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Higher-Order Abstraction Principles

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2015

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https://doi.org/10.1002/tht3.182
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Thought : A Journal of Philosophy. Wiley-Blackwell. 2015, 4(4), pp. 228-236. eISSN 2161-2234. Available under: doi: 10.1002/tht3.182

Zusammenfassung

I extend theorems due to Roy Cook (2009) on third‐ and higher‐order versions of abstraction principles and discuss the philosophical importance of results of this type. Cook demonstrated that the satisfiability of certain higher‐order analogues of Hume's Principle is independent of ZFC. I show that similar analogues of Boolos's new v and Cook's own ordinal abstraction principle soap are not satisfiable at all. I argue, however, that these results do not tell significantly against the second‐order versions of these principles.

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Fachgebiet (DDC)
100 Philosophie

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abstraction principles, higher-order logic, type theory, neologicism

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ISO 690MOUNT, Beau Madison, 2015. Higher-Order Abstraction Principles. In: Thought : A Journal of Philosophy. Wiley-Blackwell. 2015, 4(4), pp. 228-236. eISSN 2161-2234. Available under: doi: 10.1002/tht3.182
BibTex
@article{Mount2015Highe-52664,
  year={2015},
  doi={10.1002/tht3.182},
  title={Higher-Order Abstraction Principles},
  number={4},
  volume={4},
  journal={Thought : A Journal of Philosophy},
  pages={228--236},
  author={Mount, Beau Madison}
}
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