repugnant. Bradley Dowdenhttps://www.blogger.com/profile/03398822652849338607noreply@blogger.comtag:blogger.com,1999:blog-2492055523235356445.post-39493397316510590562015-04-05T16:43:02.107-07:002015-04-05T16:43:02.107-07:00Brad, thanks very much for this interesting post. ...Brad, thanks very much for this interesting post. How do you think Aristotle would have received Cantor's diagonalisation proof? Would it have blown his mind? I ask because in some ways at least it actually seems to meet Aristotle's constructivist requirements. Of course, given it's reliance on decimal fractions, maybe this isn't a coherent question.G. Randolph Mayeshttps://www.blogger.com/profile/18285281186698499962noreply@blogger.com