Alexander Pruss's Blog

Suppose infinitely many people independently roll a fair die. Before they get to see the result, they will need to guess whether the die sho...

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

Let's round out Axiom of Choice Week. :-) It’s occurred to me that there is a somewhat pleasant way to integrate the Axioms of Separati...

Assume classical mereology. Then for any formula that has a satisfier, there is a fusion of all of its satisfiers. More precisely, if ϕ is ...

Suppose that the set theory of our world is a Solovay model, where we don’t have the Axiom of Choice (AC), and where every subset of the rea...

The axioms of ZFC set theory can be divided into (a) the positive axioms, that say that a set with certain properties exist, and (b) two neg...

Here’s a claim that turns out to be equivalent to the Axiom of Choice: Given any non-empty set Ω and a collection M of [0,∞] -valued fin...

About a decade ago, I offered a counterexample to the following domination principle: Given two wagers A and B , if in every state B is...

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...

Here is a tension in some recent work of mine. In Chapter 6 of Infinity, Causation, and Paradox , I argue that (a) the Axiom of Choice for c...

I think the following is a consequence of a hyperreal variant of the Horn-Tarski extension theorem for measures on boolean algebras: Clai...

I think I can give an example of something that has no reasonable (numerical) epistemic probability. Consider Goedel’s Axiom of Constructib...

Here’s a super-weird philosophy of infinity idea. Maybe: The countable Axiom of Choice is false, There are sets that are infinite but not...

Here’s an interesting reason to accept the existence of non-measurable sets (and hence of whatever weak version of the Axiom of Choice that ...

Consider algorithms for sequentially placing a coin each day either in a heads or a tails configuration depending on how coins were placed o...

For every initial ordinal k , there is a possible world with exactly k photons. But there is no set of all initial ordinals (proof: suppos...

In my previous post , I showed that given a backwards infinite sequence of coin tosses, there is a simple strategy leveraging data about inf...

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

The mathematics that supposes the Axiom of Choice is more beautiful than the mathematics that does not. So, the Axiom of Choice is probably ...

All the main puzzles that follow from the Axiom of Choice (AC)--nonmeasurable sets, Banach-Taski and guessing future coin tosses--need only ...