Response to CampAuthor(s): John WallaceSource: Noûs, Vol. 9, No. 2 (May, 1975), pp. 187-192Published by: WileyStable URL: http://www.jstor.org/stable/2214600 .

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Response to Camp JOHN WALLACE

UNIVERSITY OF MINNESOTA

Let S be an advocate of a substitution interpretation of quantifiers and R an advocate of a referential interpretation. S and R are bound to disagree about semantics on the sub- sentential level. For example, for S, the semantics of the predicate "red" is a matter solely of the truth values of sentences of which "red" is a part; for R, it is a matter of a relation between "red" and red things. But it is not obvious that S and R disagree about semantics on the sentential level. It is at least possible that they share a project concerned with the concept of truth which can be described in terms of semantical and logical properties of whole sentences about which they agree. Put intuitively, the project is to explain why the sentences of our language have the truth conditions they have.

It appears from some detailed examples (set out in papers to which Camp refers in [1]) that in attempting to carry out this project R would succeed but that S would either fail or call on semantical devices which make his subsentential semantics indistinguishable from R's.

What can S do? His obvious first step is to ask that the truth project be clarified. Convention T shows us how to do this. The basic materials needed are an object language, a metalanguage which contains a system of structural-descriptive names of object-language sentences, and a translation of object-language sentences into metalanguage sentences. It is important here that a consequence relation be given along with the metalanguage, for the heart of Convention T is that all instances of

(1) xistrue - p

be consequences of an adequate theory of truth, where "instance" is explained in the obvious way in terms of translation and structural-descriptive naming. Notice that "truth conditions" in the intuitive formulation of the project has given

NOtJS 9 (1975) ? 1975 by Indiana University 187

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188 NOtS

way to "instances of (1)" and that "explain" has given way to "consequence" (shades of the deductive-nomological model). Notice too that from the point of view of trying to find enough common ground to launch a sharp disagreement between S and R, it is important that consequence is a relation between whole sentences about whose extension S and R may agree, however much they may disagree about its real definition. Only the extension of the consequence relation matters to Convention T.

But back to the project. Since it concerns our own language-it is the semantics of our own language that we would like to articulate-ideally we would take our own language to be both object language and metalanguage. This ideal is frustrated, in practice by the magnitude of the task and in principle by the semantical paradoxes. The customary compromise, which seems acceptable in the present case, is to take as object language some natural fragment of our language and as metalanguage this same fragment plus minimal syntacti- cal, semantical, and set-theoretic apparatus. It adds to clarity, though I think it is not otherwise conceptually important, to regard both languages as formalized. At this point, S's insistence on clarification of the project begins to pay off. In the examples I found to embarrass S, both object language and metalanguage are built on the pattern of first-order quantification theory. Another form of metalanguage might be congenial to S and might give him explanatory resources which would enable him to give the desired explanations without using R's tools. S's insistence on clarification pays off also in connection with translation. In my examples, I assumed in effect that the correct translation was simply identity: instances of "Tx < p" are obtained by putting a sentence of the object language (which is also a sentence of the metalanguage) for "p" and a structural- descriptive name of that sentence for "x". S might be able to show that this translation is somehow incorrect or inappropriate and that it should be supplanted by a translation yielding explananda which S can give without using R's tools.

In sum, it might be that S can legitimately replace the explanatory task I gave him by changing the means of explanation or by changing the ends (or of course both), and either strategy might solve the problem I posed for him. These two lines of objection, which are quite genuine, are identified and pressed by Camp.

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RESPONSE TO CAMP 189

First, new means. Camp suggests that S should find intelligible a form of language which uses a quoting functor, where it is permitted even to quantify into this functor. He proposes a metalanguage which uses such a functor (in a restricted way, so as to avoid worries about consistency); he frames in this metalanguage a theory of truth which exploits the functor in a way that, he claims, (i) satisfies the version of Convention T on which I had insisted and (ii) does not introduce R's concepts of denotation or satisfaction. He is right about (i), but he appears to be wrong about (ii). He points out correctly that "Trans 'x' = y" cannot be a definition of "y denotes x", because the position of "x" in the former is referentially opaque. As far as I can see, however, we can use "(3z) [x = z and Trans 'z' = y] " as a definition of "y denotes x". Even if Able = Baker, and thus Able denotes Baker, it is not the case that Trans 'Baker' = Able; it is, however, the case that (3 z) [Baker = z and Trans 'z' = Able]. The characteristic properties of denotation, i.e., those set out in Camp's (10)-(12), are guaranteed by this definition plus Camp's axioms (13)-(18). It appears then that R can reply to Camp as follows: I understand your quotation functor in the sense that I grasp the rules which govern its use; in particular, I understand it well enough to see that taken together with the axioms of your truth theory, it makes possible a definition of denotation, which is just what experience with metalanguages of more standard form had led me to expect. There is a sense in which R does not understand the quotation functor: he has no semantics for it. At this stage of the argument, I do not see why this should worry him any more than it does Camp.

This reply does not close off the line of objection Camp was developing. It does show, I think, that a convincing objection along these lines has yet to be made.

The second objection concerns the possibility of replacing targets of explanation like

(2) (3x)(5 < x and x < 9 and x is prime) is true >-> (3 x)(5 < x and x < 9 and x is prime),

which involve a mention-use shift, with targets more accessible to explanation with S's resources. Thus, if the translation of "(3x)(5 < x and x < 9 and x is prime)" were taken to be not

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190 NOtS

the sentence itself but "(3c)(c is a numeral and the sentence which results from substituting this numeral for x in the open

sentence 5 < x and x < 9 and x is prime is true)" or simply

"(3x)(5 < x and x < 9 and x is prime) is true", S would have no trouble explaining the desired biconditionals.

But what could make us stop wanting an explanation of the biconditionals which involve a mention-use shift and thus finding a theory which explains them at an advantage over one which does not? What could lead us to reject homophony as an optimal rule for translating our language into itself? And if homophonic translation is optimal, why should we not accept responsibility for explaining the truth biconditonals to which it gives rise? After all, the biconditionals generated by homo- phonic translation are true, and though they are infinite in number, every speaker of the language who grasps the concept of truth knows each of them. How can there be any question, then, that a theory which gives a simple, compact, clearly motivated explanation of all the biconditionals teaches us something worth knowing about our language, difficult as it may be to say exactly what it teaches us and exactly what is the value of the lesson?

I do not see that Camp's remarks in Section IV of his paper provide an answer to these questions which gets S out of his difficulty. He does make a very interesting suggestion. I take up this suggestion last, after trying to clear away apparent misunderstandings.

Camp writes: "Remember that we are concerned with truth-theories as interpretations of initially uninterpreted artifi-, cial languages" ([1]: 179). This was not my concern. I use formalization merely as a device for clarifying an explanatory job which arises in ordinary language for ordinary language. Remember, I wanted to establish a negative. One must have an absolutely sure grip on the consequence relation in order to have any chance of showing 'that a certain substitutional truth theory does not have the desired consequences. I agree that truth definitions have important uses in lending sense to the sentences of artificial languages, and I suppose that my observations about substitutional quantification shed some light on this process; but these matters were not my main interest.

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RESPONSE TO CAMP 191

Some of Camp's remarks suggest that he fears that I think we do not understand the concept of truth at all prior to being given a theory of truth. I do not think this. The project of explaining "true in L" for variable "L" is one which intrigues me, and I suppose that Convention T, Tarski's constructions, and in a much more modest way my observations about substitution quantification may have some bearing on the project if it ever gets off the ground. But the success of this project is not needed to bring out an advantage R has over S.

Camp quotes a passage in which I appear to be making what might be regarded as heavy weather of the notion of truth conditions, saying in effect that (2) gives the truth conditions of "(3x)(5 < x and x < 9 and x is prime)" but that

(3) (3x)(5 < x and x < 9 and x is prime) is true <

(3x)(5 <x andx <9 andx is prime) is true

does not. I appreciate that the notion of truth conditions cannot bear much weight, though I suspect that with a little work it can be made to bear the weight I was putting on it here. But suppose it cannot; it makes no difference to the point at issue. For let us say that both (2) and (3) give correct truth conditions for the sentence in question. R still maintains his advantage: he can explain biconditionals like (2) and ones like (3), whereas S, so far as is known, cannot explain ones like (2) without having his theory collapse into R's.

Finally, let me take up a suggestion of Camp's that seems to me to have considerable interest. Philosophers and other language users sometimes introduce abbreviations. It is a common and intelligible practice. Jones introduces a system of abbreviation a paradigm application of which is that

It sevenexes that the earth is round

abbreviates

The earth is round contains more than seven letters.

If Jones turns right around and tries to construct a truth theory which has as consequences all sentences like

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192 NOtJS

(4) It sevenexes that the earth is round is true it sevenexes that the earth is round,

he is in for trouble. And he is out of his senses. All that can reasonably be asked is that a truth theory prove

(5) It sevenexes that the earth is round is true *-> the

earth is round has seven letters.

Here at last is a justified departure from using homophonic translation in Convention T. Now suppose Jones's system of abbreviation catches on. Later generations use it but forget its origin. They will be strongly tempted to try for truth theories that explain sentences like (4). Unhappy creatures! If only they knew the history! Let us hope that they can develop a science which enables them to reconstruct the history or, even without the history, to justify aiming at (5) instead of (4). Camp, if I follow him, thinks that relative to some kinds of English sentence, we may be in a position analogous to that of these unfortunates. I agree; we may. (To connect our little story with another of its sources, belief sentences and modal sentences should be added to the list Camp gives of sentences which may be duping us.) Camp thinks also that reflecting on Convention T alone is not going to settle the question whether we are being duped by a given class of sentences. I agree again; it's not. What we need is a set of principles which helps us separate the cases in which we are right to insist on the homophonic version of Convention T from those in which we are right to relax this requirement. I would be astonished if, when the principles are in, we are not left with a central core of sentences of our language, including an infinite number of sentences with quantifiers, for which the homophonic version of Convention T is the proper explanatory goal. Surely not all our sentences have the sort of covert metalinguistic character which is present in "it sevenexes that the earth is round". If this is so, and S and R can be gotten to see that it is, then R's advantage over S in the dispute about substitutional quantification-that R explains something agreed to be worth explaining which S can explain only by having his theory collapse into R's-will withstand Camp's second line of objection.

REFERENCE

[1] Joseph L. Camp, Jr., "Truth and Substitution Quantifiers," NOUS 9(1975): 165-85.

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