Sorin Bangu: Wittgenstein on the infinite and Cantor’s diagonal proof

Tuesday March 4 2025 @11:30 (CET)
Sala B, Edificio de Humanidades, UNED & online

Abstract
Georg Cantor is widely credited with founding transfinite set theory at the end of the 19th century. A major branch of modern mathematics today, one of its central results is (now) called ‘Cantor’s theorem’, stating that there are more real numbers than natural numbers – hence infinity comes in (at least) two sizes, a truly epochal discovery. However, his well-known proof of this result is disarmingly simple, such that even a child could follow it, as Wittgenstein noted. This aspect made it suspect to him, and in the late 1930s he devoted several (in)famous disparaging, but unfortunately rather opaque, remarks to it (some of them collected in Part II of his ‘Remarks on the Foundations of Mathematics’ i.e., RFM II). The aim of this talk is to unpack several of these thoughts, since (I believe) the secondary literature on this topic is still inconclusive. In essence, I will propose a way of reading Wittgenstein on the infinite and Cantor’s proof, reading which (I claim) renders his RFM II remarks compatible with the non-revisionist line he takes in ‘Philosophical Investigations’.

Bio
Sorin Bangu is full professor at the Department of Philosophy of University of Bergen (Norway). Before joining the University of Bergen, he held positions in at Univ. of Cambridge and Univ. of Illinois at Urbana-Champaign. His research lies at the intersection of the philosophy of mathematics and the philosophy of physics, and their histories. He has long-standing interests in the history of analytic philosophy (in Quine and Wittgenstein) and has published extensively in these areas.