Abstract
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.
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References
Badesa C.: The Birth of Model Theory. Löwenheim’s Theorem in the Frame of the Theory of Relatives. Princeton University Press, Princeton (2004)
Beth, E.: Formal Methods: An Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logic. Reidel, Dordrecht (1962)
Cann R.: Formal Semantics. An Introduction. Cambridge University Press, Cambridge (1993)
Hintikka, J.: On the development of the model-theoretic viewpoint in logical theory. Synthese 77, 1–36 (1988) (reprinted in [6, pp. 104–139]).
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])
Kusch M.: Language as Calculus vs. Language as Universal Medium. A Study on Husserl, Heidegger and Gadamer. Kluwer, Dordrecht (1989)
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))
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)
Tarski, A.: The concept of truth in formalized languages. In: Tarski, A. (ed.) Logic, Semantics, Metamathematics, pp. 152–277. Clarendon Press, Oxford (1956)
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))
Wittgenstein, L.: Tractatus Logico-Philosophicus. Translated by C. K. Ogden. Kegan, Trench, Trubner, London (1922)
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))
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))
Hintikka, J.: Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieth-Century Philosophy. Kluwer, Dorrecht (1997)
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Woleński, J. Logic as Calculus Versus Logic as Language, Language as Calculus Versus Language as Universal Medium, and Syntax Versus Semantics. Log. Univers. 6, 587–596 (2012). https://doi.org/10.1007/s11787-012-0059-4
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DOI: https://doi.org/10.1007/s11787-012-0059-4