(5) Knowledge of the meaning of any sentence requires possession of the concept of truth.
(6) The concept of truth cannot be defined or analyzed.
Just as one cannot know that the conditions under which it is legal to do something are such-and-such unless one has the concept of legality, so one cannot know that the conditions under which it is true to say something are such-and-such unless one has the concept of truth. Hence the step from (4) to (5). If even toddlers who have not yet learned the word “true” would have to possess the concept of truth (presumably on the same unconscious level where speakers possess various syntactic and phonological concepts for which many never learn the words at all) before they could learn the meaning of anything, then truth is a concept so basic that there can hardly be any more basic concepts in terms of which it might be analyzed or defined. Hence the step from (5) to (6).
The thesis (6), called truth primitivism, was upheld (for reasons of his own) by Frege, but is at least implicitly rejected by every other theory of truth mentioned in this book, since all in one way or another do attempt some sort of analysis. Thus (3) threatens, via (6), not only deflationism but almost every other theory of truth. (We say “threatens” rather than “contradicts” as acknowledgment that the steps from (3) to (6) are not logically watertight.) But why should one accept any version of truth-conditional semantics? Where does truth-conditional semantics come from? The short answer is: from Donald Davidson's reaction to Tarski.
6.2 DAVIDSONIANISM
Tarski was mainly concerned to define truth for object languages useful in pure mathematics. Mathematical language lacks many features found in nonmathematical language, and this circumstance made Tarski's task easier. For instance, indexicality is absent from pure mathematics, and that is why Tarski was able to get away with working with types rather than tokens. Also, in mathematical language the logical forms of sentences are usually more or less obvious, which made it easier for Tarski to find the clauses in his recursive truth definition.
Where the logical form of a construction is unobvious, so is the form the clause for that construction should take in a recursive truth definition. To give one example, consider singular negative existentials, such as
(7) Pegasus does not exist.
This is a common enough construction outside mathematics (since only in mathematics is one required, before introducing a name, to prove the existence of its bearer). Two competing accounts assign (7) logical forms symbolizable as follows:
(8a) Np, where p is a constant denoting Pegasus and N a predicate for nonexistence.
(8b) ~xP x, where P is a predicate for being Pegasus.
And there are other proposals. How a Tarski-style truth definition should treat (7) depends on which account of its logical form is right. Thus corresponding to (8a) or (8b) one might have clauses like these:
(9a) (7) is true iff the thing denoted by “Pegasus” satisfies “x is nonexistent.”
(9b) (7) is true iff no thing satisfies “x is Pegasus.”
Corresponding to some other proposal one would have something else. Distinctions of tense and mood, propositional attitude operators (“So-and-so knows/believes that…”), and many more constructions found in nonmathematical language also have un-obvious logical forms.
To extend Tarski's definition to any large fragment of extra-mathematical language is therefore not easy. No one has done more to promote the program of doing so than Davidson, though Davidson's perspective was the opposite of Tarski's. For Tarski, truth was a problematic notion, for which a definition was sought, while the various notions of the object language were taken for granted. For Davidson, it is truth that is more or less taken for granted, and the clauses of the recursive definition give information about the logical form and other aspects of the meaning of constructions in the object language.
One feature of Tarski's procedure that impressed Davidson was the phenomenon we encountered in connection with a toy language in §2.3, where we saw that from the (finitely many) clauses of Tarski's recursive definition of truth one can derive in a canonical way, for any of the (infinitely many) sentences of the object language, a biconditional of form
(10) “ _______ ” is true in L iff _ _ _ _ _.
with the given object language sentence on the left and on the right a sentence of the metalanguage that is a translation of it. Davidson sought an extension of this result beyond toy cases to natural language. In this connection, he notoriously said that giving such a theory of truth for a language is a way of giving a theory of meaning for it.
This dictum has been variously interpreted, elaborated, and amended by Davidson's disciples and Davidson himself at different stages in the development of his ideas. As a result, there are many quite different views today that call themselves “Davidsonian.”
Now just as, given Davidsonianism's Tarskian origins, and Davidson's own militant antipropositionalism, one would not expect such views to challenge sententialism, so also, given those origins, and Davidson's heavy emphasis on the T-biconditionals (10), one would not expect them to challenge the equivalence principle, deflationism's first thesis. Some forms of “Davidsonianism,” however, may not challenge any principle of deflationism—or of any other theory of truth, for that matter. For in some the role of truth in the theory of meaning has become so very indirect that it is no longer clear that it even matters whether it is truth rather than something else that is playing the role. Such versions may not even endorse the slogan (3) and so may not even count as truth-conditional semantics as we are using that label here, however they label themselves. Other forms of Davidsonianism may endorse (3) without (4), or (4) without (5), or (5) without (6). Davidson himself, however, did emphatically endorse the thesis (6) of primitivism, the most threatening item on our list.
There is another line of thought suggesting a close connection between meaning and truth conditions, based on a naive picture of what goes on in the situation where a child is beginning to learn its first language. Davidson, it may be remarked, despite his sometimes arguing in favor of his approach on the ground that it is necessary to explain the learnability of language, was more concerned with the situation where speakers of a first language are trying to interpret a second, and many later Davidsonians seem even less concerned than Davidson himself with learning a first language. (Notoriously, at one well-known hotbed of Davidsonianism some even deny that we ever do learn a first language. On their view, we do not learn, but rather are born knowing, a language of thought; what is commonly mistaken for learning a first language is really learning to interpret a second language in this innate language; and courses mistitled “English as a Second Language” are really courses on English as a third language.) So the line of thought we have in mind is largely independent of developments in high theory deriving from Davidson.
The naive picture is simply that the child receives parental approval for itself saying “The cat is on the mat” when Felix is over here and not elsewhere, and likewise “The dog is in the bog” when Fido is over there and nowhere else, and so on, and comes to associate with these sentences—along with others formed by recombining components—the conditions under which approval has been experienced and/or is to be expected, which is to say, the conditions under which the sentences in question are true. The nebulous conclusion here, that knowledge of meaning involves “associating” truth conditions with sentences, stops well short of hardcore truth-conditional semantics, let alone truth primitivism. But any argument against truth-conditionalism broad enough to rule out the nebulous, naive version will a fortiori suffice to rule out the hardcore version, and so rescue any threatened theories of truth. And though rescuing deflationism was the furthest thing from his thoughts, a quite broad purported refutation of truth-conditionalism is precisely what is offered us by—to get back to him at last—Dummett.
6.3 DUMMETTIANISM VS DAVIDSONIANISM
Dummett is centrally concerned with what knowledge of meaning consists in, and so is conce
rned to refute truth-conditional semantics only in versions that claim to tell us something about that—essentially, what we have called hardcore versions. For Dummett, knowledge of the meaning of the most elementary parts of a first language is crucial, because such knowledge must be tacit, whereas knowledge of the meaning for more advanced parts may be verbalizable, expressible using vocabulary from the more elementary parts, as knowledge of meaning for a second language may be expressible using a first language. For Dummett, the verbalizable/tacit distinction is central, for assimilating it to the theoretical/practical distinction, he concludes that knowledge of meaning is ultimately not a matter of knowing-that, but of knowing-how. It is not a matter of having a certain thought, but of having a certain ability.
Which ability? According to the verification-conditional semantics that Dummett opposes to truth-conditional semantics, learning the meaning of a sentence is acquiring an ability to recognize whether or not something constitutes a verification (or warrant for assertion) thereof. Thus to know the meaning of
(11) The cat is on the mat.
is to be able to recognize whether or not a given experience constitutes an observation of the cat's being on the mat. Note that the ability in question is not an ability to tell whether the cat is on the mat, or whether it is true that the cat is on the mat, since we have no such ability: If someone asks whether the cat is on the mat, we will be able to tell if we happen to be in the room with the cat and the mat, and unable to tell if we are far away; but we grasp the meaning of the question equally well wherever we may be.
Knowledge of meaning as a recognitional ability is supposed to extend beyond such elementary examples. Knowing the meaning of, say, Goldbach's conjecture
(12) Every even number greater than four is a sum of two primes.
is supposed to consist in being able to recognize whether or not a given argument constitutes a proof of (12).
What would count as a proof, by the way, what logical steps are permitted in a proof, itself depends on the meaning of the logical vocabulary. Here verification-conditional semantics, like truth-conditional semantics, assumes that the meanings of compound sentences are determined by the meanings of their components and the mode of composition, but replaces the truth-conditional account of each mode of composition by a verification-conditional account.
In the case of disjunction, for example, the Tarski-style condition
(13a) “______ or _ _ _ _ _” is true iff one of the pair
“_______” and “_ _ _ _ _” is true.
is replaced by the condition
(13b) Something is a verification of “______ or _ _ _ _ _” iff it is a verification of one of the pair “_______” and “_ _ _ _ _.”
The difference between classical and intuitionistic mathematics (over excluded middle, for instance) is supposed to trace back ultimately to such differences as that between (13a) and (13b), and Dummett argues for intuitionist as against classical mathematics by arguing for making verification (or warranted assertability), rather than truth, central to meaning.
His main argument starts from the premise
(14) Ascription of tacit knowledge makes sense only if one can say what would constitute manifestation of that knowledge.
Dummett then claims that verification-conditional theories can meet the challenge of identifying what constitutes manifestation of tacit knowledge of meaning in a way truth-conditional theories cannot. The positive side of Dummett's claim is that if knowledge of meaning is an ability to recognize when a sentence has been verified (or when assertion of it is warranted), there is no problem about saying what constitutes a manifestation of that ability. It is manifested when speakers show themselves willing (unwilling) to assert or assent to the sentence when presented with something that does (doesn't) constitute a verification of it. The negative side of Dummett's claim is that there is no plausible candidate for what manifestation of tacit knowledge of truth conditions would be, given that we have no general ability to recognize truth.
The premise (14) of Dummett's manifestation argument sounds similar to the rhetoric of the behaviorists who dominated psychology and linguistics around the middle of the last century, as do other of his formulations. Since psychologists and linguists today regard behaviorism as outmoded and discredited, this makes Dummett easy for Davidsonians to ignore or dismiss. But let us think of Dummett as attempting, not to give a knock-down argument, but to raise an embarrassing question: What could grasp of truth conditions—never mind the behavioristic demand for manifestation of that grasp—consist in?
In the case of (11), there may be a “mental representation” or “picture in the head” of the cat on the mat. But imagining what it would look like for the cat to be on the mat (for (11) to be true) is indistinguishable from imagining what it would be like to see the cat on the mat (to verify (11)). Thus having the mental picture could with no less and arguably more justice be called a “grasping a verification condition” rather than “grasping a truth condition.” And in any case, if we switch from examples about cats and mats to examples about, say, catalysis and matriculation, let alone Goldbach's conjecture, there will be no relevant picture in the head.
6.4 DUMMETTIANISM VS DEFLATIONISM
There is no obvious reason why either a truth-conditional or a verification-conditional theorist should deny that the meaning of the word “true” is given by some version of the equivalence principle. Corresponding to the contrast between (13a) and (13b) we would have a contrast between the following:
(15a) “It is true that _______” is true iff ______ is true.
(15b) Something is a verification of “It is true that ______” iff it is a verification of “_______.”
But a truth-conditional semanticist who is committed to (5) will have to say that to learn the meaning of the word “true” is not to acquire a new concept, but merely to learn the label for a concept one already had on some level, as Monsieur Jourdain did when he learned the word “prose.” Verification-conditional semanticists are not committed to (5), and so lack this reason to deny that the concept of truth is acquired when the word “true” is learned, suggesting that they may be able to go a step further in agreement with deflationism than truth-conditional semanticists can. (In this connection note the contrast that, while “true” is mentioned on the left side in both (15a) and (15b), it is used only in (15a) and not in (15b).)
Yet there seems to remain a conflict between Dummettianism and deflationism insofar as the latter is committed to there being no interesting property coextensive with truth across the whole range of truths, while the former advances the slogan “There is no verification-transcendent truth,” apparently committing Dummettians to the thesis that truth is coextensive with verifiability. One may question, however, how serious the conflict is.
On the one hand, is Dummettianism after all seriously committed to this verifiability thesis? It is not obvious how to get to the verifiability thesis from verification-conditional semantics. For instance, how exactly are we supposed to get from the first to the second of the following?
(16) To know what it means to say that there is intelligent life in other galaxies is to be able to recognize whether or not something constitutes a verification that there is.
(17) If there is intelligent life in other galaxies, then it is at least in principle possible to verify that there is.
One route to (17) exploits a verification-conditional account of the conditional “if…then….” Corresponding to the contrast between (13a) and (13b) we would have a contrast between the following:
(18a) “If ______, then _ _ _ _ _” is true iff, if “______” is true, then “_ _ _ _ _” is true.
(18b) Something is a verification of “if _____, then_ _ _ _ _” iff it is a verification that a specified method will convert any verification of “_______” into a verification of “_ _ _ _ _”
If (18b) gives the meaning of the conditional construction, then to verify the particular conditional (17) all we need
to do is specify a method that verifiably will convert any verification of (i) “There is intelligent life in other galaxies” into a verification of (ii) “It is verifiable that there is intelligent life in other galaxies.” That seems easy. The method is just this: According to (16), we have an ability to recognize a verification of (i) when presented with one; so given a verification of (i), just apply that recognitional ability to it, to see that (i) has been verified and hence a fortiori is verifiable; for to see this is to verify (ii).
There is an air of hocus-pocus, however, to such argumentation, and some uneasiness that it may prove too much. For we don't want a proof that
(17*) If there is intelligent life in other galaxies, then it has actually been verified that there is.
The situation is complicated by the existence of an argument, Fitch's paradox of knowability, purporting to show that the validity of the principle “If A then it is verifiable that A” would imply the validity of the principle “If A then it has been verified that A.” While there is almost universal agreement that there is a fallacy somewhere in the Fitch argumentation, there is no agreement as to just where. But the substantial literature on this topic cannot be gone into here.
Truth (Princeton Foundations of Contemporary Philosophy) Page 11