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Notes and references
I term the substitution instance of (T) s is true if and only if p. trivial if the name that replaces ‘s’ is the metalanguage (ML) name of the object language (L) sentence that replaces ‘p’ (or its translation). If, in a substitution instance of (T), the name that replaces ‘s’ is the name of a sentence of L but not the name of the L sentence (or its ML translation) that replaces ‘p’, I refer to the substitution instance as weak or non-trivial.
Donald Davidson, ‘Truth and Meaning’, reprinted in Philosophical Logic, ed. J. W. Davis, D. J. Hockney, and W. K. Wilson (Dordecht, 1969), p. 7.
A ‘theory of interpretation’ for Davidson, however, seems to include more than a Tarskian theory of meaning as traditionally conceived, a semantic theory based upon a recursive definition of satisfaction. See the ‘postscript’ to this paper.
Donald Davidson, ‘Radical Translation’, Dialecta, Vol. XXVII, No. 3–4 (1973), p. 318.
Donald Davidson, ‘Theories of Meaning and Learnable Languages’ in Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science (Amsterdam, 1966), p. 387.
Ibid.
‘Truth and Meaning’, p. 6.
Ibid.
Ibid., pp. 8–9.
Richmond H. Thomason, ‘Introduction’ to Formal Philosophy: Selected Papers of Richard Montague (New Haven and London, 1974), pp. 48–49.
See, for example, Richard Montague, ‘Pragmatics and Intensional Logic’, reprinted in Formal Philosophy: Selected Papers of Richard Montague, ed. Richmond H. Thomason (New Haven and London, 1974), pp. 119–147. For an interesting combination of a context-free categorial grammar with a model-theoretic semantics see David Lewis, ‘General Semantics’, in Semantics of Natural Language, ed. Donald Davidson and Gilbert Harman (Dordrecht, 1972), pp. 169–218. Although Lewis does not produce an explicit recursive definition of truth or satisfaction, the fundamental notion in his semantic theory is truth-at-an-index (a sequence containing a possible world coordinate, several contextual coordinates for dealing with indexical expressions, and an “assignment coordinate” for dealing with variables that is similar to Tarski's sequences in the Wahrheitsbegriff).
Alfred Tarski, ‘The Concept of Truth in Formalized Languages’, in Logic, Semantics, Metamathematics: Papers from 1923 to 1938, trans. J. H. Woodger (Oxford, 1956), p. 193.
Thomason, ‘Introduction’, fn. 45, p. 48.
Interestingly enough, Tarski allows that the metatheory for an artificial language like the one he develops in the Wahrheitsbegriff for the calculus of classes can also entail sentences that are not trivial T-sentences. In a metatheory for a language, Tarski allows, in addition to ‘general logical axioms’ and axioms permitting the construction of metalanguage ‘names’ of object language expressions, “axioms which have the same meaning as the axioms of the science under investigation or are logically stronger than them, but which in any case suffice (on the basis of the rules of inference adopted) for the establishment of all sentences having the same meaning as the theorems of the science investigated.” (Tarski, ‘The Concept of Truth’, p. 211). For example, the metatheory for set theory will entail, in addition to a trivial T-sentence for each sentence of the (object) language in which the propositions of set theory are expressed, LPC theorems and the theorems of set theory. This further set of axioms added to the semantics for the artificial ‘languages of the sciences’ are, in certain respects, analogous to meaning postulates for a theory of meaning for a natural language. The added axioms ‘shrink the models’ so that only certain relations, i.e., inclusion relations, can be assigned to the two-place predicate ‘I’. Meaning postulates for the one-place predicate ‘B’ also shrink the models, but perhaps not to such a great degree.
Davidson, ‘Truth and Meaning’, p. 8.
Ibid., pp. 9–10.
Davidson, ‘Radical Translation’, p. 321.
Several such discussions have occurred, concentrating for the most part on the translation part of Davidson's program. One colloquium in which W. V. O. Quine and David Lewis responded to Davidson occurred at the University of Connecticut in 1973. Davidson's presentation and Quine's and Lewis' responses were published in Synthese, XXVII, nos. 3–4 (July–August, 1974). See also Alan, Reeves, ‘On Truth and Meaning’, Nous, VIII (1974), pp. 343–359.
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White, M.J. Davidson and non-trivial T-sentences. Erkenntnis 10, 87–97 (1976). https://doi.org/10.1007/BF00167769
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DOI: https://doi.org/10.1007/BF00167769