  This paper presents and defends an argument that the continuum hypothesis is
false, based on considerations about objective chance and an old theorem due to
Banach and Kuratowski. 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.
Since it is possible to randomly pick out a point on a continuum, for instance
using a roulette wheel or by flipping a countable infinity of fair coins, it
follows, given the axioms of ZFC, that there are many different cardinalities
between countable infinity and the cardinality of the continuum.
