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Number of Extensions of Non-Fregean Logics

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Abstract

We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF.

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Authors and Affiliations

  1. Institute of Philosophy, University of Warsaw, Krakowskie Przedmieście 3, 00-047, Warszawa, Poland

    Joanna Golińska-Pilarek

  2. Department of Mathematics, University of Helsinki, P.O. Box 68, FIN-00014, Finland

    Taneli Huuskonen

Authors
  1. Joanna Golińska-Pilarek
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  2. Taneli Huuskonen
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Correspondence to Joanna Golińska-Pilarek.

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Golińska-Pilarek, J., Huuskonen, T. Number of Extensions of Non-Fregean Logics. J Philos Logic 34, 193–206 (2005). https://doi.org/10.1007/s10992-004-6366-3

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  • DOI: https://doi.org/10.1007/s10992-004-6366-3

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