Alexander Pruss's Blog

Are general purpose LLMs useful to figuring things out in set theory? Here is a story about two experiences I recently had. Don’t worry abou...

I’ve been playing with the question of what if anything we can say with plural quantification that we can’t say with, say, sets and classes....

Imagine Alice claimed she could just see , with reliability, which unprovable large cardinal axioms are true. We would be initially sceptic...

Suppose that we embrace these intuitive theses about sets of natural numbers: If A is a proper subset of B , then B has more members tha...

Say that a set S is causally countable if and only if it is metaphysically possible for someone to causally think through all the items in ...

This probably won’t work out, but I’ve been thinking about the Cantor and Russell Paradoxes and proper classes and had this curious idea: Ma...

If the worries in this post work, then the argument in this one needs improvement. Suppose there are two groups of people, the A s and the...

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...

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  ≤  ...

The number of degrees of freedom in a system is the number of numerical parameters that need to be set to fully determine the system. Scient...

Here’s a curious tale about sets and possible worlds: What sets there are varies between metaphysically possible worlds and for any possible...

Some people don't want to say that there are just as many even natural numbers as natural numbers. But suppose that you and I will spend...

A lot of people find Cantor's discovery that there are different infinities paradoxical. To be honest, there are many counterintuitive t...

Some people think it is absurd to say, as Cantorian mathematics does, that there are no more real numbers from 0 to 100 than from 0 to 1. Bu...

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...

This result is probably known, and probably not optimal. A conditional probability function P is conglomerable provided that for any partit...

The bijection principle says that if we have two sets A and B and we can pair up all the objects of the two sets, then the the ...

The modal profile of an object tells us which worlds the object exists in and what it consists of in those worlds. The unrestricted moda...

The basic idea behind Leibniz's characteristique is that all concepts are generated out of simple concepts , and there are no non-t...

One of the Kolmogorov axioms of probability says that if A 1 , A 2 ,... is a countable sequence of disjoint sets, then P ( A 1 ∪ A 2...