Alexander Pruss's Blog

Assume Peano Arithmetic (PA) is consistent. Then it can’t prove its own consistency. Thus, there is a model M of PA according to which PA i...

In the Republic , Plato says philosophy education shouldn’t start until age 30. I’ve long worried about Plato’s concern about providing youn...

Let T 0 be ZFC. Let T n be T n  − 1 plus the claim Con( T n  − 1 ) that T n  − 1 is consistent. Let T ω be the union of all the T n fo...

According to the principle of existential inertia: If x exists at t 1 and t 2  >  t 1 and there is no cause of x ’s not existing at ...

A simplified version of Goedel’s first incompleteness theorem (it’s really just a special case of Tarski’s indefinability of truth) goes lik...

A year or two ago, some juvenile alligators moved into our area or were moved in (we are right on the edge of the alligator zone in Waco). I...

I will give an argument for causal finitism from a premise I don’t accept: Necessary Arithmetical Alethic Incompleteness (NAAI): Necessari...

The most common argument that mathematical truth is not provability uses Tarski’s indefinability of truth theorem or Goedel’s first incomple...

To promise something, I need to communicate something to you. What is that thing that I need to communicate to you? To a first approximation...

In some games like Mafia, uttering falsehoods is a part of the game mechanic. These falsehoods are no more lies than falsehoods uttered by a...

I have for a long time inclined towards ifthenism in mathematics: the idea that mathematics discovers truths of the form " If these ax...

In the previous post, I offered a criticism of defining logical consequence by means of proofs. A more precise way to put my criticism would...

There are two main accounts of ψ being a logical consequence of ϕ : Inferentialist: there is a proof from ϕ to ψ Model theoretic: every...

There is a certain kind of symmetry between praise and blame. We praise someone who incurs a cost to themselves by going above and beyond ob...

It seems very plausible that for any specific Turing machine M there is a fact of the matter about whether M would halt. We can just imagi...