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The Philosophical Problem Of Truth-Of

Published online by Cambridge University Press:  01 January 2020

Robert Cummins
Robert Cummins*
Affiliation:
The Johns Hopkins University
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Extract

There is a certain view abroad in the land concerning the philosophical problems raised by Tarskian semantics. This view has it that a Tarskian theory of truth in a language accomplishes nothing of interest beyond the definition of truth in terms of satisfaction, and, further, that what is missing — the only thing that would yield a solution to the philosophical problem of truth when added to Tarskian semantics — is a reduction of satisfaction to a non-semantic (and ultimately physical) relation. It seems to me that this view either misidentifies the philosophical problem altogether, or encourages a seriously misleading picture of the nature of the problem.

The view I have in mind is nowhere more persuasively at work than in a recent paper by Hartry Field.1 In this paper Field argues that a Tarskian theory of truth for a natural language is impossible if we insist on Tarski's case-by-case elimination of ‘satisfies'. More fundamentally, however, he argues that a Tarskian theory could provide nothing of philosophical interest beyond the admittedly interesting reduction of truth to satisfaction, and his ground for this claim is, roughly, that a Tarskian theory does not reduce its primitive semantic relation — satisfaction — to a non-semantic relation.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 5 , Issue 1 , September 1975 , pp. 103 - 122
Copyright
Copyright © The Authors 1975

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References

1 Field, Hartry “Tarski's Theory of Truth,” The Journal of Philosophy, LXIX (1971), 347–375.Google Scholar

2 Tarski, A. “The Concept of Truth in Formalized languages,” in Logic, Semantics and Metamathematics. (Oxford: The Clarendon Press, 1956.)Google Scholar

3 I assume here that the object language L is included in the metalanguage (“mathematical English” in this case). If not, then the use of ‘⊆’ on the right of the biconditional must’ be replaced by its translation in the metalanguage.

4 The recursive definition only allows elimination from contexts of the form ‘s is true (in L)’ where ‘s’ is schematic for a description of a sentence of L from which the syntactic analysis of the sentence itself can be recovered. A standard maneuver allows one to upgrade the recursive definition to an explicit definition, but then understanding the set theory required for the upgrading (in the meta-metalanguage) will be part of the bargain.

5 I take these remarks to be a gloss of Quine's remark that convention T renders attribution of truth to ‘snow is white’ as clear as attribution of whiteness to snow. Cf., Quine, W.V. “Notes on the Theory of Reference,” in from a Logical Point of View (Cambridge: Harvard University Press, 1964), p. 138Google Scholar. For criticism along lines distinct from those pursued by Field, see Stich, S.P. “Dissonant Notes on the Theory of Reference,” Nous, IV (1970), 385–397.CrossRefGoogle Scholar

6 Field, Op. Cit., p. 369.Google Scholar

7 Ibid.

8 Surely if F and G are acceptable, so is their disjunction. Yet the disjunction need have no physical significance: ‘x bonds with or dissolves in y’ identifies no significant physical relation. What is required is that every case of “bonding-or-dissolving“ be physically explicable somehow or other.

9 See, for example, Quine's, discussion in chapter one of The Philosophy of Logic (Englewood Cliffs: Prentice Hall, 1971)Google Scholar, especially the first full paragraph on page three.

10 Curiously, the objection does seem to have some force in the witchcraft case. It is hard to imagine how we could have any confidence in a list-type elimination of ‘casts a spell over’ without having some idea how spells are to be explained. This may be sheer prejudice, however, deriving from the fact that we cannot in fact formulate a theory which identifies the spells.

11 Field, of course, does not dispute this point. See pp. 361–2 and footnote fourteen of “Tarski's Theory of Truth.” What Field does dispute is the utility of an extensionally adequate theory which eliminates semantic terms without reducing them.

There is another way to see the benefit that may accrue to a theory in virtue of the availability of a recursive elimination of its otherwise primitive terms. For, in principle anyway, such an elimination can be seen as a technique for promoting certainty about the use of the eliminable term in a finite number of clear cases into certainty about the use of the term generally: if we can find it in ourselves to accept a finite number of clauses like (1), together with a theory like Field's T1 which gives the satisfaction conditions of complex expressions as a function of the satisfaction conditions of constituents, then we can find it in ourselves to accept statements of satisfaction and truth conditions generally. We thus reduce our total epistemological commitment in semantics to whatever is involved on the right hand side of clauses like (1).

12 Field, Op. Cit., p. 363.Google Scholar

13 Field doesn't explain what he means by “structural properties of atoms.” A clear case would be attribution of tab-and-slot or hook-and-eye type shapes. We might then explain that molecules hold together in the manner of jig-saw puzzles. Actual properties of atoms ? number and kind of elementary particles together with their quantum states ? hardly seem “structural,” but I think the point is fairly clear. Potassium bonds with oxygen. To take this as a primitive dispositional property of Potassium atoms is “chemicalism“; physicalists must be able to explain why potassium bonds with oxygen by appeal to laws governing the constituent elementary particles. With this understanding, I will continue to express the matter in Field's way.

14 Field, Op. Cit., p. 363.Google Scholar

15 The actual facts, I think, provide nothing like this clear a case ? hence the fantasy.

16 Unless, of course, one thinks that all that can be done in the way of explaining this fact is to show that There is some initial plausibility to this view. Asked why ‘red x3 is satisfied by < snow, cheese, blood, … > a natural response would be to answer, “Because blood is red.” If we accept a redundancy theory of truth, then Tarskian semantics provides all there is to provide in the way of explaining “the facts of satisfaction.” The trouble with this line is that we can easily construct a language containing the expression ‘Red x3’ such that the proper answer to the question is, “Because blood is a liquid.” This seems explicable only if we assume that, in constructing such a language, we would be establishing a relation between that expression and liquids. If we are to explain matters in this way, then we must, eventually, explain the explaining relation.

17 Of course, (5) could be of no use to physicalists unless a physicalistic account of the psychological notion of response were available. I propose to ignore this as it raises problems tangential to my concerns here.

18 I use “reductive” in a way analogous to the use of “law-like“: (4) is reductive because it is the sort of thing which would actually allow us to reduce valence to a physical property if it were true.

19 I know of no way to characterize illuminatingly the sort of explanation (4) but not (3*) would provide. Plainly, more than subsumption under general laws is involved, since either (3) or (3*) would open the way to deductive- nomological explanations of bonding, and in “structural terms” at that!

20 For the purposes of the ensuing discussion, this need be regarded as no more than a terminological stipulation.

21 Field may mean to count as reduction things like (6) which, as I say, analyze valence away. I doubt it, though: I don't think Field could have been thinking that something analogous to (6) could throw any philosophical light on semantics, and he clearly was thinking that a “reduction” would.

22 This deals only with monadic predicates. Generalization to n-adic predicates involves obvious but (for present purposes) irrelevant complications. Notice, by the way, that application is not language-relative on this construal.

23 This would constitute an abandonment of physicalism as we know it, for we should have to admit that the behavior of physically complex entities (molecules) is not explicable solely by appeal the laws governing their ultimate physical constituents. (To see that this “componentialism” is central to physicalism, imagine what we would have to say if it turned out that the gravitational acceleration experienced by a hydrogen molecule at a distance d from a mass m were not double that experienced by a hydrogen atom at a distance d from m.)

24 If (8) is to be useful, we must assume that events which are tokenings in L can be distinguished from events which are not. Usually, the token produced will settle this matter, but where it does not we are free to appeal to the etiology of the event in question.

25 See, for example, Fodor, J. A. Psychological Explanation (N.Y.: Random House, 1968), pp. 32–48.Google Scholar

26 Ibid., p. 118.

27 See, for example, David Lewis’ discussion of Putnam in his review of Capitan and Merrill, eds., Art, Mind, and Religion, The Journal of Philosophy, LXVI (1969) pp. 22–27.Google Scholar

28 One might dispute even this: perhaps different persons (or the same person on different occasions) produce tokenings having the same application via processes which have radically different functional analyses (i.e., by executing different programs) just as two adders may produce sums in virtue of realizing radically different algorithms.

29 It seems to me that the well-attested fact of redundancy in the brain, and the fact that linguistic performances are manifestations of learned capacities acquired under widely divergent conditions, together make it likely that etiologies of tokenings having the same application are functionally equivalent at most. But I would not insist on this point.

30 Since the scientific problem is not well-specified, there is no way to assess alleged solutions to it. Hence our feeling of being at sea when confronted with (5).

31 Of course, accepting (F) as a stipulation is not strictly speaking a necessary condition of knowing English. One may know English without understanding, or even encountering, tokenings of ‘fish'. So a rule of English is not simply something one must accept as a stipulation to count as knowing English. This is an aspect of the fact that knowing a language is a matter of degree.