Carnap's Contribution to Tarski's Truth.
DOI:
https://doi.org/10.15173/jhap.v3i10.1514Abstract
In his seminal work “The Concept of Truth in Formalized Languages” (1933), Alfred Tarski showed how to construct a formally correct and materially adequate definition of true sentence for certain formalized languages. These results have, eventually, been accepted and applauded by philosophers and logicians nearly in unison. Its Postscript, written two years later, however, has given rise to a considerable amount of controversy. There is an ongoing debate on what Tarski really said in the postscript. These discussions often regard Tarski as putatively changing his logical framework from type theory to settheory.
In what follows, we will compare the original results with those presented two years later. After a brief outline of Carnap’s program in The Logical Syntax of Language we will determine its significance for Tarski’s final results.
References
Awodey, S. and A.W. Carus, 2009. “From Wittgenstein’s Prison to the Boundless Ocean: Carnap’s Dream of Logical Syntax.” In Wagner (2009), pp. 79–106.
Betti, A., 2008. “Polish Axiomatics and its Truth: On Tarski’s Leśniewskian Background and the Adjukiewicz Connection.” In New Essays on Tarski and Philosophy, edited by D. Patterson, pp. 44–72. Oxford: Oxford University Press.
Carnap, R., 1934. Logische Syntax der Sprache. Vienna: Springer. Translated as Carnap (1937).
------, 1937. The Logical Syntax of Language. London: Kegan Paul, Trench, Trubner & Co. Ltd. A translation of Carnap (1934) by A. Smeaton.
------, 1963. “Intellectual Autobiography.” In The Philosophy of Rudolf Carnap, edited by P.A. Schlipp, pp. 3–84. La Salle, IL: Open Court.
Coffa, A., 1987. “Carnap, Tarski and the Search for Truth.” Noûs 21: 547–572.
Coquand,T., 2010.“Type Theory.”Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/type-theory/ (accessed February 20, 2014).
Creath, R., 1999.“Carnap’s Move to Semantics: Gains and Losses.” In Woleński and Köhler (1999), pp. 65–76.
Davidson, D., 1984. Inquiries into Truth and Interpretation. Oxford: Oxford University Press.
de Rouilhan, P., 1998. “Tarski et l’université de la logique: Remarques sur le post-scriptum au ‘Wahrheitsbegriff’.”In Le formalisme en question: Le tournant des annés 30, edited by F. Nef and D. Vernant, pp. 85–102. Paris: Vrin, Problèmes et controverses.
Feferman, S., 2002.“Conceptual Analysis of Semantical Notions.”Stanford Encyclopedia of Philosophy. http://math.stanford.edu/~feferman/papers/conceptanalysis.pdf (accessed April 20, 2014).
Ferreirós, J., 2007. Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics. Basel: Birkhäuser Verlag AG, second revised ed.
Field, H., 2008. Saving Truth from Paradox. Oxford: Oxford University Press.
Friedman, M., 1999.Reconsidering Logical Positivism.Cambridge: Cambridge University Press.
Frost-Arnold, G., 2004.“Was Tarski’s Theory of Truth Motivated by Physicalism?”History and Philosophy of Logic 25: 265–280.
Gómez-Torrente, M., 2004. “The Indef i nability of Truth in the ‘Wahrheitsbegriff’.” Annals of Pure and Applied Logic 126: 27–34.
-----, 2011.“Alfred Tarski.”Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/tarski/ (accessed February 20, 2014).
Gruber, M., 2013. “Tarski, Blow by Blow.” PhD Thesis, University of Salzburg.
Gupta, A. and N. Belnap, 1993. The Revision Theory of Truth. Cambridge, MA: MIT Press.
Horwich, P., 1998. Truth. Oxford: Oxford University Press.
Jadacki, J., ed., 2003. Alfred Tarski: dedukcja i semantyka (déduction et sémantique). Warsaw: Wydawnictwo Naukowe Semper.
Kripke, S., 1975. “Outline of a Theory of Truth.” The Journal of
Philosophy 72: 690–716.
Leśniewski, S., 1929.“Grundzüge eines neuen Systems der Grundlagen der Mathematik.” Fundamenta Mathematicae 14: 1–81.
Loeb, I., 2014. “Towards Transfinite Type Theory: Rereading Tarski’s Wahrheitsbegriff.” Synthese 191: 2281–2299.
Mormann, T., 2000. Rudolf Carnap. Munich: Verlag.
Nowaczyk, A., 2003.“Co naprawdę powiedział Tarski o prawdzie w roku 1933?” In Jadacki (2003), pp. 61–76.
Patterson, D., 2012. Alfred Tarski: Philosophy of Language and Logic. Basingstoke: Palgrave Macmillan.
Quine, W.V., 1963. Set Theory and Its Logic. Cambridge, MA: Harvard University Press.
Ray, G., 2005. “On the Matter of Essential Richness.” Journal of Philosophical Logic 34: 433–457.
Schurz, G., 1999.“Tarski and Carnap on Logical Truth – or: What Is Genuine Logic?” In Woleński and Köhler (1999), pp. 77–94.
Sundholm, B.G., 2003. “Tarski and Leśniewski on Languages with Meaning versus Languages without Use: A 60th Birthday Provocation for Jan Woleński.” In Philosophy and Logic: In Search of the Polish Tradition, edited by J. Hintikka, T. Czarnecki, K. Kijania-Packet, T. Placek, and A. Rojszczak, pp. 109–128. Dordrecht: Kluwer.
Tarski, A., 1933.“Pojęcie prawdy w językach nauk dedukcyjnych.” Reprinted in Zygmunt, J., ed., Tarski, A. Pisma logiczno-filozoficzne. Tom 1. Prawda. Warsaw: Wydawnictwo Naukowe PWN, 1995, pp. 3–172.
-----, 1935.“Der Wahrheitsbegriff in den formalisierten Sprachen.” Studia Philosophica 1: 261–405.
------, 1936. “The Concept of Logical Consequence.” Reprinted in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 2nd ed. Indianapolis, Hackett Publishing Company, 2006, pp. 408–420.
------, 1944. “The Semantic Conception of Truth and the Foundations of Semantics.”Philosophy and Phenomenological Research 4: 341–376.
------, 2006. “The Concept of Truth in Formalized Languages.” Reprinted in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 2nd ed. Indianapolis, Hackett Publishing Company, 2006, pp. 152–278.
Uebel, T., 2009. “Carnap’s Logical Syntax in the Context of the Vienna Circle.” In Wagner (2009), pp. 53–76.
Wagner, P., ed., 2009. Carnap’s Logical Syntax of Language. Basingstoke: Palgrave Macmillan.
Woleński, Jan, 1999. “Semantic Revolution – Rudolf Carnap, Kurt Gödel, Alfred Tarski.” In Wole´ nski and Köhler (1999), pp. 1–16.
------, 2003.“Języki sformalizowane a prawda.”In Jadacki (2003), pp. 67–76.
Woleński, Jan and Eckehart Köhler, eds., 1999. Alfred Tarski and the Vienna Circle: Austro-Polish Connections in Logical Empiricism. Dordrecht: Kluwer Academic Publishers.
Betti, A., 2008. “Polish Axiomatics and its Truth: On Tarski’s Leśniewskian Background and the Adjukiewicz Connection.” In New Essays on Tarski and Philosophy, edited by D. Patterson, pp. 44–72. Oxford: Oxford University Press.
Carnap, R., 1934. Logische Syntax der Sprache. Vienna: Springer. Translated as Carnap (1937).
------, 1937. The Logical Syntax of Language. London: Kegan Paul, Trench, Trubner & Co. Ltd. A translation of Carnap (1934) by A. Smeaton.
------, 1963. “Intellectual Autobiography.” In The Philosophy of Rudolf Carnap, edited by P.A. Schlipp, pp. 3–84. La Salle, IL: Open Court.
Coffa, A., 1987. “Carnap, Tarski and the Search for Truth.” Noûs 21: 547–572.
Coquand,T., 2010.“Type Theory.”Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/type-theory/ (accessed February 20, 2014).
Creath, R., 1999.“Carnap’s Move to Semantics: Gains and Losses.” In Woleński and Köhler (1999), pp. 65–76.
Davidson, D., 1984. Inquiries into Truth and Interpretation. Oxford: Oxford University Press.
de Rouilhan, P., 1998. “Tarski et l’université de la logique: Remarques sur le post-scriptum au ‘Wahrheitsbegriff’.”In Le formalisme en question: Le tournant des annés 30, edited by F. Nef and D. Vernant, pp. 85–102. Paris: Vrin, Problèmes et controverses.
Feferman, S., 2002.“Conceptual Analysis of Semantical Notions.”Stanford Encyclopedia of Philosophy. http://math.stanford.edu/~feferman/papers/conceptanalysis.pdf (accessed April 20, 2014).
Ferreirós, J., 2007. Labyrinth of Thought. A History of Set Theory and Its Role in Modern Mathematics. Basel: Birkhäuser Verlag AG, second revised ed.
Field, H., 2008. Saving Truth from Paradox. Oxford: Oxford University Press.
Friedman, M., 1999.Reconsidering Logical Positivism.Cambridge: Cambridge University Press.
Frost-Arnold, G., 2004.“Was Tarski’s Theory of Truth Motivated by Physicalism?”History and Philosophy of Logic 25: 265–280.
Gómez-Torrente, M., 2004. “The Indef i nability of Truth in the ‘Wahrheitsbegriff’.” Annals of Pure and Applied Logic 126: 27–34.
-----, 2011.“Alfred Tarski.”Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/tarski/ (accessed February 20, 2014).
Gruber, M., 2013. “Tarski, Blow by Blow.” PhD Thesis, University of Salzburg.
Gupta, A. and N. Belnap, 1993. The Revision Theory of Truth. Cambridge, MA: MIT Press.
Horwich, P., 1998. Truth. Oxford: Oxford University Press.
Jadacki, J., ed., 2003. Alfred Tarski: dedukcja i semantyka (déduction et sémantique). Warsaw: Wydawnictwo Naukowe Semper.
Kripke, S., 1975. “Outline of a Theory of Truth.” The Journal of
Philosophy 72: 690–716.
Leśniewski, S., 1929.“Grundzüge eines neuen Systems der Grundlagen der Mathematik.” Fundamenta Mathematicae 14: 1–81.
Loeb, I., 2014. “Towards Transfinite Type Theory: Rereading Tarski’s Wahrheitsbegriff.” Synthese 191: 2281–2299.
Mormann, T., 2000. Rudolf Carnap. Munich: Verlag.
Nowaczyk, A., 2003.“Co naprawdę powiedział Tarski o prawdzie w roku 1933?” In Jadacki (2003), pp. 61–76.
Patterson, D., 2012. Alfred Tarski: Philosophy of Language and Logic. Basingstoke: Palgrave Macmillan.
Quine, W.V., 1963. Set Theory and Its Logic. Cambridge, MA: Harvard University Press.
Ray, G., 2005. “On the Matter of Essential Richness.” Journal of Philosophical Logic 34: 433–457.
Schurz, G., 1999.“Tarski and Carnap on Logical Truth – or: What Is Genuine Logic?” In Woleński and Köhler (1999), pp. 77–94.
Sundholm, B.G., 2003. “Tarski and Leśniewski on Languages with Meaning versus Languages without Use: A 60th Birthday Provocation for Jan Woleński.” In Philosophy and Logic: In Search of the Polish Tradition, edited by J. Hintikka, T. Czarnecki, K. Kijania-Packet, T. Placek, and A. Rojszczak, pp. 109–128. Dordrecht: Kluwer.
Tarski, A., 1933.“Pojęcie prawdy w językach nauk dedukcyjnych.” Reprinted in Zygmunt, J., ed., Tarski, A. Pisma logiczno-filozoficzne. Tom 1. Prawda. Warsaw: Wydawnictwo Naukowe PWN, 1995, pp. 3–172.
-----, 1935.“Der Wahrheitsbegriff in den formalisierten Sprachen.” Studia Philosophica 1: 261–405.
------, 1936. “The Concept of Logical Consequence.” Reprinted in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 2nd ed. Indianapolis, Hackett Publishing Company, 2006, pp. 408–420.
------, 1944. “The Semantic Conception of Truth and the Foundations of Semantics.”Philosophy and Phenomenological Research 4: 341–376.
------, 2006. “The Concept of Truth in Formalized Languages.” Reprinted in Logic, Semantics, Metamathematics. Papers from 1923 to 1938, 2nd ed. Indianapolis, Hackett Publishing Company, 2006, pp. 152–278.
Uebel, T., 2009. “Carnap’s Logical Syntax in the Context of the Vienna Circle.” In Wagner (2009), pp. 53–76.
Wagner, P., ed., 2009. Carnap’s Logical Syntax of Language. Basingstoke: Palgrave Macmillan.
Woleński, Jan, 1999. “Semantic Revolution – Rudolf Carnap, Kurt Gödel, Alfred Tarski.” In Wole´ nski and Köhler (1999), pp. 1–16.
------, 2003.“Języki sformalizowane a prawda.”In Jadacki (2003), pp. 67–76.
Woleński, Jan and Eckehart Köhler, eds., 1999. Alfred Tarski and the Vienna Circle: Austro-Polish Connections in Logical Empiricism. Dordrecht: Kluwer Academic Publishers.
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