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

Preview

Text output(7).pdf Download (320kB) | Preview

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.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Preprint
Creators:	Creators Email ORCID Barton, Neil bartonna@gmail.com 0000-0002-3637-1730
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:	https://philsci-archive.pitt.edu/id/eprint/14634

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item