Intuitionism

In this short talk I (P. Pablo Rivas Robledo) will try to provide a concise and self-contained introduction to Non-deterministic semantics for modal logic, which are sometimes dubbed as ‘semantics for modal logic without possible worlds’ or ’truth-tables for modal logic’. We will start from the weakest (non-normal) modal logic and recover significant fragments of the modal cube. To do so, we will use standard tools of the literature, namely Coniglio’s snapshots and Gräz’s algorithm to recover necessitation. I will finish by mentioning some recent applications of the semantic framework to non-classical modal logic and intuitionistic logic. Please bring something to write and where to do it, so that you can see the magic for yourselves.

For this session, our dear classmate Edoardo will tell us all about Martin-Löf’s impact on the philosophy of math and logic. The aim is to cover the topic in general, but for a text of focus we have the first two chapters of Per Martin-Löf’s On the Meanings of the Logical Constants and the Justifications of the Logical Laws.

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.

We will join for a Zoom tea where we will discuss constructive and non-constructive proofs.

We ask participants, although not necessary, to have a constructive and a non-constructive proof of a theorem they find interesting or illustrative, along with a relevant philosophical input.).