Alexander Pruss's Blog

It is sometimes claimed that arbitrary mereological fusions and plural quantification are a metaphysical free lunch, just a new way of talki...

Some people don’t like Cantorian ways of comparing the sizes of sets because they want to have a “whole is bigger than the (proper) part” pr...

Non-measurable events are ones to which the probability function in the situation assigns no probability. Philosophically speaking, non-meas...

Some people want to be able to compare the sizes of sets in a way that respects the principle: If A is a proper subset of B , then A  ≤  ...

Suppose we have an infinite sequence of independent and fair coins. A betting portfolio is a finite list of subsets of the space of outcome...

Consider a countably infinite sequence of fair and independent coin tosses. Given the Axiom of Choice, there is no finitely additive probabi...

Suppose that a point z will be uniformly randomly chosen on the surface of a sphere S and you are asked to place bets as to which set ...

Paper posted here (forthcoming in Synthese ). Among goodies in the paper is a proof that the order extension principle (even in a weak fo...

For a totally ordered field K , say a hyperreal one, write x ≈ y (and say that they are approximately equal) provided that x − y is 0 ...

Earlier I claimed that even without the Axiom of Choice, the proof of the Banach-Tarski Paradox yields paradoxical results, so th...