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

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 Jim Franklin and A/Prof Norman Wildberger of the School of Mathematics and Statistics, Faculty of Science, UNSW, debate the pros and cons of `infinity' in mathematics. Along the way we'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?'

As for questions at the end, we had lots of interesting ones. Perhaps people can ask them again in the comments section, and we can try to answer them! And thanks to Nguyen Le for videoing.