Venturi, Giorgio (2019) Genericity and Arbitrariness. [Preprint]

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Abstract

We compare the notions of genericity and arbitrariness on the basis of the realist import of the method of forcing. We argue that Cohen's Theorem, similarly to Cantor's Theorem, can be considered a meta-theoretical argument in favor of the existence of uncountable collections. Then we discuss the effects of this meta-theoretical perspective on Skolem's Paradox. We conclude discussing how the connection between arbitrariness and genericity can offer arguments in favor of Forcing Axioms.

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Item Type:	Preprint
Creators:	Creators Email ORCID Venturi, Giorgio gio.venturi@gmail.com 0000-0001-9089-4340
Keywords:	Set theory, arbitrary sets, genericity, forcing, Skolem Paradox, Cantor's Theorem, Cohen's Theorem, Axiom of Choice, Forcing Axioms
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology General Issues > Realism/Anti-realism
Depositing User:	Dr. Giorgio Venturi
Date Deposited:	25 Aug 2019 14:07
Last Modified:	25 Aug 2019 14:07
Item ID:	16367
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology General Issues > Realism/Anti-realism
Date:	August 2019
URI:	https://philsci-archive.pitt.edu/id/eprint/16367

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