Abstract
In “The Concept of Truth in Formalized Languages,” Tarski set out an equivalence condition for the introduction of a truth predicate into a linguistic schema.1 Known as Convention-T,this condition requires that a “formally correct definition” of a truth predicate introduced into or defined in a metalanguage for a schema L,will be “adequate” if,for any statement of L,it has as a consequence a biconditional holding between a metalinguistic transcription of the statement and a metalinguistic sentence ascribing the truth predicate to the statement.2 In his early paper,as well as in the later “The Semantic Conception of Truth,” Tarski linked Convention-T to both “the classical Aristotelian conception of truth” expressed in Aristotle’s assertion:
To say of what is that it is not,or of what is not that it is,is false,while to say of what is that it is,or of what is not that it is not,is true.3
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NOTES
A. Tarski, “The Concept of Truth in Formalized Languages,” reprinted in A. Tarski, Logic, Semantics, Metamathematics trans. J. H. Woodger, (Oxford: 1956), pp. 152–278. On the dating see the bibliographical note, p. 152 and the footnotes on p. 154 and pp. 247–248.
Tarski, 1956, pp. 187–188.
Tarski, 1956, p. 155 and A. Tarski, “The Semantic Conception of Truth,” Philosophy and Phenomenological Research, 4, 1944, pp. 342–343.
Tarski, 1944, p. 343.
Tarski, 1944, p. 356.
L. Wittgenstein, Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F. McGuinness, (London: 1961), p. 41. We should note that an alternative way of construing a correspondence theory that appeals to situations is to take situations to be constituents of positive or negative facts. Thus, instead of recognizing existent and non-existent facts or situations, one recognizes positive and negative facts, both of which are existents, that contain constituent situations, much as Aristotelian substances, in one sense, contain prime matter. Just as prime matter is not an entity, but involved in the analysis of entities, so possibilities would not be entities but involved in the analysis of entities. This distinction, while of little importance for our purposes, can be important in discussions of purported possible worlds.
I am quite aware that Wittgenstein struggled to avoid the “shadowy” entities we are taking as situations or possibilities, by taking the possibilities to be given by the natures or “essential” or “internal” properties of objects. On this see H. Hochberg, “Facts, Possibilities and Essences in the Tractatus,” in E. D. Klemke ed., Essays on Wittgenstein (Urbana: 1971), pp. 530–533. The question is whether Wittgenstein’s appeal to internal properties of objects and corresponding internal properties of their representatives, in thought or in language, carry the burden of correlating a complex, a proposition, to its truth condition. For, the correlation of the respective constituents will not do unless one takes it to be internal to being a sign, ‘a’, for example, or a token of a sign, not only that it can combine with another, ‘F’ say, in a certain arrangement, but that the resulting arrangement represents the situation that a is F. But this is not to correlate complexes by correlating their constituents, it is to correlate complexes directly, though it is dependent on the correlation of constituents. For, it amounts to correlating the arrangement ‘Fa’ to the situation. The internal property that the sign has is that it can combine with another in an arrangement that is understood to represent the situation. In any case, little is gained by giving objects such essential or logical properties in order to avoid possible facts. At best, one ends up with a having the internal property of possibly being F, instead of having a be a constituent of the situation represented by ‘Fa’.
That the coherence theorist can take [[aRb] coheres with C] and [[[aRb] coheres with C] coheres with C*] to have the same truth value is irrelevant. The point is that he must hold that the truth ground for one proposition is the truth of another proposition. The regress is blocked by taking C=C*, holding that the propositions are logically equivalent, and that logically equivalent propositions are identical. But this amounts to making the proposition its own ground of truth.
In spite of some passages in Tarski’s original paper and the way the “semantic conception” of truth is sometimes discussed, as, for example, by E. W. Beth in The Foundations of Mathematics, (Amsterdam: 1959), p. 340: “..the clause ”t is in K“ explicitly describes the state of affairs which the sentence T(t*) of A is to express. The statement (T) strongly resembles traditional definitions of truth as adaequatio rei et intellectus.” it is misleading to link Tarski’s views with the correspondence theory. In Tarski, 1944, p. 343, Tarski quite explicitly holds that taking sentences to designate “states of affairs” is the kind of formulation that leads “to various misunderstandings” since it is not sufficiently “precise and clear”.
For Carnap’s version of a linguistic hierarchy and Convention-T, see R. Carnap, The Logical Syntax of Language, (London: 1937), especially pp. 205–32.
B. A. W. Russell, “On the Relations of Universals and Particulars,” Proceedings of the Aristotelian Society, 1911–12, pp. 1–24.
G. Frege, “The Thought: A Logical Inquiry,” trans. by A. M. and M. Quinton, Mind, 65, 1956, reprinted in Essays on Frege, ed. E. D. Klemke, (Urbana: 1968), p. 510. Frege’s argument is reminiscent of F. H. Bradley’s attack on all relations, including a correspondence relation.
Tarski, 1956, p. 188.
In the present discussion I follow Tarski’s use of ’s’. It is worth noting that Tarski offers a definition of the “semantical concept” designates such that: 0 designates rr iff ß = rr, where ‘0’ is a metalinguistic name of the sign ß’. Tarski, 1944, p. 373, n. 2. If we apply this pattern to sentences like ‘aRb’, by taking the sentence to name something, a situation or state of affairs, while treating the occurrence of the sentence in quotes as a name of the sentence, we get: ‘aRb’ designates aRb iff aRb = aRb.
Tarski, 1944, p. 361.
Tarski, 1944, p. 353.
On such questions see H. Hochberg, “Negation and Generality,” Nous, 3 1969, pp. 32543, and “Russell, Ramsey and Wittgenstein on Ramification and Quantification, Erkenntnis, 27, 1987, pp. 257–81.
See G. E. Moore, “Facts and Propositions,” Aristotelian Society Supplementary, vol. vii, 1927, reprinted in Philosophical Papers, (London: 1959), pp. 60–88; F. P. Ramsey, “Facts and Propositions,” Aristotelian Society Supplementary, vol. vii, 1927, reprinted in F. P. Ramsey, The Foundations of Mathematics,ed. R. B. Braithwaite, (London: 1931), pp. 138–55, for the Ramsey-Moore debate.
For example, 4. 0621.
B. Russell, “Introduction,” in Wittgenstein, 1961, p. xxii.
See, for example, S. Kripke, “Outline of a Theory of Truth,” The Journal of Philosophy, 72, 1975, pp. 690–716; H. G. Herzberger, “Notes on Naive Semantics,” Journal of Philosophical Logic,I1, 1982, pp. 61–102; A. Gupta, “Truth and Paradox,” Journal of Philosophical Logic, 11, 1982, pp. 1–60. All three papers are reprinted in R. L. Martin, Recent Essays on Truth and the Liar Paradox (Oxford: 1984).
For Lukasiewicz’s use of truth value gaps, see J. Lukasiewicz, “On Determinism,” in Polish Logic, 1920–1939, ed. Storrs McCall, (Oxford: 1967), pp. 19–39. The ascription of the idea of truth value gaps to Frege is based on his discussion of fictional names in “On Sense and Reference,” his classification of thoughts as true, false, or fictitious in an 1897 logic manuscript, and his stating that the sentence ‘the sum of the Moon and the Moon is one’ is neither true nor false in his Grundgesetze. However, he might merely have meant that non-denoting singular terms and sentences containing them (“transparently”) need not be given serious consideration. I am indebted to Ignacio Angelelli for this cautionary note.
A. N. Whitehead and B. A. W. Russell, Principia Mathematica, vol. 1, 2cnd. ed., pp. 44–45.
B. A. W. Russell, “The Philosophy of Logical Atomism,” reprinted in Logic and Knowledge: Essays 1901–1950,ed. R. Marsh, (London: 1956), pp. 236–37.
One reason for Frege’s introduction of the objects The True and The False, as basic objects denoted by propositions (“thoughts”) and sentences, may well have been his view that no analysis or theory of truth was viable. Hence, one could only state that a proposition was true or false — denoted The True or The False.
In Martin, 1984, p. 80. In the above discussion I have ignored the irrelevant complication that non-paradoxical self-referential statements can be given arbitrary evaluations, instead of retaining truth-value gaps.
In Martin, 1984, pp. 80–81.
Thus he writes “The necessity to ascend to a meta-language may be one of the weaknesses of the present theory.” In Martin, 1984, p. 80.
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Hochberg, H. (1992). Truth Makers, Truth Predicates, and Truth Types. In: Mulligan, K. (eds) Language, Truth and Ontology. Philosophical Studies Series, vol 51. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2602-1_7
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