Speaker: Hannes Leitgeb (LMU Munich)
Date and Time: Thursday, February 24th 2022, 16:30-18:00, Amsterdam time.
Venue: online. Recording available – click here.
Title: A Finitistic Semantics for Mathematics
Abstract.
Is mathematics (arithmetic, analysis, set theory,…) committed to the existence of infinitely many objects? The aim of my talk will be to argue the answer is: No.
For that purpose, I will introduce a new semantics (“role semantics“) according to which mathematical statements can be understood as having only finite ontological commitments. I will assess the semantics, show that its properties are similar to those of standard Tarskian semantics, and hence conclude that there is not much disadvantage in interpreting mathematics by the new semantics. At the same time, the finitistic role semantics does not come with any epistemological benefit: if anything, our epistemic access to finitistic models of mathematics is mediated by standard infinitary ones.