Term Models for Abstraction Principles

Oystein Linnebo, Leon F M Horsten

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
273 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Philosophical Logic
Volume45
Issue number1
Early online date10 Feb 2015
DOIs
Publication statusPublished - Feb 2016

Keywords

  • Abstraction
  • Logicism
  • Groundedness
  • Term model
  • Frege
  • Paradox
  • Dummett

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