2013 seminar talk: Does set theory refute Platonism?

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


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.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.