Truth

The PhiMath reading group is back for the academic year 2025/2026! We kick off with William Tait’s compelling exposition of the tension between Truth and Proof in Mathematics. Are mathematical proofs constructed or discovered by means of a proof? In the decade-long debate between constructivist and platonists, Tait defends Platonism by attacking some of Dummett’s main claims in favour of intuitionism. By adopting a similar approach towards the relaionship between language and reality as Dummet’s, he aims to downsize the accusations intuitionists wage against mathematical realists, arguing that proofs are merely representations of mathematical truth. The issues Tait brings up in this paper are extremely engaging for Intuitionists and Platonists alike, so come plenty and take part in the discussion!

This time our classmates, Matteo and Josje, will presenet Panu Raatikainen’s Conceptions of truth in intuitionism.

We often summarize the intuitionist notion of truth as “truth as provability”, which marks a fundamental difference with the classical logicians. But in doing so, we overlook the fact that there are multiple competing conceptions of truth within intuitionism itself. Raatikainen presents a systematic overview of these different accounts, ranging from actualist to possibilist, and ultimately offers a critique of each, putting into question about the coherence of the intuitionist framework as a whole.