Richness and Reflection

Philosophia Mathematica 24 (3):330-359 (2016)
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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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Author's Profile

Neil Barton
University of Oslo

References found in this work

Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.
What is Cantor's Continuum Problem?Kurt Gödel - 1947 - The American Mathematical Monthly 54 (9):515--525.

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