Philosophia Mathematica 24 (3):330-359 (2016)

Authors
Neil Barton
Universität Konstanz
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.
Keywords philosophy of mathematics  foundations of mathematics  set theory  reflection principle
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Reprint years 2016
DOI 10.1093/philmat/nkv036
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References found in this work BETA

Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.
The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Journal of Symbolic Logic. Oxford University Press. pp. 176--187.

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