# 2013 seminar talk: Does set theory refute Platonism?

Talk held by Claudio Ternullo (KGRC) at the KGRC seminar on 2013-01-24.

### Abstract

Platonism is an influential and well-established conception of mathematics and mathematical practice,
which states that the axioms of mathematics *refer* to an independently existing realm of mathematical entities.

In particular, set-theoretic platonism entails the view that the axioms of set theory refer to an independently
existing realm of objects (the *universe of sets*) and that, given any reasonably formulated set-theoretic
statement φ, φ has a *definite* truth-value.

In my talk, I will address the question of whether there any sufficient grounds to advocate platonism in view of
contemporary set theory. In particular, the *truth-value indeterminacy* connected to the independence phenomenon
in ZFC and its extensions does not seem to validate platonists’ epistemic optimism concerning our ability to have
access to *unique* truths.

I will be particularly concerned with Gödel’s platonism and its ontological and epistemological implications, but I also intend to pay attention to several alternative formulations which are deemed to belong to the big family of realism in mathematics. Naturalism, full-blooded platonism, extreme platonism, conceptual realism will also be taken into account. My aim is to show that they may not perform better than Gödel’s conception.