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Antireductionism and Ordinals

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2019

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https://doi.org/10.1093/philmat/nky025
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Philosophia Mathematica. Oxford University Press (OUP). 2019, 27(1), pp. 105-124. ISSN 0031-8019. eISSN 1744-6406. Available under: doi: 10.1093/philmat/nky025

Zusammenfassung

I develop a novel argument against the claim that ordinals are sets. In contrast to Benacerraf’s antireductionist argument, I make no use of covert epistemic assumptions. Instead, my argument uses considerations of ontological dependence. I draw on the datum that sets depend immediately and asymmetrically on their elements and argue that this datum is incompatible with reductionism, given plausible assumptions about the dependence profile of ordinals. In addition, I show that a structurally similar argument can be made against the claim that cardinals are sets.

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100 Philosophie

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ISO 690MOUNT, Beau Madison, 2019. Antireductionism and Ordinals. In: Philosophia Mathematica. Oxford University Press (OUP). 2019, 27(1), pp. 105-124. ISSN 0031-8019. eISSN 1744-6406. Available under: doi: 10.1093/philmat/nky025
BibTex
@article{Mount2019Antir-52657,
  year={2019},
  doi={10.1093/philmat/nky025},
  title={Antireductionism and Ordinals},
  number={1},
  volume={27},
  issn={0031-8019},
  journal={Philosophia Mathematica},
  pages={105--124},
  author={Mount, Beau Madison}
}
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