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Journal of Philosophical Logic

, Volume 45, Issue 1, pp 1–23 | Cite as

Term Models for Abstraction Principles

  • Leon Horsten
  • Øystein Linnebo
Article

Abstract

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.

Keywords

Abstraction Logicism Groundedness Term model Frege Paradox Dummett 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.University of BristolBristolEngland
  2. 2.University of OsloOsloNorway

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