Skip to main content
Log in

Carnapian and Tarskian semantics

Synthese Aims and scope Submit manuscript

Abstract

Many papers have been devoted to the semantic turn Carnap took in the late 1930s after Tarski had explained to him his method for defining truth and his work on the establishment of scientific semantics. Commentators have often argued that the major turn in Carnap’s approach to languages had already been taken in the Logical Syntax of Language, but they have usually assumed that Carnap was happy to subsequently follow Tarski and adopt Tarskian semantics. In this paper, it is argued that this assumption needs to be qualified and that Carnap was actually far from following Tarski when he decided to complement his syntactic method with a semantic one. Carnap and Tarski had different goals, divergent programs, and dissenting views on truth and semantics. After exploring several possible methods for the explication of logical concepts such as L-truth and L-implication, Carnap opted for definitions based on concepts he had found in Wittgenstein’s Tractatus and Waismann’s work on a logical interpretation of probability. Carnap’s reasons for taking a semantic turn are to be understood in the context of his principle of tolerance. He first hoped he could use Tarski’s technique to recover in the semantic setting the completeness result he had tried to establish in the Logical Syntax. His eventual adoption of non-Tarskian semantics can be accounted for by his program of a logical analysis of science—including empirical science—and his ambition to elaborate a unified logical framework for deductive, inductive, and modal logic, and for explicating analyticity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Notes

  1. LSL” from now on, unless a distinction needs to be made between the German original and the English translation of 1937.

  2. A brief summary of Carnap’s technique is given in Niiniluoto (2003, pp. 5–6).

  3. See Carnap (1942, p. vii).

  4. Another place where the issue is touched upon is a series of conversations on logic, mathematics, science, and especially on finitism, that Carnap, Tarski, Quine, and others had at Harvard during the academic year 1940–1941. The notes Carnap took during these conversations have been preserved and they have recently been translated, published, and studied in Frost-Arnold (2013). Mancosu (2005) also provides an important analysis of these notes. Although the main topics discussed in these notes are finitism, nominalism, and the language of science, issues related to the semantic method are mentioned at some points, such as the relationship between the notions of state of affairs and model. In the whole, these notes also help us have a better understanding of Carnap and Tarski’s disagreements about the topics discussed and more generally about their philosophical ideas.

  5. In earlier papers such as Carnap (1936), he had defended the idea of defining truth (as opposed to “confirmation”) against verificationist objections of various stripes, but he had not explained his personal views about semantics yet.

  6. It may be remarked that Carnap had already used some concept of model in his Investigations on General Axiomatics, a manuscript which goes back to the late 20s, before Carnap’s so-called “syntactic period”. This manuscript has been posthumously published as Carnap (2000).

  7. It is well-known that in the second half of the twentieth century, Tarskian semantics has become standard and this historical point is assumed here as background knowledge. But this by no means implies any Whiggish bias in our analysis of Tarskian and Carnapian semantics. In other words, we of course do not assume that model theory based on Tarski’s work is the correct way of doing semantics and that Carnap was wrongheaded in following his own non-Tarskian way.

  8. To give just a very brief sample of these numerous studies, we can mention Feferman and Feferman (2004), Mancosu (2006, 2008, 2010), Patterson (2008, 2012), and Wolenski and Köhler (1998).

  9. I am indebted to the anonymous reviewer who pointed out to me that this remark is of crucial importance for understanding the reasons why Carnap does not follow Tarski and chooses one particular “non-Tarskian” semantic method, at the time he decides to take the semantic turn. More on this point below.

  10. The issue of fixed- versus variable domain interpretation has been the focus of many recent studies related to Tarski’s notion of logical consequence. For an overview, see Mancosu (2010). This issue has also been raised about the interpretation of Carnap’s so-called “early semantics”; see Schiemer (2013). This particular issue will not be discussed in this paper.

  11. For example, here is what Tarski writes about the possibility of drawing a sharp boundary between logical and extra-logical terms: “Perhaps it will be possible to find important objective arguments which will enable us to justify the traditional boundary between logical and extra-logical expressions. But I also consider it quite possible that investigations will bring no positive results in this direction so that we shall be compelled to regard such concepts as ‘logical consequence’, ‘analytical statements’, and ‘tautology’ as relative concepts which must, on each occasion, be related to a definite, although in greater or less degree arbitrary division of terms into logical and extra-logical” Tarski (1936c/1956, p. 420). As for Carnap, he acknowledges that “Tarski seems to doubt whether there is an objective difference [between factual truth and logical truth] or whether the choice of a boundary line is not more or less arbitrary” Carnap (1942, p. vii). See also another quotation from Tarski (1936c) given below (§4, first quotation).

  12. I am indebted to the anonymous reviewer who pointed out the importance of this quotation for the present paper.

  13. Typically: the construction of languages for which a proper explication of the distinction between logical truth and factual truth can be provided, as in LSL, or the construction of languages for achieving a proper explication of the principles of empiricism, as in Carnap (1936-1937). (Although Carnap does not use the word “explication” in print before 1945, he himself later applies it to his previous work, for example in the preface to the second edition of Carnap (1928), published in 1961. More on “explication” below.)

  14. It is not our business to set up prohibitions, but to arrive at conventions. (...) In logic, there are no morals. Everyone is at liberty to build up his own logic, i.e. his own form of language, as he wishes”, Carnap (1937, pp. 51–52).

  15. See the quotation from Carnap’s intellectual autobiography given below (§3, third quotation).

  16. On the issue of explication in Carnap, see Wagner (2012).

  17. Here again, I am indebted to the anonymous reviewer who pointed out this quotation to me, and suggested to be more explicit about Carnap’s and Tarski’s views on explication.

  18. “Tarski says further that the characterization given is also in agreement with the ordinary use of the word ‘true’. It seems to me that he is right in this assertion, at least as far as the use in science, in judicial proceedings, in discussions of everyday life on theoretical questions is concerned” (Carnap 1942, p. 29). Again, I am indebted to the anonymous reviewer who pointed out this quotation to me.

  19. The connection of Tarski’s definition of truth with the ordinary use of this term has of course been the focus of many discussions, but this particular issue is beyond the scope of the present paper.

  20. This paper was to be included in the English translation of Carnap (1934a).

  21. For an analysis of Carnap’s criterion of logicality, see Bonnay (2009) and Creath (2015).

  22. A definition of truth is materially adequate if all the T-sentences are consequences of the definition (a T-sentence is a sentence of the form “x is true if and only if p”, where “x” is the name of a sentence and “p” is its translation in the metalanguage).

  23. In spite of the differences between Tarski’s notion of logical consequence in Tarski (1936c) and the now classical notion of logical consequence of model theory pointed out by commentators such as Etchemendy (1999).

  24. For the languages Carnap considers in his (1947), an atomic sentence “holds in a given state description” iff it belongs to it; the negation of sentence S holds in a state description iff S does not hold in it; the conjunction of two sentences holds in a s.d. iff both of them hold in it; and a universal sentence such as (\(x){ Px}\) holds in a s.d. iff all substitutional instances of its scope (‘Pa’, ‘Pb’, etc.) hold in it. See Carnap (1947, § 2). What is striking here is that the definition of “holding in a state description” is actually syntactic: it does not depend on concepts such as truth, satisfaction, or reference at all.

  25. This by no means implies that Wittgenstein and Waismann were the main source of inspiration for his program of inductive logic. Other major influences include John Maynard Keynes and Harold Jeffreys, among many others, as Carnap explains in Carnap (1963a, pp. 72–73).

References

  • Awodey, S. (2007). Carnap’s quest for analyticity: The studies in semantics. In M. Friedman & R. Creath (Eds.), The Cambridge companion to Carnap (pp. 226–247). Cambridge, MA: Cambridge University Press.

    Chapter  Google Scholar 

  • Awodey, S. (2012). Explicating ‘Analytic’. In P. Wagner (Ed.), Carnap’s ideal of explication and naturalism (pp. 131–143). Basingstoke: Palgrave Macmillan.

    Chapter  Google Scholar 

  • Awodey, S., & Carus, A. W. (2009). From Wittgenstein’s prison to the boundless ocean: Carnap’s dream of logical syntax. In P. Wagner (Ed.), Carnap’s logical syntax of language (pp. 79–106). Basingstoke: Palgrave Macmillan.

    Google Scholar 

  • Bonnay, D. (2009). Carnap’s criterion of logicality. In P. Wagner (Ed.), Carnap’s logical syntax of language (pp. 147–164). Basingstoke: Palgrave Macmillan.

    Chapter  Google Scholar 

  • Carnap, R. (1922). Der Raum. Ein Beitrag zur Wissenschaftslehre. Berlin: Reuthner & Reichard. Kant-Studien, Ergänzungshefte, 56.

  • Carnap, R. (1928). Der logische Aufbau der Welt. Berlin: Weltkreis. Second edition, 1961. Hamburg: Felix Meiner.

  • Carnap, R. (1934a). Logische Syntax der Sprache. Vienna: Springer. Translated into English as Carnap (1937).

  • Carnap, R. (1934b). Die Antinomien und die Unvollständigkeit der Mathematik. Monatshefte für Mathematik und Physik, 41, 263–284.

    Article  Google Scholar 

  • Carnap, R. (1935). Ein Gültigkeitskriterium für die Sätze der klassischen Mathematik. Monatshefte für Mathematik und Physik, 42, 163–190.

    Article  Google Scholar 

  • Carnap, R. (1936). Wahrheit und Bewährung. In Actes du Congrès international de philosophie scientifique, Sorbonne, Paris, 1935 (Vol. 4, pp. 18–23). Paris: Hermann.

  • Carnap, R. (1936–1937). Testability and meaning. Philosophy of Science, 3, 419–471; 4, 1–40.

  • Carnap, R. (1937). The logical syntax of language. London: Kegan Paul Trench, Trubner, and Co.

    Google Scholar 

  • Carnap, R. (1939). Foundations of logic and mathematics. In International encyclopedia of unified science. Chicago: University of Chicago Press.

  • Carnap, R. (1942). Introduction to semantics. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Carnap, R. (1943). Formalization of logic. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Carnap, R. (1945a). The two concepts of probability. Philosophy and Phenomenological Research, 5, 513–532.

    Article  Google Scholar 

  • Carnap, R. (1945b). On inductive logic. Philosophy of Science, 12, 72–97.

    Article  Google Scholar 

  • Carnap, R. (1947). Meaning and necessity. A study in semantics and modal logic (2nd ed., 1956). Chicago: University of Chicago Press.

  • Carnap, R. (1950). Logical foundations of probability (2nd ed., 1962). Chicago: University of Chicago Press.

  • Carnap, R. (1952). Meaning postulates. Philosophical Studies, 3, 65–73.

    Article  Google Scholar 

  • Carnap, R. (1954). Einführung in die symbolische Logik, mit besonderer Berücksichtigung ihrer Anwendungen. Vienne: Springer. Translated into English as Carnap (1958).

  • Carnap, R. (1955). Notes on semantics. Hectographed. Los Angeles. Published in 1972. Philosophia, 2, 3–54.

    Google Scholar 

  • Carnap, R. (1958). Introduction to symbolic logic and its applications. New York: Dover Publications.

    Google Scholar 

  • Carnap, R. (1963a). Intellectual autobiography. In P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (pp. 1–84). LaSalle, IL: Open Court.

    Google Scholar 

  • Carnap, R. (1963b). My conception of semantics. In P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (pp. 900–905). LaSalle, IL: Open Court.

    Google Scholar 

  • Carnap, R. (1963c). E. W. Beth on constructed language systems. In P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (pp. 927–933). LaSalle, IL: Open Court.

    Google Scholar 

  • Carnap, R. (1963d). P. F. Strawson on linguistic naturalism. In P. A. Schilpp (Ed.), The philosophy of Rudolf Carnap (pp. 933–940). LaSalle, IL: Open Court.

    Google Scholar 

  • Carnap, R. (1971). A basic system of inductive logic. In R. Carnap & R. Jeffrey (Eds.), Studies in inductive logic and probability (Vol. 1, pp. 35–165). Los Angeles: University of California Press.

    Google Scholar 

  • Carnap, R. (2000). In Th. Bonk & J. Mosterin (Eds.), Untersuchungen zur allgemeinen Axiomatik. Darmstadt: Wissenschaftliche Buchgesellschaft.

  • Carus, A. W. (1999). Carnap, syntax, and truth. In J. Peregrin (Ed.), Truth and its nature (if any) (pp. 15–35). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Creath, R. (1990). The unimportance of semantics. PSA 1990: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2, 405–416.

    Google Scholar 

  • Creath, R. (1999). Carnap’s move to semantics: Gains and losses. In J. Wolenski & E. Köhler (Eds.), Alfred Tarski and the Vienna Circle (pp. 65–76). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Creath, R. (2015). The logical and the analytic. Synthese, published online 24 February 2015.

  • Etchemendy, J. (1999). The concept of logical consequence. Stanford, CA: CSLI.

    Google Scholar 

  • Feferman, S., & Feferman, A. (2004). Alfred Tarski, life and logic. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  • Frost-Arnold, G. (2013). Carnap, Tarski, and Quine at Harvard. Conversations on logic, mathematics, and science. Chicago: Open Court.

    Google Scholar 

  • Goldfarb, W. (1997). Semantics in Carnap: A rejoinder to Alberto Coffa. Philosophical Topics, 25, 51–66.

    Article  Google Scholar 

  • Hilbert, D., & Ackermann, W. (1928). Grundzüge der theoretischen Logik. Berlin: Springer.

    Google Scholar 

  • Kemeny, J. (1948). Models of logical systems. Journal of Symbolic Logic, 13, 16–30.

    Article  Google Scholar 

  • Kemeny, J. (1956). A new approach to semantics. Part I and Part II. Journal of Symbolic Logic, 21, 1–27 and 149–161

  • Mac Lane, S. (1938). Carnap on logical syntax. Bulletin of the American Mathematical Society, 44, 171–176.

    Article  Google Scholar 

  • Mancosu, P. (2005). Harvard 1940–1941: Tarski, Carnap and Quine on a finitistic language of mathematics for science. History and Philosophy of Logic, 26, 327–357.

    Article  Google Scholar 

  • Mancosu, P. (2006). Tarski on models and logical consequence. In J. Ferreiros & J. Gray (Eds.), The architecture of modern mathematics (pp. 209–238). New York: Oxford University Press.

    Google Scholar 

  • Mancosu, P. (2008). Tarski, Neurath, and Kokoszynska on the semantic conception of truth. In D. Patterson (Ed.), New essays on Tarski and philosophy (pp. 192–224). New York: Oxford University Press.

    Chapter  Google Scholar 

  • Mancosu, P. (2010). Fixed- versus variable-domain interpretations of Tarski’s account of logical consequence. Philosophy Compass, 5(9), 745–759.

    Article  Google Scholar 

  • Niiniluoto, I. (2003). Carnap on truth. In Th Bonk (Ed.), Language, truth, and knowledge. Contributions to the philosophy of Rudolf Carnap (pp. 1–25). Dordrecht: Kluwer.

    Google Scholar 

  • Patterson, D. (Ed.). (2008). New essays on Tarski and philosophy. New York: Oxford University Press.

    Google Scholar 

  • Patterson, D. (2012). Alfred Tarski: Philosophy of language and logic. New York: Palgrave Macmillan.

    Book  Google Scholar 

  • Ricketts, Th. (1996). Carnap: From logical syntax to semantics. In R. N. Giere & A. W. Richardson (Eds.), Origins of logical empiricism (pp. 231–250). Minneapolis, MN: University of Minnesota Press.

    Google Scholar 

  • Rouilhan, Ph. de (2012). Carnap and the semantical explication of analyticity. In P. Wagner (Ed.), Carnap’s ideal of explication and naturalism (pp. 144–158). Basingstoke: Palgrave Macmillan.

  • Schiemer, G. (2013). Carnap’s early semantics. Erkenntnis, 78, 487–522.

    Article  Google Scholar 

  • Sluga, H. (1999). Truth before Tarski. In J. Wolenski & E. Köhler (Eds.), Alfred Tarski and the Vienna Circle (pp. 27–41). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Stegmüller, W. (1957). Das Wahrheitsproblem und die Idee der Semantik. Eine Einführung in die Theorien von A. Tarski und R. Carnap. Vienna: Springer.

    Book  Google Scholar 

  • Tarski, A. (1932). Der Wahrheitsbegriff in den Sprachen der deduktiven Disziplinen. Akademischer Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-naturwissenschaftliche Klasse, 69, 23–25.

    Google Scholar 

  • Tarski, A. (1933). Projęcie prawdy w językach nauk dedukcyjnych. Nakładem / Prace Towarzystwa Naukowego Warszawskiego, wydzial III, 34. Translated into German as Tarski (1936a).

  • Tarski, A. (1936a). Der Wahrheitsbegriff in den formalisierten Sprachen. Studia Philosophica, 1, 261–405. Offprints dated 1935. Translated into English as “The Concept of Truth in Formalized Languages”, in Tarski (1956, pp. 152–278).

  • Tarski, A. (1936b). Grundlegung der wissenschaftlichen Semantik. Actes du Congrès international de philosophie scientifique, Sorbonne, Paris 1935 (Vol. III). Paris: Hermann. Translated into English as “The Establishment of Scientific Semantics” in Tarski (1956, pp. 401–408).

  • Tarski, A. (1936c). Über den Begriff der logische Folgerung. Actes du Congrès international de philosophie scientifique, Sorbonne, Paris 1935 (Vol. VII). Paris: Hermann. Translated into English as “On the Concept of Logical Consequence”, in Tarski (1956, pp. 409–420) and as Tarski (2002).

  • Tarski, A. (1944). The semantic conception of truth and the foundations of semantics. Philosophy and Phenomenological Research, 4, 341–376.

    Article  Google Scholar 

  • Tarski, A. (1954). Contributions to the theory of models, I. Indigationes Mathematicae, 16, 572–588.

    Article  Google Scholar 

  • Tarski, A. (1956). Logics, semantics, and metamathematics. Translated into English and edited by J. H. Woodger. Oxford: Oxford University Press. 2nd éd. with an introduction by J. Corcoran, 1983. Indianapolis, IN: Hackett Publishing Company.

  • Tarski, A. (2002). On the concept of following logically. English translation of Tarski (1936c). History and Philosophy of Logic, 23, 155–196.

    Article  Google Scholar 

  • Wagner, P. (Ed.). (2012). Carnap’s ideal of explication and naturalism. Basingstoke: Palgrave Macmillan.

    Google Scholar 

  • Waismann, F. (1930). Logische Analyse des Wahrscheinlichkeitsbegriff. Erkenntnis, 1, 228–248. Translated into English as “A Logical Analysis of the Concept of Probability”. In B. McGuinness (Ed.), Friedrich Waismann. Philosophical papers (pp. 4–21). Dordrecht: D. Reidel.

  • Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. London: Kegan Paul, Trench, Trubner, and Co.

    Google Scholar 

  • Wolenski, J., & Köhler, E. (Eds.). (1998). Alfred Tarski and the Vienna Circle. Austro-Polish connections in logical empiricism. Dordrecht: Kluwer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pierre Wagner.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wagner, P. Carnapian and Tarskian semantics. Synthese 194, 97–119 (2017). https://doi.org/10.1007/s11229-015-0853-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-015-0853-7

Keywords

Navigation