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Richness and Reflection

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2016

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https://doi.org/10.1093/philmat/nkv036
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Philosophia Mathematica. Oxford University Press (OUP). 2016, 24(3), pp. 330-359. ISSN 0031-8019. eISSN 1744-6406. Available under: doi: 10.1093/philmat/nkv036

Zusammenfassung

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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100 Philosophie

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ISO 690BARTON, Neil, 2016. Richness and Reflection. In: Philosophia Mathematica. Oxford University Press (OUP). 2016, 24(3), pp. 330-359. ISSN 0031-8019. eISSN 1744-6406. Available under: doi: 10.1093/philmat/nkv036
BibTex
@article{Barton2016Richn-52677,
  year={2016},
  doi={10.1093/philmat/nkv036},
  title={Richness and Reflection},
  number={3},
  volume={24},
  issn={0031-8019},
  journal={Philosophia Mathematica},
  pages={330--359},
  author={Barton, Neil}
}
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