Dear all, our next speaker in the Philosophy of Science Colloquium organized by the Institute Vienna Circle is Sebastian G. Speitel (IVC Fellow), who will give a talk on March 6, 4.45-6.15 pm. All are welcome! ---------------------------------------------------------------------------------------- Philosophy of Science Colloquium TALK: Sebastian G. Speitel (IVC Fellow) Mathematical Determinacy Philosophy of Science Colloquium The Institute Vienna Circle holds a Philosophy of Science Colloquium with talks by our present fellows. Date: 06/03/2025 Time: 16h45 Venue: New Institute Building (NIG), Universitätsstraße 7, 1010 Wien, HS 3A Abstract: The existence of non-standard models of important mathematical theories, such as first-order Peano-Arithmetic, threatens to undermine the claim of the moderate mathematical realist that non-mysterious access to mathematical structures is possible on the basis of our best mathematical theories. The move to frameworks stronger than FOL to articulate ‘better’ versions of these theories is denied to the moderate realist on the grounds that it merely shifts the indeterminacy ‘one level up’ into the meta-theory by — illegitimately, — assuming determinacy of the notions needed to formulate such logics. In this talk I want to outline the beginnings of a response to the determinacy challenge facing the moderate mathematical realist. I argue that the unique determinability of notions that enable categorical characterizations of important mathematical structures provides grounds for claiming naturalistically acceptable access to these structures, sufficient to resolve the determinacy challenge. I will illustrate the idea by showing how the mathematical realist may achieve arithmetical determinacy, and discuss ways to extend this approach to richer mathematical theories.