In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics. Springer Verlag (2016)

Giorgio Venturi
University of Campinas
In this article we analyze the method of forcing from a more philosophical perspective. After a brief presentation of this technique we outline some of its philosophical imports in connection with realism. We shall discuss some philosophical reactions to the invention of forcing, concentrating on Mostowski’s proposal of sharpening the notion of generic set. Then we will provide an overview of the notions of multiverse and the related philosophical debate on the foundations of set theory. In conclusion, we connect this modern debate and Mostowski’s proposal, suggesting a way to analyze the notion of genericity within the framework of a multiverse structure.
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DOI 10.1007/978-3-319-31644-4_12
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Ideal Objects for Set Theory.Santiago Jockwich, Sourav Tarafder & Giorgio Venturi - 2022 - Journal of Philosophical Logic 51 (3):583-602.

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