Coin flips, Spinning Tops and the Continuum Hypothesis

SEP 28, 2020 | 4:15 PM TO 6:15 PM



The Graduate Center


September 28, 2020: 4:15 PM-6:15 PM




Logic and Metaphysics


The Logic and Metaphysics Workshop will meet on September 28th from 4:15-6:15 (NY time) via Zoom for a talk by Daniel Hoek (Virginia Tech).

Title: Coin flips, Spinning Tops and the Continuum Hypothesis

Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here:

This event is part of The Graduate Center's Philosophy Program.