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Term Models for Abstraction Principles

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2016

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Linnebo, Øystein

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https://doi.org/10.1007/s10992-015-9344-z
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Journal of Philosophical Logic. Springer. 2016, 45(1), pp. 1-23. ISSN 0022-3611. eISSN 1573-0433. Available under: doi: 10.1007/s10992-015-9344-z

Zusammenfassung

Kripke’s notion of groundedness plays a central role in many responses to the semantic paradoxes. Can the notion of groundedness be brought to bear on the paradoxes that arise in connection with abstraction principles? We explore a version of grounded abstraction whereby term models are built up in a ‘grounded’ manner. The results are mixed. Our method solves a problem concerning circularity and yields a ‘grounded’ model for the predicative theory based on Frege’s Basic Law V. However, the method is poorly behaved unless the background second-order logic is predicative.

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100 Philosophie

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ISO 690HORSTEN, Leon, Øystein LINNEBO, 2016. Term Models for Abstraction Principles. In: Journal of Philosophical Logic. Springer. 2016, 45(1), pp. 1-23. ISSN 0022-3611. eISSN 1573-0433. Available under: doi: 10.1007/s10992-015-9344-z
BibTex
@article{Horsten2016-02Model-48680,
  year={2016},
  doi={10.1007/s10992-015-9344-z},
  title={Term Models for Abstraction Principles},
  number={1},
  volume={45},
  issn={0022-3611},
  journal={Journal of Philosophical Logic},
  pages={1--23},
  author={Horsten, Leon and Linnebo, Øystein}
}
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