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Richness and Reflection

Barton, Neil (2016) Richness and Reflection. [Preprint]

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Abstract

A pervasive thought in contemporary Philosophy of Mathematics is that in order to justify reflection principles, one must hold Universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting Universism with a Zermelian form of Multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the Universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, the status of reflection principles as axioms is left open for the Zermelian.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
Keywords: reflection principle, set theory, multiversism
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Depositing User: Dr. Neil Barton
Date Deposited: 06 May 2018 15:31
Last Modified: 06 May 2018 15:31
Item ID: 14634
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: 2016
URI: http://philsci-archive.pitt.edu/id/eprint/14634

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