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Carnap on Truth

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Language, Truth and Knowledge

Part of the book series: Vienna Circle Institute Library [2003] ((VCIL,volume 2))

Abstract

During his long career, Rudolf Carnap held various different views about the concept of truth and its philosophical significance. As a good logical empiricist, he insisted on the distinction between logical and factual statements, and employed his technical powers to give rigorous characterizations of the notions of logical, analytic, and factual truth. The development of Carnap’s views reflected his ability to quickly absorb new influences and his broad interests ranging from logic to epistemology, philosophy of language, and philosophy of science (Sections 1 and 2). Carnap was the co-founder of logical semantics with Alfred Tarski (Section 3), and therefore it is especially interesting to see how Carnap’s work was related to Tarski’s early definition of truth and to the later Tarskian model theory (Section 4). In Section 5, we discuss some difficulties in Carnap’s liberally empiricist treatment of scientific theories. The final section 6 makes some remarks on Carnap’s contemporary relevance.

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Notes

  1. For a survey, see Ilkka Niiniluoto, “Theories of Truth: Vienna, Berlin, and Warsaw”, in: Jan Wolenski, Eckehart Köhler (eds.), Alfred Tarski and the Vienna Circle, Dordrecht: Kluwer, 1999, pp. 17–26.

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  2. See J. Alberto Coffa, The Semantic Tradition from Kant to Carnap: To the Vienna Station, Cambridge: Cambridge University Press, 1991;

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  3. Alan W. Richardson, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism, Cambridge: Cambridge University Press, 1998;

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  4. Michael Friedman, Reconsidering Logical Positivism, Cambridge: Cambridge University Press, 1999. For Carnap’s own statement of his aims, see the Preface to The Logical Structure of the World & Pseudoproblems in Philosophy, Berkeley and Los Angeles: University of California Press, 1967.

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  5. Eino Kaila stated in 1930 that “the constitution theory is supposed to be a ‘rational reconstruction’ of the actual cognitive process”. See E. Kaila, Experience and Reality, Dordrecht: D. Reidel, 1979, p. 19.

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  6. See Carnap, op. cit., pp. 325–327.

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  7. See Rudolf Carnap, “Intellectual Autobiography”, in: Paul Arthur Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle: Open Court, 1963, p. 29.

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  8. See Jaakko Hintikka, Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieth-Century Philosophy, Dordrecht: Kluwer, 1997.

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  9. Carnap maintained this Fregean idea even in his later work in semantics.

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  10. See Rudolf Carnap, Abriss der Logistik, Wien: Julius Springer, 1929, p. 3.

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  11. For accounts of this manuscript, see Coffa, op.cit., pp. 273–280; S. Adowey, A.W. Cams, “Carnap, Completeness, and Categoricity: The Gabelbarkeitssatz of 1928”, Erkenntnis 54, 2001, pp. 145–172. Carnap presented his paper on “Axiomatik” at the Prague Conference on September 1929, and its brief summary was published in Erkenntnis 1, 1930, pp. 303–307. The manuscript has recently been edited by Thomas Bonk and Jesus Mosterin, and published as Untersuchungen zur allgemeinen Axiomatik. Darmstadt: Wissenschafliche Buchgesellschaft, 2000.

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  12. See Kurt Gödel, Collected Works, Vol. I, Oxford: Oxford University Press, 1986, p. 63.

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  13. Carnap’s relations to Tarski are described in his “Intellectual Autobiography”, op. cit., p. 31.

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  14. See Rudolf Carnap, The Logical Syntax of Language, London: Routledge & Kegan Paul, 1937. For Carnap’s lectures on metalogic in 1931, see

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  15. Friedrich Stadler, The Vienna Circle: Studies in the Origins, Development, and Influence of Logical Empiricism, Wien: Springer, 2001, pp. 279–299.

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  16. See Moritz Schlick, Philosophical Papers, vol. II, Dordrecht: D. Reidel, 1979, p. 400.

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  17. See Thomas E. Uebel, “Rational Reconstruction as Elucidation? Carnap in the Early Protocol Sentence Debate”, Synthese 93, 1992, pp. 107–140.

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  18. See Carl G. Hempel, “On the Logical Positivists’ Theory of Truth”, in: Analysis 2, 1935, pp. 49–59;

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  19. Michael Friedman, “Hempel and the Vienna Circle”, in: James Fetzer (ed.), Science, Explanation, and Rationality: Aspects of the Philosophy of Carl G. Hempel, Dordrecht: Kluwer, 2000, p. 49.

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  20. For discussions of Carnap’s definition of analytic truth in his Syntax, see Coffa, op.cit., pp. 286–305; Richard Creath, “The Unimportance of Semantics”, in: Arthur Fine, Michael Forbes, Linda Wessels (eds.), PSA 1990, vol. 2, East Lansing: Philosophy of Science Association, 1991, pp. 405–416;

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  21. Sahotra Sarkar, “‘The Boundless Ocean of Unlimited Possibilities’: Logic in Carnap’s Logical Syntax of Language”, Synthese 93, 1992, pp. 191–237;

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  22. Thomas Oberdan, “The Concept of Truth in Carnap’s Logical Syntax of Language”, Synthese 93, 1992, pp. 239–260;

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  23. David Devidi, Graham Solomon, “Tolerance and Metalanguage in Carnap’s Logical Syntax of Language”, Synthese 103, 1995, pp. 123–139.

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  24. See S.C. Kleene, “Review of Rudolf Carnap, The Logical Syntax of Language”, Journal of Symbolic Logic 4, 1939, pp. 82–87.

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  25. For the English translation, “The Concept of Truth in Formalized Languages”, see Alfred Tarski, Logic, Semantics, Metamathematics, Oxford: Oxford University Press, 1956, pp. 152–278.

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  26. See R. Carnap, “Intellectual Autobiography”, op.cit., pp. 60–61.

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  27. See Rudolf Carnap, “Wahrheit und Bewärung”, in: Actes du Congrès International de Philosophie Scientifique, Sorbonne, Paris 1935, Paris: Hermann, 1936, pp. IV. 19–23. The expanded English translation, “Truth and Confirmation”, is published in Herbert Feigl, Wilfrid Sellars (eds.), Readings in Philosophical Analysis, New York: Appleton-Century-Crofts, 1949, pp. 119–127.

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  28. See Carl G. Hempel, “Some Remarks on Tacts’ and ‘Propositions’”, Analysis 2, 1935, pp. 93–96.

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  29. Cf. M. Friedman, “Hempel and the Vienna Circle”. Material related to this debate can be found in the Otto Neurath Nachlass.

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  30. See Rudolf Carnap, “Testability and Meaning”, Philosophy of Science 3, 4, 1936, pp. 419– 471;

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  31. See Rudolf Carnap, “Testability and Meaning”, Philosophy of Science 4, 1, 1937, pp. 1–40.

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  32. See Rudolf Carnap, “Remarks on Induction and Truth”, Philosophy and Phenomenological Research 6, 4, 1946, pp. 590–602, 609–611. See also “Truth and Confirmation”, op. cit.

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  33. See Rudolf Carnap, Foundations of Logic and Mathematics, Chicago: The University of Chicago Press, 1939.

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  34. See Rudolf Carnap, Introduction to Semantics, Cambridge, MS: Harvard University Press, 1942.

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  35. See Rudolf Carnap, Meaning and Necessity: A Study in Semantics and Modal Logic, Chicago: The University of Chicago Press, 1947. Second expanded edition, 1956.

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  36. See Rudolf Carnap, Logical Foundations of Probability, Chicago: The University of Chicago Press, 1950.

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  37. See John G. Kemeny, “A Logical Measure Function”, Journal of Symbolic Logic 18, 1953, pp. 289–308.

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  38. See Rudolf Carnap, Richard Jeffrey (eds.), Studies in Inductive Logic and Probability, Vol. 1, Berkeley: University of California Press, 1971.

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  39. See Jaakko Hintikka, “Modality as Referential Multiplicity”, Ajatus 20, 1957, pp. 49–64;

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  40. Ghita Holmström-Hintikka, Sten Lindström, Rysiek Sliwinski (eds.), Collected Papers of Stig Ranger with Essays on his Life and Works I–II, Dordrecht: Kluwer, 2001.

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  41. This is convincingly argued in Jaakko Hintikka, “Carnap’s Heritage in Logical Semantics”, in: Jaakko Hintikka (ed.), Rudolf Carnap, Logical Empiricist, Dordrecht: D. Reidel, 1975, pp. 217–242. Hintikka states that Carnap was “the first and foremost herald of a new epoch of possible-worlds semantics”, but also argues that Carnap failed to interpret his models “as genuine possible worlds, i.e. real-life alternatives to our actual world”. It is no doubt philosophically significant whether possible worlds are understood “realistically”. But it is fair to Carnap to point out that most studies in this field have assumed that possible worlds are in some way relative to language — or even can be represented by linguistic expressions (e.g. Carnap’s state descriptions, Hintikka’s model sets and constituents). Note that Hintikka distinguishes the issues of realism and completeness of possible words, and he has allowed that possible worlds are replaced by “small worlds”.

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  42. See Rudolf Carnap, “Meaning and Synonymy in Natural Languages”, Philosophical Studies 6, 3, 1955, pp. 33–47. Reprinted in Meaning and Necessity, 2nd edn., op.cit., 1956.

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  43. See Hintikka, “Carnap’s Heritage”, p. 236.

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  44. Carnap’s “Notes in Semantics” is mentioned in the Bibliography of the Schilpp volume, op. cit., 1963, p. 1045. See also Rudolf Carnap, “Replies and Systematic Expositions”, in: Schilpp, op. cit., pp. 889–905.

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  45. Hintikka points out that Carnap allows descriptive predicates to be “arbitrarily reinterpreted” in different ways in his models. However, if the function deseqr is a part of a semantical system, it in any case assigns extensions to the same predicate in different models.

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  46. See Jan Wolehski, Peter Simons, “De Veritate: Austro-Polish Contributions to the Theory of Truth from Brentano to Tarski”, in: Klemens Szaniawski (ed.), The Vienna Circle and the Lvow-Warsaw School, Dordrecht: Kluwer, 1989, pp. 391–442.

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  47. See Jan Wolehski, “Theories of Truth in Austrian Philosophy”, Reports on Philosophy 18, 1998, pp.13–49.

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  48. See A. Tarski, “The Concept of Truth”, pp. 166–167.

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  49. Ibid., pp. 199, 207, 239.

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  50. See Ilkka Niiniluoto, “Tarskian Truth as Correspondence — Replies to Some Objections”, in: Jaroslaw Peregrin (ed.), Truth and its Nature (if any), Dordrecht: Kluwer, 1999, pp. 91–104.

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  51. See Alfred Tarski, “The Semantic Concept of Truth and the Foundations of Semantics”, Philosophy and Phenomenological Research 4, 1944, pp. 341–376.

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  52. See also Alfred Tarski, “Truth and Proof”, Scientific American 6, 1969, pp. 63–77.

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  53. See Alfred Tarski, Robert Vaught, “Arithmetical Extensions of Relational Systems”, Compositio Mathematicae 13, 1957, pp. 81–102.

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  54. See Wilfrid Hodges, “Truth in a Structure”, Proceedings of the Aristotelian Society 86, 1986, pp. 135–152.

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  55. See Alfred Tarski, “On the Concept of Logical Consequence”, in: Logic, Semantics, Metamathematics, Oxford: Oxford University Press, 1956, pp. 416–417. The same definition is repeated in Sections 37–38 of

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  56. A. Tarski, Introduction to Logic and to the Methodology of the Deductive Sciences, Oxford: Oxford University Press, 1941.

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  57. Tarski added that this situation occurs only in those cases where a theory can be given several alternative interpretations but we do not wish to give a preference to one of them. See Introduction to Logic, 3rd edn, 1965, p. 129. Hodges discussed this issue in a lecture given in the Tarski Centennial Conference in Warsaw, May 2001. See also Ilkka Niiniluoto, “Tarski’s Definition and Truth-Makers”, forthcoming in the Proceedings of the Tarski Centennial Conference.

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  58. Another influential figure was Alonzo Church at Princeton. An important summary of the “logistic method” was given in his Introduction to Logic, vol. 1, Princeton: Princeton University Press, 1956. (The shorter first edition appeared in 1944.) Church’s students John Kemeny and Leon Henkin made important contributions to model theory. Henkin’s 1947 completeness proof used a method where a model of a theory is constructed from the individual constants of its language. He did not mention Carnap’s similar intralinguistic method of valuation in The Logical Syntax, however. See L. Henkin, “The Discovery of My Completeness Proofs”, The Bulletin of Symbolic Logic 2, 1996, pp. 127–158.

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  59. See R. Carnap, “Intellectual Autobiography”, p. 79.

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  60. See R. Carnap, Introduction to Semantics, p. vii.

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  61. This issue was discussed by Carnap and Tarski already in 1930. See R. Carnap, “Intellectual Autobiography”, p. 30.

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  62. See, for example, J.D. Monk, Mathematical Logic, New York: Springer-Verlag, 1976.

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  63. See Hartry Field, “Tarski’s Theory of Truth”, Journal of Philosophy 69, 1972, pp. 347–375.

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  64. See A. Tarski, “The Concept of Truth”, p. 188.

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  65. See R.L. Kirkham, Theories of Truth: A Critical Introduction, Cambridge, MS: MIT Press 1992, p. 132. Kirkham’s schema differs slightly from (C), since it replaces proposition p by a state of affairs.

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  66. See Rudolf Carnap, “Replies and Systematic Expositions”, in: Paul Arthur Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle: Open Court, 1963, p. 901.

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  67. See Rudolf Carnap, Physikalische Begriffsbildung, Karlsruhe in Baden: G. Braun, 1926, p. 45.

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  68. See Ernest Nagel, The Structure of Science, Indianapolis: Hackett, 1961.

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  69. For my own formulations and defences of scientific realism, see Ilkka Niiniluoto, Truthlike-ness, Dordrecht: D. Reidel 1987;

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  70. For my own formulations and defences of scientific realism, see Ilkka Niiniluoto, Critical Scientific Realism, Oxford: Oxford University Press, 1999.

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  71. See R. Carnap, Foundations of Logic and Mathematics, p. 62. This point was repeated by Hempel in the Schilpp volume. He added that, even though theoretical existential hypotheses might have factual reference and truth conditions, their translation to the metalanguage does not help us to understand the theory, unless the metalanguage is antecedently understood. Here the motivation for the partial interpretation view is epistemological rather than semantical. See Carl G. Hempel, “Implications of Carnap’s work for the Philosophy of Science”, in: P.A. Schilpp (ed.), The Philosophy of Rudolf Carnap, 1963, pp. 695–696.

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  72. See Fred Suppe (ed.), The Structure of Scientific Theories, 2nd edn., Urbana: University of Illinois Press, 1977. Most influential in this development was Carnap’s article “The Methodological Character of Theoretical Concepts”, in: Herbert Feigl and Michael Scriven (eds.), The Foundations of Science and and the Concepts of Psychology and Psychoanalysis, Minneapolis: University of Minnesota Press, 1956, pp. 38–76.

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  73. See Herbert Feigl, “Existential Hypotheses: Realistic versus Phenomenalistic Interpretations”, Philosophy of Science 17, 1950, pp. 35–62. Feigl had already in the 1935 Congress in Paris discussed the possibility of giving a naturalist and empiricist interpretation of scientific realism.

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  74. See Herbert Feigl, “Sense and Nonsense in Scientific Realism”, in: Actes du Congrès International de Philosophie Scientifique, Paris: Hermann, 1936, pp. III.50–56.

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  75. For a detailed assessment of Carnap’s “neutralism”, see Ch. 3 of Stathis Psillos, Scientific Realism: How Science Tracks Truth, London: Routledge, 1999. See also Wesley Salmon, “Carnap, Hempel and Reichenbach on Scientific Realism”, in: Wesley Salmon and Gereon Wolters (eds.), Logic, Language and the Structure of Scientific Theories, Pittsburgh: University of Pittsburgh Press, pp. 237–254; Paolo Parrini; “With Carnap, Beyond Carnap: Metaphysics, Science, and the Realism/Instrumentalism Controversy”, ibid., pp. 255–277. Carnap’s position as a “structural realist” is discussed by Stathis Psillos, “Carnap, the Ramsey Sentence and Realistic Empiricism”, Erkenntnis 52, 2000, pp. 253–279.

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  76. See Carnap, “Intellectual Autobiography”, p. 79.

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  77. See Rudolf Carnap, “Empiricism, Semantics and Ontology”, Revue Internationale de Philosophie 4, 1950, pp. 20–40. Reprinted in Meaning and Necessity, 1956.

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  78. See Carnap, “Intellectual Autobiography”, p. 46.

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  79. See Rudolf Carnap, An Introduction to the Philosophy of Science, edited by Martin Gardner, New York: Basic Books, 1974, p. 256. The book is originally based on Carnap’s lecture course in the fall of 1958.

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  80. See R. Carnap, Logical Foundations of Probability, 2nd edn, 1962, pp. 572–575.

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  81. See Jaakko Hintikka, Ilkka Niiniluoto, “An Axiomatic Foundation for the Logic of Inductive Generalization”, in: Richard Jeffrey (ed.), Studies in Inductive Logic and Probability, vol. 2, Berkeley and Los Angeles: University of California Press, 1980, pp. 157–181. The role of theories and theoretical concepts in inductive inference is studied in

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  82. Ilkka Niiniluoto, Raimo Tuomela, Theoretical Concepts and Hypothetico-Inductive Inference, Dordrecht: D. Reidel, 1973.

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  83. See Carl G. Hempel, “The Theoretician’s Dilemma: A Study in the Logic of Theory Construction”, in: Herbert Feigl, Michael Scriven, Grower Maxwell (eds.), Concepts, Theories and the Mind-Body Problem, Minneapolis: University of Minnesota Press, 1958, pp. 37–98.

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  84. See Rudolf Carnap, “Beobachtungssprache und theoretische Sprache”, Dialectica 12, 1958, pp. 236–248: English translation “Observational Language and Theoretical Language”, in: Jaakko Hintikka (ed.), Rudolf Carnap, Logical Empiricist, 1975, pp. 75–85.

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  85. See John A. Winnie, “Theoretical Analyticity”, in J. Hintikka (ed.), Rudolf Carnap, Logical Empiricist, 1975, pp. 143–159;

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  86. Raimo Tuomela, Theoretical Concepts, Wien: Springer, 1973.

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  87. See Niiniluoto, Critical Scientific Realism; Psillos, Scientific Realism. Historically speaking, Carnap’s insistence on finding the analytic component of a given theory can be traced to the doctrine of “relativized a priori”.

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  88. See R. Carnap, Introduction to the Philosophy of Science, 1974, p. 268.

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  89. See R. Carnap, “Observational Language and Theoretical Language”, pp. 80–81.

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  90. See R. Carnap, “Replied and Systematic Expositions”, 1963, pp. 963.

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  91. This is the main point of the article by Jaakko Hintikka and Ilkka Niiniluoto, “On Theoretical Terms and Their Ramsey-Elimination”, published (only) as a Russian translation in Filosofskiye Nauki 1973, pp. 49–61. Recall that a standard interpretation of second-order logic allows the one-place predicate variables to range over all subsets of the domain. So one way of ontologically specifying a non-standard interpretation is to require that the members of a permissible subset share a common physical property.

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  92. See Rudolf Carnap, “Von der Erkenntnistheorie zur Wissenschaftslogik”, in: Actes du Congrès International de Philosophie Scientifique, Paris: Hermann, 1936, p. 40.

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  93. See R. Carnap, “Replies and Systematic Expositions”, 1963, p. 870.

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  94. See R. Carnap, The Logical Structure of the World, 1967, p. xi.

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  95. See Hilary Putnam, Reason, Truth, and History, Cambridge: Cambridge University Press, 1981.

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  96. A.W. Carus claims that Carnap did not “switch to a correspondence theory of truth after 1935”, since his “linguistic pluralism eliminates talk of “reality” outside the framework of a particular language”. See A.W. Carus, “Carnap, Syntax and Truth”, in: Jarostaw Peregrin (ed.), Truth and its Nature (if any), Dordrecht: Kluwer, 1999, pp. 15–35. I prefer to read Carnap and Tarski so that their semantics successfully combines correspondence theory with linguistic pluralism.

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  97. See, for example, the comments on the relations between Carnap and Thomas Kuhn in John Earman, “Carnap, Kuhn, and the Philosophy of Scientific Methodology”, in: Paul Horwich (ed.), World Changes: Thomas Kuhn and the Nature of Science, Cambridge, MS: The MIT Press, 1993, pp. 9–36.

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  98. For pioneering works in this area, see Marian Przetcki, The Logic of Empirical Theories, London: Routledge and Kegan Paul, 1969;

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  99. Patrick Suppes, Studies in the Methodology and Foundations of Science: Selected Papers from 1951 to 1969, Dordrecht: D. Reidel, 1969.

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  1. Department of Philosophy, University of Helsinki, Finland

    Ilkka Niiniluoto

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  1. Ludwig-Maximilians-Universität, München, Germany

    Thomas Bonk

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Niiniluoto, I. (2003). Carnap on Truth. In: Bonk, T. (eds) Language, Truth and Knowledge. Vienna Circle Institute Library [2003], vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0151-8_1

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