Journal of Philosophical Logic 45 (1):1-23 (2016)

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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DOI 10.1007/s10992-015-9344-z
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References found in this work BETA

Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
The Limits of Abstraction.Kit Fine - 2002 - Oxford University Press.
Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
Reading Frege's Grundgesetze.Richard Heck - 2012 - Oxford University Press.

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Unified Grounding.Casper Hansen - 2016 - Erkenntnis 81 (5):993-1010.

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