Logics and Their Galaxies

Part of the Studies in Universal Logic book series (SUL)


This chapter introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated with each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic. We explore some consequences of these developments.


Universal logic · Antilogics · Counterlogics · Galaxies 

Mathematics Subject Classification (2000)

Primary 03B22 · Secondary 03A99 



Thanks to Arnold Koslow and Graham Priest for discussions concerning ideas of this paper.


  1. 1.
    Beziau, J.-Y.: Universal logic. In: Childers, T., Majer, O. (eds.) Logica’94 – Proceedings of the 8th International Symposium, Prague, pp. 73–93 (1994) Google Scholar
  2. 2.
    Beziau, J.-Y.: From consequence operator to universal logic: a survey of general abstract logic. In: Log. Univers.: Towards a General Theory of Logics. Birkhäuser (2005) Google Scholar
  3. 3.
    Beziau, J.-Y, Buchsbaum, A.: Let us be antilogical: Anti-classical logic as a logic. In: Moktefi, A., Moretti, A., Schang, F. (eds.) Let Us be Logical. College Publication, London (2013) Google Scholar
  4. 4.
    Bohn, E.: Must there be a top level? Philos. Q. 59(235), 193–201 (2009) CrossRefGoogle Scholar
  5. 5.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001) CrossRefzbMATHGoogle Scholar
  6. 6.
    CAICEDO, X.: A formal system for the non-theorems of the propositional calculus. Notre Dame J. Form. Log. 19, 147–151 (1978) CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Fine, K.: Tense and reality. In: Modality and Tense – Philosophical Papers. Clarendon Press, Oxford (2005) CrossRefGoogle Scholar
  8. 8.
    Gabbay, D, Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-dimensional Modal Logics: Theory and Applications. Studies in Logic and the Foundations of Mathematics. Elsevier, Amsterdam (2003) Google Scholar
  9. 9.
    Hitchcock, C.: Prevention, preemption, and the principle of sufficient reason. Philos. Rev. 116(4), 495–532 (2007) CrossRefGoogle Scholar
  10. 10.
    Lewis, D.: Causation. J. Philos. 70, 556–567 (1973) CrossRefGoogle Scholar
  11. 11.
    Lewis, D.: On the Plurality of Words. Blackwell, Oxford (1986) Google Scholar
  12. 12.
    Łukasiewicz, J.: Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic. Clarendon Press, Oxford (1951) zbMATHGoogle Scholar
  13. 13.
    Martin, C.B.: Dispositions and conditionals. Philos. Q. 44, 1–8 (1994) CrossRefGoogle Scholar
  14. 14.
    Moretti, A.: Geometry for modalities? Yes: through n-opposition theory. In: Aspects of Universal Logic, vol. 17, p. 102–145. CdRS Université de Neuchâtel, Neuchâtel (2004) Google Scholar
  15. 15.
    PRIEST, G.: In Contradiction. Clarendon Press, Oxford (2006) CrossRefGoogle Scholar
  16. 16.
    Stalnaker, R.: Mere Possibilities. Princeton University Press, Princeton (2012) Google Scholar
  17. 17.
    Słupecki, J., Bryll, G., Wybraniec-Skardowska, U.: Theory of Rejected Propositions I. Stud. Log. 29, 75–123 (1971) CrossRefzbMATHGoogle Scholar
  18. 18.
    Skura, T.: A Refutation Theory. Log. Univers. 3, 293–302 (2009) CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Stone, M.: The theory of representation for Boolean algebras. Trans. Am. Math. Soc. 40, 37–111 (1936) Google Scholar
  20. 20.
    Tarski, A.: Remarks on fundamental concepts of the methodology of mathematics. In: Universal Logic: An Anthology, translated by R. Purdy and J. Zygmunt. Birkhäuser (2010), Original: 1929 Google Scholar
  21. 21.
    Varzi, A.: Complementary logics for classical propositional languages. Kriterion 4, 20–24 (1992) Google Scholar
  22. 22.
    Williamson, T.: Modal Logics as Metaphysics. Oxford University Press, Oxford (2013) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Campus Universitário Darcy Ribeiro, Instituto de Ciências Humanas, Departamento de Filosofia, ICC Ala NorteUniversidade de BrasíliaBrasiliaBrazil
  2. 2.Departamento de FilosofiaUniversidade de São PauloSão PauloBrazil

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