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  1. Term Models for Abstraction Principles.Leon Horsten & Øystein Linnebo - 2016 - Journal of Philosophical Logic 45 (1):1-23.
    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 (...)
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  • Frege on Indirect Proof.Ivan Welty - 2011 - History and Philosophy of Logic 32 (3):283-290.
    Frege's account of indirect proof has been thought to be problematic. This thought seems to rest on the supposition that some notion of logical consequence ? which Frege did not have ? is indispensable for a satisfactory account of indirect proof. It is not so. Frege's account is no less workable than the account predominant today. Indeed, Frege's account may be best understood as a restatement of the latter, although from a higher order point of view. I argue that this (...)
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  • The Status of Value-Ranges in the Argument of Basic Laws of Arithmetic I §10.Thomas Lockhart - 2017 - History and Philosophy of Logic 38 (4):345-363.
    Frege's concern in GGI §10 is neither with the epistemological issue of how we come to know about value-ranges, nor with the semantic-metaphysical issue of whether we have said enough about such objects in order to ensure that any kind of reference to them is possible. The problem which occupies Frege in GGI §10 is the general problem according to which we ‘cannot yet decide’, for any arbitrary function, what value ‘’ has if ‘ℵ’ is a canonical value-range name. This (...)
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  • The Semantics of Value-Range Names and Frege’s Proof of Referentiality.Matthias Schirn - 2018 - Review of Symbolic Logic 11 (2):224-278.
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  • Polymorphism and the Obstinate Circularity of Second Order Logic: A Victims’ Tale.Paolo Pistone - 2018 - Bulletin of Symbolic Logic 24 (1):1-52.
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