Alexander Pruss's Blog

I wish one could formulate and defend a version of explanatory finitism, roughly saying that nothing has infinitely many explanations or an ...

Arithmetical truth-value realists hold that any proposition in the language of arithmetic has a fully determined truth value. Arithmetical t...

For years I have thought the finite to be mysterious, and needs something metaphysical like divine illumination or causal finitism to pick i...

Truth-value realism about (first-order) arithmetic is the thesis that for any first-order logic sentence in the language of arithmetic (i.e....

Eliminative structuralist philosophers of mathematics insist that what mathematicians study is structures rather than specific realizations...

Say that a structure N that has a distinguished element 0, a unary function S , and binary operations + and ⋅ is a causal Robinson Arithme...

In his famous “Mathematics is Megethology” , Lewis gives a brilliant reduction of set theory to mereology and plural quantification. A centr...

Suppose I want to figure out a good approximation to the eigenvalues of a certain Hamiltonian involving a moderately large number of Coulomb...

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...

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

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...

I think it is sometimes said that it is anachronistic to attribute to the ancient Greeks the discovery that the square root of two is irrati...

The usual examples of a posteriori necessities are identities between kinds and objects under two descriptions, at least one of which invol...

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

Our physics is based on the real numbers. Physicists use the real numbers all over the place: quantum mechanics takes place in a complex Hil...

Assume the correct physics has precise particle positions (similar questions can be asked in other contexts, but the particle position conte...

I’ve come to be impressed by the idea that where there is apparent arbitrariness, there is probably contingency in the vicinity. The earth ...

Videos of my 2019 Wilde Lectures in Natural Theology and Comparative Religion at Oxford’s Oriel College are now available online . Here are...

Here is an interesting metaphysical thesis about mathematics: Σ 1 0 alethic Platonism. According to Σ 1 0 alethic Platonism, every sentenc...