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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 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. ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at   / njwildberger   Your support would be much appreciated. Here are the Insights into Mathematics Playlists:    • MathHistory: A course in the History ...      • WildTrig: Intro to Rational Trigonometry      • Math Foundations      • Wild Linear Algebra      • Famous Math Problems      • Box Arithmetic      • Elementary Mathematics (K-6) Explained      • Year9Maths      • Ancient Mathematics      • Wild West Banking      • Sociology and Pure Mathematics      • Sociology and Pure Physics      • Old Babylonian Mathematics      • Probability and Statistics: an introd...      • Boole's Logic and Circuit Analysis      • Universal Hyperbolic Geometry      • Differential Geometry      • Algebraic Topology      • MathSeminars      • Playing Go      • Diffusion Symmetry: A bridge between ...   Here are the Wild Egg Maths Playlists (some available only to Members!)    • Algebraic Calculus One      • Classical to Quantum (Members only)      • Algebraic Calculus Two      • Advice for mathematics exploration (M...      • Solving Polynomial Equations (Members...      • The Hexagrammum Mysticum (Members only)      • Algebraic Calculus and dCB curves (Me...      • Dynamics on Graphs (Members only)      • Плейлист      • Triangle Geometry      • Explorations with q-series (Members o...      • Six: An elementary course in Pure Mat...      • Maxel Inverses and Orthogonal Polynom...   ************************