Term models for abstraction principles

• Autores: Leon Horsten, Oystein Linnebo
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 45, Nº. 1, 2016, págs. 1-23
• Idioma: inglés
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• Resumen

  • 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.