The aim of this series of talks is to look at the traditional Dutch book arguments
and accuracy arguments for probabilism in the setting where there are infinitely many
propositions. The framework is one in which the propositions are rendered as elements
of a Boolean algebra, and in the case of accuracy arguments we’ll render talk of
the proximity of credences in terms of the notion of a Banach space from functional
analysis. The idea is to do the proofs in detail, and to introduce and review the
relevant concepts (Boolean algebras, Banach spaces) as we go along.
This series of talks is part of the C-ALPHA Seminar in Mathematical Philosophy. Walsh’s talks will last five sessions, beginning on Wednesday September 28 and ending on Wednesday October 26.