Logica Universalis

, Volume 6, Issue 3–4, pp 587–596 | Cite as

Logic as Calculus Versus Logic as Language, Language as Calculus Versus Language as Universal Medium, and Syntax Versus Semantics

  • Jan Woleński


This paper discusses the distinctions indicated in its title. It is argued that the distinction between syntax and semantics is much more important for the present situation in logic than other distinctions. In particular, doing formal syntax and formal semantics requires the use of an informal melanguage based on ordinary mathematics.

Mathematics Subject Classification



Formal informal metalogic interpretation model 


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  1. 1.
    Badesa C.: The Birth of Model Theory. Löwenheim’s Theorem in the Frame of the Theory of Relatives. Princeton University Press, Princeton (2004)Google Scholar
  2. 2.
    Beth, E.: Formal Methods: An Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logic. Reidel, Dordrecht (1962)Google Scholar
  3. 3.
    Cann R.: Formal Semantics. An Introduction. Cambridge University Press, Cambridge (1993)CrossRefGoogle Scholar
  4. 4.
    Hintikka, J.: On the development of the model-theoretic viewpoint in logical theory. Synthese 77, 1–36 (1988) (reprinted in [6, pp. 104–139]).Google Scholar
  5. 5.
    Hintikka, J.: Is truth ineffable? In: Scardona, N. (ed.) Les Formes Actuelles du Vrai: Entretiens de Palermo, pp. 89–120. Enhiridion, Palermo (1989) (reprinted in [6, pp. 20–45])Google Scholar
  6. 6.
    Kusch M.: Language as Calculus vs. Language as Universal Medium. A Study on Husserl, Heidegger and Gadamer. Kluwer, Dordrecht (1989)Google Scholar
  7. 7.
    Post, E.: Introduction to a general theory of elementary propositions. Am. J. Math. 43, 163–185 (reprinted in E. Post: Solvability, Provability, Definability: The Collected Works of Emil L. Post, pp. 21–43. Birkhäuser, Basel (1994))Google Scholar
  8. 8.
    Sieg, W.: Toward finitist proof theory. In: Hendricks, V.F., Pedersen, S.A, Jørgensen, K.F. (eds.) Proof Theory. History and Philosophical Significance, pp. 95–114. Kluwer, Dordrecht (2000)Google Scholar
  9. 9.
    Tarski, A.: The concept of truth in formalized languages. In: Tarski, A. (ed.) Logic, Semantics, Metamathematics, pp. 152–277. Clarendon Press, Oxford (1956)Google Scholar
  10. 10.
    Van Heijenoort, J.: Logic as calculus and logic as language. Synthese 17, 324–330 (1967) (reprinted in J. van Heijenoort, Selected Essays, pp. 11–16. Bibliopolis, Naples (1985))Google Scholar
  11. 11.
    Wittgenstein, L.: Tractatus Logico-Philosophicus. Translated by C. K. Ogden. Kegan, Trench, Trubner, London (1922)Google Scholar
  12. 12.
    Woleński, J.: Husserl and the development of formal semantics. Philos. Sci. l.4, 151–158 (1997) (reprinted in J. Woleński: Essays in the History of Logic and Logical Philosophy, pp. 110–114. Jagiellonian University Press, Kraków (1999))Google Scholar
  13. 13.
    Woleński, J.: What is formal in formal semantics? Dialectica 58, 427–436 (2004) (reprinted in J. Woleński: Essays on Logic and Its Applications in Philosophy, pp. 81–90. Peter Lang, Frankfurt am Main (2011))Google Scholar
  14. 14.
    Hintikka, J.: Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieth-Century Philosophy. Kluwer, Dorrecht (1997)Google Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Sucha BeskidzkaPoland

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