Journal of Philosophical Logic

, Volume 34, Issue 2, pp 193–206

Number of Extensions of Non-Fregean Logics



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.


denotation non-classical propositional logic sense sentential calculus with identity situation 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institute of PhilosophyUniversity of WarsawWarszawaPoland
  2. 2.Department of MathematicsUniversity of HelsinkiFinland

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