Publikation:

Hume's Principle, Bad Company, and the Axiom of Choice

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2023

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Shapiro, Stewart

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The Review of Symbolic Logic. Cambridge University Press. 2023, 16(4), pp. 1158-1176. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020322000144

Zusammenfassung

One prominent criticism of the abstractionist program is the so-called Bad Company objection. The complaint is that abstraction principles cannot in general be a legitimate way to introduce mathematical theories, since some of them are inconsistent. The most notorious example, of course, is Frege’s Basic Law V. A common response to the objection suggests that an abstraction principle can be used to legitimately introduce a mathematical theory precisely when it is stable: when it can be made true on all sufficiently large domains. In this paper, we raise a worry for this response to the Bad Company objection. We argue, perhaps surprisingly, that it requires very strong assumptions about the range of the second-order quantifiers; assumptions that the abstractionist should reject.

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100 Philosophie

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ISO 690ROBERTS, Sam, Stewart SHAPIRO, 2023. Hume's Principle, Bad Company, and the Axiom of Choice. In: The Review of Symbolic Logic. Cambridge University Press. 2023, 16(4), pp. 1158-1176. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020322000144
BibTex
@article{Roberts2023Humes-57720,
  year={2023},
  doi={10.1017/S1755020322000144},
  title={Hume's Principle, Bad Company, and the Axiom of Choice},
  number={4},
  volume={16},
  issn={1755-0203},
  journal={The Review of Symbolic Logic},
  pages={1158--1176},
  author={Roberts, Sam and Shapiro, Stewart}
}
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