PhilSci Archive

Genericity and Arbitrariness

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

[img]
Preview
Text
Genericity and arbitrariness.pdf

Download (319kB) | Preview

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.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
Creators:
CreatorsEmailORCID
Venturi, Giorgiogio.venturi@gmail.com0000-0001-9089-4340
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: http://philsci-archive.pitt.edu/id/eprint/16367

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item