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Abolition of the fregean axiom

  • Roman Suszko
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 453)

Keywords

Modal Logic Boolean Algebra Kripke Model Completeness Theorem Modal Algebra 
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Bibliography

  1. 1).
    Scott, D: On engendering an illusion of understanding, The Journal of Philosophy 68(1971), 787–807.CrossRefGoogle Scholar
  2. 2).
    Quine, W.V.: Comments, in Boston Studies in the Philosophy of Science. D. Reidel Publishing Co., Dordrecht, 1963, pp. 97–104.Google Scholar
  3. 3).
    Scott, D: Advice on Modal Logic, in Philosophical Problems in Logic, edited by K. Lambert, D. Reidel Publ. Comp. 1970, pp. 143–173.Google Scholar
  4. 4).
    Weyl, H: The Ghost of Modality, in Philosophical Essays in memory of E. Husserl, edited by M. Farbes, Harvard Univ. Press, 1940, reprinted by Greenwood Press, New York, 1956.Google Scholar
  5. 5).
    Church, A: Introduction to mathematical logic, Vol. I, Princeton, N.J. 1968.Google Scholar
  6. 6).
    Suszko, R: An Essay in the formal theory of extension and of intension, Studia Logica 20(1967), 7–34.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7).
    Bernays, P: Betrachtungen zum Sequenzekalkul, in contributions to Logic and Methodology in honor of I.M. Bochenski, edited by A.T. Tymieniecka in collaboration with Ch. Parsons, North Holland, Amsterdam 1965, pp. 1–44.Google Scholar
  8. 8).
    Los, J. & Suszko, R: Remarks on sentential logics, Proc. Neth. Akad. van Weten., Ser. A, 67(1958), 177–183.MathSciNetGoogle Scholar
  9. 9).
    Suszko, R: Identity connective and modality, Studia Logica 27(1971), 7–39.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10).
    Suszko, R: Non-Fregean Logic and Theories, Analele Universitatii Bucuresti, Acta Logica 9(1968), 105–125.Google Scholar
  11. 11).
    Bloom, S.L.: A completeness theorem for "Theories of Kind W", Studia Logica 27(1971), 43–55.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12).
    Quine, W.V.: From a Logical Point of View, Harvard Univ. Press, Cambridge, Mass., 1953.zbMATHGoogle Scholar
  13. 13).
    Suszko, R.: Quasi-Completeness in non-Fregean Logic, Studia Logica 29(1971), 7–14.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14).
    Bloom, S. & Suszko, R.: Semantics for the Sentential Calculus with Identity, Studia Logica 28(1971), 77–81.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15).
    __________: Investigations Into the Sentential Calculus with Identity, Notre Dame Journal of Formal Logic, 13(1972), 289–308.MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16).
    Suszko, R.: Sentential Calculus with Identity (SCI) and G-theories, an abstract to appear in The Journal of Symbolic Logic 36(1971).Google Scholar
  17. 17).
    ____: SCI and Modal Systems, an abstract to appear in The Journal of Symbolic Logic 37(1972).Google Scholar
  18. 18).
    Scroggs, S.J.: Extensions of the Lewis System S5, The Journal of Symbolic Logic 16(1951), 112–120MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19).
    Lewis, C.I., Langford, O.H.: Symbolic Logic, 2nd ed., Dover Publications, 1959.Google Scholar
  20. 20).
    Rasiowa, H., Sikorski, R.: The Mathematics of the Metamathematics, PWN Warsaw, 1963.Google Scholar
  21. 21).
    Kagan, J.D.: An Axiomatization of Topological Boolean Algebras to appear in Zeitschrift fur Mathematische Logik und Grandlagen der Mathematik.Google Scholar
  22. 22).
    McKinsey, J.C.C., Tarski, A.: The algebra of topology, Annals of Mathematics 45(1944), 141–191.MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23).
    Lemmon, E.J.: An extension algebra and the modal system T, Notre Dame Journal of Formal Logic 1(1960), 3–12.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24).
    Scott, D.: A Proof of Independence of the Continuum Hypothesis, Mathematical Systems Theory 1(1967), 89–111.MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25).
    Brown, D.J., Suszko, R.: Abstract Logics, Dissertationes Mathematicae, Vol. 102(1973).Google Scholar
  26. 26).
    Stupecki, J.: Uber die Regeln des Aussagenkalkuls, Studia Logica 1(1953), 19–40.MathSciNetCrossRefGoogle Scholar
  27. 27).
    Hiz, H.: Complete sentential calculus admitting extensions, Summer Institute of Symbolic Logic in 1957 at Cornell University, Vol. 2, 260–262.Google Scholar
  28. 28).
    Suszko, R.: Concerning the method of logical schemes, the notion of logical calculus and the role of consequence relations, Studia Logica II(1961), 185–214.MathSciNetCrossRefGoogle Scholar
  29. 29).
    Wojcicki, R.: Logical matrices adequate for structural sentential calculi, Bull., Acad. Polon. Sci. (Ser. Sci. Math. Astronom. Phys.) 17(1969), 333–335.MathSciNetzbMATHGoogle Scholar
  30. 30).
    Bloom, S.L., Brown, D.J., Suszko, R.: Some theorems on abstract logics, Algebra i Logika Sem. g(1970), 274–280.MathSciNetGoogle Scholar
  31. 31).
    Suszko, R.: Adequate models for the non-Fregean sentential calculus (SCI), in Logic, Language and Probability, edited by R.J. Bogdan and I. Niiniluoto, D. Reidel, Pub., (1973),pp. 49–54.Google Scholar
  32. 32).
    Bloom, S.L., Brown, D.J.: Classical abstract logics, in Dissertationes Mathematicae, Vol. 102(1973).Google Scholar
  33. 33).
    Los, J.: The algebraic treatment of the methodology of elementary deductive systems, Studia Logica 2(1955), 151–211.MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34).
    Los, J., Suszko, R.: On the extending of models II, Fundamenta Mathematicae 42(1955), 343–347.MathSciNetzbMATHGoogle Scholar
  35. 35).
    Hallen, S.: On the semantic non-completeness of certain Lewis calculi, the Journal of Symbolic Logic 16(1951), 127–129.MathSciNetCrossRefGoogle Scholar
  36. 36).
    Diamond, A.H.: Simplification of the Whitehead-Huntington set of postulates for the algebra of logic, Bulletin of the American Mathematical Society, Vol. 40 (1934), 599–601.MathSciNetCrossRefGoogle Scholar
  37. 37).
    Suszko, R., Zandarowska, W.: Lewis' systems S4 and S5 and the identity connective (in Polish), Studia Logica 29 (1971), 169–177.MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38).
    McKinsey, J.C., Tarski, A.: Some theorems about the Lewis and Heyting calculi, The Journal of Symbolic Logic 13(1948), 1–15.MathSciNetzbMATHCrossRefGoogle Scholar
  39. 39).
    McKinsey, J.C., Systems of modal logic which are not unreasonable in the sense of Hallden, The Journal of Symbolic Logic 18(1953) 109–113.MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40).
    Scroggs, S.J.: Extensions of the Lewis system S5, The Journal of Symbolic Logic 16(1951), 112–120.MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41).
    Wojcicki, R.: On reconstructability of classical propositional logic in intuitionistic logic, Bull. Acad. Polon. Sci. (Ser. Sci. Math. Astronom. Phys.) 18(1970), 421–422.MathSciNetzbMATHGoogle Scholar
  42. 42).
    Kripke, S.A.: Semantical considerations on modal logic, Acta Philosophica Phennica 16(1963), 83–94.MathSciNetzbMATHGoogle Scholar
  43. 43).
    Lemmon, E.J.: Algebraic semantics for modal logics, The Journal of Symbolic Logic 31(1966), 46–65 and 191–218.MathSciNetCrossRefGoogle Scholar
  44. 44).
    Makinson, D.C.: A generalisation of the concept of a relational model for modal logic, Theoria 36(1970), 331–335.MathSciNetCrossRefGoogle Scholar
  45. 45).
    Lemmon, E.J.: A note on Hallden-incompleteness, Notre Dame Journal of Formal Logic 7(1966), 296–300.MathSciNetzbMATHCrossRefGoogle Scholar
  46. 46).
    Cresswell, M.J.: Classical intensional logics, Theoria 36(1970), 347–372.MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47).
    Montagne, R.: Pragmatics in R. Klibansky ed., contemporary philosophy-la philosophie contemporaine, Florence 1968, 102–122.Google Scholar
  48. 48).
    _____: Universal grammer, Theoria 36, 1970, 373–398.MathSciNetCrossRefGoogle Scholar
  49. 49).
    Cresswell, M.J.: Functions of propositions, The Journal of Symbolic Logic 31(1966), 545–560.MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50).
    Suszko, R.: Reifikacja sytuacji (Reification of situations), Studia Filozoficzne 69(1971), 65–82.Google Scholar
  51. 51).
    _____: Ontology in the Tractatus of L. Wittgenstein, Notre Dame Journal of Formal Logic 9(1968), 7–33.MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52).
    _____: Consistency of some non-Fregean theory, Notices of A.M.S. 16(1969), abstract 664-23.Google Scholar
  53. 53).
    Prior, A.N.: Is the concept of referential opacity really necessary? Acta Philosophica Fennica 16(1963), 189–198.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1975

Authors and Affiliations

  • Roman Suszko

There are no affiliations available

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