Infinity: does it exist?? A debate with James Franklin and N J Wildberger

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• published: 28 Sep 2014
• views: 21577

Infinity has long been a contentious issue in mathematics, and in philosophy. Does it exist? How can we know? What about our computers, that only work with finite objects and procedures? Doesn't mathematics require infinite sets to establish analysis? What about different approaches to the philosophy of mathematics--can they guide us? In this friendly debate, Prof James Franklin and A/Prof Norman Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW, debate the question of `infinity' in mathematics. Along the way you'll hear about Jim's new book: `An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure', published this year by Palgrave MacMillan. Unfortunately, the microphone could not pick up audience questions and responses very well. The correct answer to Norman's question at the end of the game he described was given by Roberto Riedig: `any number you want'! As for this interesting game itself, Norman seems to remember getting the idea from Wolfgang Mueckenheim, who also ventures into heretical waters: see for example his paper "Physical Constraints of Numbers", Proceedings of the First International Symposium of Mathematics and its Connections to the Arts and Sciences, A. Beckmann, C. Michelsen, B. Sriraman (eds.), Franzbecker, Berlin 2005, p. 134 - 141. For those interested in this kind of non-standard position, they can also look for Norman's paper: `Set Theory: Should you Believe?' You can also check out my blog entry at http://njwildberger.com/2015/11/26/infinity-religion-for-pure-mathematicians/. Thanks to Nguyen Le for videoing. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .