Studia Logica

, Volume 104, Issue 2, pp 209–234 | Cite as

On the Minimal Non-Fregean Grzegorczyk Logic

  • Joanna Golińska-Pilarek
Open Access


The paper concerns Grzegorczyk’s non-Fregean logics that are intended to be a formal representation of the equimeaning relation defined on descriptions. We argue that the main Grzegorczyk logics discussed in the literature are too strong and we propose a new logical system, \({\mathsf{MGL}}\), which satisfies Grzegorczyk’s fundamental requirements. We present a sound and complete semantics for \({\mathsf{MGL}}\) and we prove that it is decidable. Finally, we show that many non-classical logics are extensions of \({\mathsf{MGL}}\), which makes it a generic non-Fregean logic.


Non-Fregean logic Descriptive equivalence Equimeaning Extensionality 


  1. 1.
    Golińska-Pilarek, J. and T. Huuskonen, Logic of descriptions. A new approach to the foundations of mathematics and science, Studies in Logic, Grammar and Rhetoric 40:63–94, 2012.Google Scholar
  2. 2.
    Golińska-Pilarek, J. and T. Huuskonen, Grzegorczyk’s non-Fregean logics and their formal properties, Submitted to the book Applications of Formal Philosophy, 2015.Google Scholar
  3. 3.
    Grzegorczyk A.: Filozofia logiki i formalna logika niesymplifikacyjna. Zagadnienia Naukoznawstwa 47(4), 445–450 (2012)Google Scholar
  4. 4.
    Suszko R.: Non-Fregean logic and theories. Analele Universitatii Bucuresti, Acta Logica 11, 105–125 (1968)Google Scholar
  5. 5.
    Suszko R.: Semantics for the sentential calculus with identity. Studia Logica 28, 77–81 (1971)CrossRefGoogle Scholar
  6. 6.
    Suszko, R., Abolition of the Fregean axiom, in R. Parikh (ed.), Logic Colloquium: Symposium on Logic held at Boston, 1972–73, vol. 453 of Lecture Notes in Mathematics, Springer, Heidelberg, 1975, pp. 169–239.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Institute of PhilosophyUniversity of WarsawWarsawPoland

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