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Three Trivial Truth Theories

Published online by Cambridge University Press:  01 January 2020

Ernest Lepore  and
Barry Loewer
Ernest Lepore
Affiliation:
Rutgers University
Barry Loewer
Affiliation:
University of South Carolina
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Extract

According to Tarski, a theory of truth for a language L is a theory which logically implies for each sentence S of L a sentence of the form:

S is true-in-L if and only if p,

where rS1 is replaced by a canonical description of a sentence of L and rp1 is replaced by that sentence if L is contained in the metalanguage or by a translation of S if it is not so contained. Tarski constructed consistent and finitely axiomatized theories of truth for various formal languages and showed how to explicitly define ‘is true in L’ within these theories. We all agree that Tarski's theories of truth have enormous philosophical significance, but there is much less agreement on precisely what that significance consists in.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 13 , Issue 3 , September 1983 , pp. 433 - 447
Copyright
Copyright © The Authors 1983

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Footnotes

*

An earlier draft of this paper was presented at the Western American Philosophical Association meetings in Milwaukee, April, 1981. We would like to thank Donald Davidson, Michael Root, and the editors of the Canadian Journal of Philosophy for their comments on that draft.

References

1 Tarski, A. ‘The Concept of Truth in Formalized Languages,’ in his Logic, Semantics, and Metamathematics (Oxford: Clarendon Press 1956), 152–278Google Scholar

2 In work aimed mainly at philosophers, Tarski relates classical philosophical issues to his work in semantics. Cf. A. Tarski, ‘The Semantic Conception of Truth,’ Philosophy and Phenomenological Research, 4 (1944) 341-75. Cf. also his ‘Truth and Proof,’ Scientific American, 220 (1969) 63-77.

3 Davidson has presented his views on these subjects in many places, e.g., ‘In Defense of Convention T,’ in Leblanc, H. ed., Truth, Syntax and Modality (Amsterdam: North-Holland Publishing Co. 1973) 76–86Google Scholar (henceforth referred to as IDCTI; ‘Belief and the Basis of Meaning,’ Synthese 27 (1974) 309-23 (henceforth referred to as BBM); ‘Radical Interpretation,’ Dialectica 27 (1973) 314-28 (henceforth referred to as RI); ‘Reality Without Reference,’ Dialectica, 31 (1977) 247-58(henceforth referred to as RWR); ‘Reply to Foster,’ in Evans, G. and McDowell, J. eds., Truth and Meaning: Essays in Semantics (Oxford: Clarendon Press 1976), 33–41Google Scholar.

4 Davidson has made some rather strong claims on this point: ‘theories of absolute truth necessarily provide an analysis of structure relevant to truth and inference. Such theories yield a non-trivial answer to the question ‘what is to count as the logical form of a sentence,’ (IDCT); cf. also (BBM: 319; RI: 314). In ‘Truth and Inference,’ Erkenntnis, 18 (1982) 379-95, LePore argues that Davidson offers no good reasons for his claims about the relationship between a truth theory and a theory of logical form for a language. LePore attempts to provide one by realizing a connection in Davidson's views between truth and inference.

5 Belnap, N.D. Jr. and Grover, D.L. ‘Quantifying In and Out of Quotes,’ in Leblanc, H. ed., Truth, Syntax and Modality (Amsterdam: North-Holland Publishing Co. 1973), 17–47CrossRefGoogle Scholar; Kripke, S. ‘Is There a Problem About Substitutional Quantification?', in McDowell, J. and Evans., G. eds., Truth and Meaning (Oxford: Clarendon Press 1976), 325–419Google Scholar; Harman, G. ‘Meaning and Semantics,’ in Munitz, M. and Unger, P. eds., Semantics and Philosophy (New York: New York University Press 1974), 1–16Google Scholar.

6 Tarski, 160

7 Platts, Mark Ways of Meaning (London: Routledge and Kegan Paul 1979)Google Scholar

8 Platts, 14

9 In this paper we will let single quotes usually name expressions, but sometimes they will be variously interpreted to make sense of the three trivial truth theories.

10 Belnap and Grover; S. Kripke

11 Platts, 15

12 Davidson himself seems confused about this point. In IDCT, he says, ‘theories of truth based on the substitutional interpretation of quantification do not in general yield the T-sentences demanded by convention T’ (79-80).

13 Platts, 15

14 Davidson, D. ‘Semantics for Natural language,’ in Davidson, D. and Harman, D. eds., The Logic of Grammar (New York: Dickenson Publishing Co. Inc. 1975), 19.Google Scholar Cf. also BBM: 348.

15 We use the expression ‘utters’ in the present context (in contrast to ‘says that’) in such a way that a speaker may utter (on a particular occasion) some words without his or our knowing what these words mean. On ‘holds true,’ Davidson says: ‘a good place to begin is with the attitude of holding a sentence true, of accepting it as true … .’ It is an attitude an interpretor may plausibly be taken to be able to identify before he can interpret, since he may know that a person intends to express a truth in uttering a sentence without having any idea what truth. Not that sincere assertion is the only reason to suppose that a person holds a sentence to be true. Lies, commands, stories, irony, if they are detected as attitudes, can reveal whether a speaker holds his sentences to be true. There is no reason to rule out other attitudes towards sentences, such as wishing true, wanting to make true, believing one is going to make true, and so on, but I am inclined to think that all evidence of this kind may be summed up in terms of holding sentences to be true’ (RI: 322).

16 Fodor, J. The Language of Thought (New York: Crowell 1975)Google Scholar; Harman, G. ‘Meaning and Semantics,’ in Munitz, M. and Unger, P. eds., Semantics and Philosophy (New York: New York University Press 1974), 1–16Google Scholar, and Harman, G. ‘Three Levels of Meaning,’ in Steinberg, D. and Jakobovits, I. eds., Semantics (Cambridge: Cambridge University Press 1971), 66–75Google Scholar. A number of other authors have agreed with Harman and Fodor in seeing little difference, if any, between specifying meaning by translation and specifying meaning in terms of truth conditions. For example, Field, H. ‘Logic, Meaning and Conceptual Role,’ Journal of Philosophy, 74 (1977) 379–402Google Scholar; Putnam, Hilary ‘The Meaning of ‘Meaning’,’ in Gunderson, K. ed., Minnesota Studies in the Philosophy of Science, Vol. VII (Minneapolis: University of Minnesota Press 1975), 131–93Google Scholar.

17 For example, Tennant, N. ‘Truth, Meaning and Decidability,’ Mind, 86 (1977) 368–9CrossRefGoogle Scholar, and Haack, R.J. ‘Davidson on Learnable Languages,’ Mind, 87 (1978) 234Google Scholar.

18 Convention T, in skeletal form I have given it, makes no mention of extensionality, truth functionality, or first order logic. It invites us to use whatever devices we can contrive appropriately to bridge the gap between sentence mentioned and sentence used; restrictions on ontology, ideology, or inferential power find favor, from the present point of view, only if they result from adopting Convention T as a touchstone. What I want to defend is the convention as a criterion for theories, not any particular theories that have been shown to satisfy the convention in particular cases, or the resources to which they have been limited. (IDCT: 79)