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Ontological Reductions of First Order Models (Alfredo Freire)

The Logic and Metaphysics Workshop will meet on October 22nd from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Alfredo Freire (Campinas).

Title: Ontological Reductions of First Order Models

Abstract: Since the discovery of the Loweinheim-Skolem theorem, it has been largely held that there is no purely formal way of fixing a model for any first order theory. Because of this, many have focused on having a relative account of models, establishing the expressive power of one model in its ability to internalize models for other theories. One can, for instance, define a plurality of models for PA from a given model for ZF, and this may be understood as evidence for the ontology of arithmetics being reducible to the ontology of set theory. In this presentation, I argue that a close attention to what it means to reduce an ontology shows that methods of reduction are generally not neutral and make it possible for weaker models to reduce stronger ones. For this, I analyze the known model-theoretical reduction of NBG into ZF proved by Novak, showing that a more demanding method makes it impossible for ZF to internalize NBG. We finish this presentation by showing how this view, together with some technical results, provide a positive account in defense of the multiversalist perspective on set theory.

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