Tarski, Davidson, and Theories of Truth

by David Larson *

Summary In developing his claim that meaning cannot be understood independently of truth, Donald

Davidson argues that a theory of meaning will take the form of a Tarskian theory of truth. In this essay I seek to describe more fully the structure of a Davidsonian theory of meaning and the extent to which Davidson modifies Tarski’s account. 1 consider and reject John Foster’s claim that Davidson takes, or should take, truth as a formal primitive, and argue that it is Davidson’s principle of charity which plays the essential role in giving theories of truth empirical applica- tion.

Resumt En developpant sa these selon laquelle la signification ne peut pas Ctre comprise independam-

ment de la verite, Donald Davidson affirme qu’une theorie de la signification prendra la forme d’une theorie tarskienne de la veritt. Dans cet essai, j’essaye de decrire plus complttement la structure d’une theorie davidsonnienne de la signification et la mesure dans laquelle Davidson modifie la these tarskienne. J e discute et rejette la these de John Foster, B savoir que Davidson prend ou devrait prendre la vkrite comme une notion formellement primitive, et montre que c’est le principe de charite de Davidson qui joue le r6le essentiel parce que c’est lui qui permet aux theories de la vkritC de s’appliquer a l’exptrience.

Zusammenfassung lndem er den Standpunkt vertritt, dass Bedeutung nicht unabhangig von Wahrheit verstan-

den werden kann, argumentiert Davidson, dass eine Bedeutungstheorie die Form einer Tarski- schen Wahrheitstheorie annehmen wird. In der vorliegenden Arbeit versuche ich, die Struktur von Davidsons Bedeutungstheorie genauer zu beschreiben und zu zeigen, inwieweit Davidson Tarskis Auffassung verandert. Ich betrachte und verwerfe John Fosters Behauptung, wonach Davidson Wahrheit als primitiven Term im formalen System einfiihrt oder das tun sollte, und zei- ge, dass es Davidsons Prinzip der Nachsicht (“principle of charity”) ist, das eine wesentliche Rolle fur die empirische Anwendung von Wahrheitstheorien spielt.

The concept of meaning cannot be understood independently of the con- cept of truth, according to Donald Davidson. In his extensive development and defense of this claim Davidson describes the process of interpreting a lan- guage as a process of constructing a theory of meaning for that language.

* University of Kansas, Lawrence, Kansas

Dialectica Vol. 42, No 1 (1988)

4 David Larson

Such a theory of meaning is supposed to be modeled after the formal theories of truth described by Alfred Tarski (see “The Concept of Truth in Formalized Languages”), but Davidson also regularly describes such theories as empiri- cal. In this essay I seek to explain just how Davidson incorporates Tarskian truth theories in his account and the extent to which Davidson finds it necessary to modify Tarski’s account in the process. It is not part of my pro- ject to consider the merits of Davidson’s proposal.

I .

Convention T, on Tarski’s account, is a statement of the significance of certain formal systems; in particular, it expresses a sufficient condition of a theory being a theory of truth. We can tell we have successfully constructed a theory of truth when that theory passes the test of Convention T. A theory is a theory of truth if it contains a formally correct and materially adequate defini- tion of truth, and it is, properly speaking, the material adequacy of this defini- tion which is addressed by Convention T. Here is Tarski’s statement of the Convention:

(T) A formally correct definition of the symbol ‘Tr’, formulated in the metalanguage, will be called an adequate definition of truth if it has the following consequences:

(a) all sentences which are obtained from the expression ‘XE Tr if and only if p’ by substituting for the symbol ‘x’ a structural-descriptive name of any sentence of the language in question and for the symbol ‘p’ the expression which forms the translation of this sentence into the metalanguage;

(b) the sentence ‘for any x, if x E Tr then x E S’ (in other words ‘Tr E S’). (Tarski, p. 187).

Clause (a) describes the so-called T-sentences which are the theorems of an adequate theory of truth; clause (b) says that it follows from an adequate definition of truth that only sentences are true.

A definition of truth which satisfies Convention T determines the exten- sion of a truth predicate in its application to the sentences of a given language. Relative to that language, the truth predicate and its definition are metalin- guistic. I shall reserve the term ‘T-theory’ for formal theories of truth which, like the theory descriptive of the calculus of classes described by Tarski, con- tain a definition of a truth predicate which satisfies Convention T. T-theories are always expressed in a metalanguage relative to the language for which truth is defined. Convention T itself, because it mentions sentences of the T-theory, can be expressed neither in the object language nor in the metalan-

Tarski, Davidson, and Theories of Truth 5

guage but must be metalinguistic with respect to the metalanguage; that is, Convention T is meta-metalinguistic with respect to the language for which truth is being defined.

Tarski defines truth one language at a time; he offers no general defini- tion. It is often said that Tarski analyzes truth in terms of meaning. This would be obviously false if it meant that the particular definitions employ a notion of meaning, but the point rather is that insofar as Tarski offers an analysis of the general concept of truth, that analysis is in terms of meaning. Tarski sheds light on the general concept by giving a criterion of adequacy for any proposed particular definition. Nothing can be inferred about truth in general from particular definitions until the particular predicates defined are established to be co-extensive with the general truth predicate in its applica- tion to particular languages. Convention T provides the only connection be- tween the particular predicates defined within T-theories and the general con- cept of truth, and Convention T depends on a notion of translation or meaning. It is in order to avoid suggesting that the formal theories Tarski describes define the general concept of truth that I find it advisable in the cur- rent context to call these theories T-theories rather than theories of truth.

A T-theory, as described by Tarski, contains three sorts of axioms. The first sort are of a general logical character. Some axioms of this sort are needed by any formal theory whether it defines truth or not. These axioms contain such primitive expressions as the class inclusion operator, the identity sign, and the conditional operator. Axioms of a second sort are the equiva- lents, or translations, of axioms in the object language. Axioms of this sort do not express any equivalences; they are the equivalents of axioms expressed in the lower level language without themselves identifying the axioms with which they are equivalent. Metalanguage expressions equivalent to object language expressions occur primitively in these axioms. The third sort of axioms, the only sort listed by Tarski, provide the T-theory with the notions of ‘expres- sion’ and ‘concatenation’ as well as with names of particular expressions. These are the only axioms which mention expressions of the object language and they are concerned only with making possible the precise description of the syntactic structure of those expressions.

Tarski’s first nine definitions introduce into the metalanguage shorter names of object language expressions than the names allowed by the axioms. These definitions allow, for example, the negation of an expression e to be re- ferred to by means of a barred e rather than by means of an expression in which the concatenation functor explicitly operates on two names. Definitions 10-12 are concerned with the definition of the concept of a sentence; 13-17 with that of logical consequence; and 18-21 with those of deductive system,

6 David Larson

consistency, and completeness. In Definition 22 the notion of the satisfaction of a sentence by an infinite sequence of classes is defined, and this allows a concise definition of a truth predicate to be given as Definition 23. The defini- tions of satisfaction and truth, like the earlier definitions, contain no primitive predicates not found in the axioms themselves, though this fact is obscured by recursive formulation of Definition 22. Since the axioms are purely syn- tactical, or structural-descriptive, the definitions of satisfaction and truth are syntactical as well. Together, the axioms and definitions entail the theorems of the T-theory, among which are the T-sentences required by Convention T.

The only reason for calling Definition 23 a definition of truth as opposed to a definition of something else is that, with the truth predicate so defined, the obligation imposed by Convention T is fulfilled (see Davidson, “In Defense of Convention T”, p. 66). Convention T is the sole criterion of the material adequacy of a definition of truth; any predicate fulfilling it counts as a truth predicate. Similarly, a definition of satisfaction need only make pos- sible an adequate definition of truth in order to be adequate itself. Should alternative definitions of satisfaction ever equally suffice to define truth, then, aside from considerations such as simplicity, any choice between those defini- tions would be arbitrary.

11.

Davidson departs from Tarski at two critical points. Davidson drops Tarski’s requirement that truth be given a formally correct definition and he modifies the statement of material adequacy given in Convention T. Both departures are directly due to Davidson’s interest in meaning and natural lan- guage as compared to Tarski’s interest in truth and formalized language. As a result of these two departures from Tarski, Davidson’s form of Convention T functions as an empirical criterion of the adequacy of theories, or sets of axioms, rather than as an apriori criterion of the adequacy of definitions.

The worst obstacle, on Tarski’s view, to the construction of a definition of truth for a natural language is the universality of natural language (see Tarski pp. 164-5). Within a natural language it is possible to refer to anything at all. In particular, it is possible to refer to expressions of the language itself, and this possibility is responsible for such semantical antinomies as the Liar’s Par- adox. The antinomies make doubtful the possibility either of correctly defining or even of consistently using a truth predicate.

Davidson, in his essay “In Defense of Convention T,” describes the uni- versality of natural language and then indicates that it is what makes the first departure from Tarski necessary:

Tarski, Davidson, and Theories of Truth 7

Once all this is allowed into the language, semantic antinomies result. The ideal of a theory of truth for a natural language in a natural language is therefore unattainable if we restrict ourselves to Tarski’s methods. The question then arises, how to give up as little as possible, and here theories allowed by Convention T seem in important respects optimal. Such theories can bestow the required properties on a truth predicate while drawing on no conceptual resources not in the language to which the predicate applies. It is only the truth predicate itself (and the satisfaction predicate) that cannot be in the object language. Here it is essential to require no more than a theory of truth; to go beyond to an explicit definition does widen the gap between the resources of the object language and of the metalanguage. (“In Defense of Convention T”, p. 73)

To ask for an explicit definition of truth which does not result in semantic par- adoxes is, in the case of a natural language, to ask the impossible. The par- adoxes can be stated whenever a language has the means of referring to its own expressions and contains its own truth predicate. Now, every natural lan- guage, in virtue of its universality, has the means of referring to its own expressions. If, then, a truth predicate for a natural language either occurs in, or can be translated into, that language, the use of that predicate will be inconsistent. Now suppose a truth predicate has been defined, in a language L’, for a natural language L. Then it follows that the definition, and the truth predicate, can be translated into L, since L contains its own syntactical termi- nology. Since this would in turn allow the paradoxes to be generated, explicit definition of truth for natural languages must be forsworn (for helpful discus- sion, see Mark Platts, pp. 40-2).

When Davidson changes Tarski’s account by dropping the requirement that a definition of truth be given, this makes a difference in which theories will count as adequate theories of truth. Tarski’s convention presupposes a formally correct definition of truth, but Davidson’s convention presupposes only a consistent axiomatic characterization of truth. Theories which pre- viously did not count as adequate theories of truth because they failed to explicitly define truth will now be acceptable provided that they fulfill the material criterion of Davidson’s convention. This expansion of the class of truth theories is exactly what Davidson intends in making his first departure from Tarski. In particular, if Davidson is correct, some theories of truth for natural language will now be formally acceptable as T-theories.

Davidson’s second departure from Tarski differs from the first in that it is not designed to change the class of theories which count as T-theories, although it may nevertheless have that change as an unintended effect. Davidson reformulates Convention T in such a way that it no longer depends on any notion of translation or meaning. This modification is not motivated by any need to change what actually counts as a materially adequate theory of truth, but by a need for the statement of the criterion of adequacy to reflect

8 David Larson

Davidson’s interest in explaining meaning. Tarski wanted to show how to con- struct a definition of truth, and it was no defect of this attempt that he assumed a notion of translation in stating a criterion of successful definition. Davidson, however, expects the description of theories of truth to be instruc- tive with regard to meaning, and this expectation would be groundless if his only criterion for theories of truth were that they correctly, that is, synony- mously, translated object language expressions. He therefore needs to restate Convention T in such a way that it does not take for granted the very concept he hopes a consideration of theories of truth to illuminate.

Davidson’s modification of Convention T, then, replaces talk about translation with talk which does not presuppose a notion of meaning so that meaning may be non-circularly explained by theories which remain recog- nizable as theories of truth. Instead of requiring that theories of truth contain as theorems those biconditionals the left hand side of which predicates truth of an object language sentence and the right hand side of which consists of a translation of that sentence, the modified convention requires only that the right hand side make the biconditional true. Davidson’s hope is that in thus eliminating from Convention T any dependence on a notion of meaning he has left the convention strong enough to serve as a criterion of what may rea- sonably be called theories of truth. Here then is my formulation of a conven- tion which reflects both of Davidson’s departures from Tarski: (T’) A consistent set of axioms, characterizing a predicate ‘Tr’ and formulated in the

metalanguage, will be called an adequate theory of truth if it has the following consequences:

(a) for every sentence of the language in question, some sentence which is true and is obtained from the expression ‘xis Tr if and only if p’ by substituting for the symbol ‘x’ a structural-descriptive name of the sentence of the language in ques- tion and for the symbol ‘p’ some sentence of the metalanguage;

(see “Radical Interpretation”, p. 134, for a moderately explicit statement of this by Davidson.)

Davidson not only recognizes, but also welcomes the apparent weakness of what I have expressed as clause (a), expressing confidence that in spite of the removal of the notion of translation from the convention it is nevertheless strong enough to identify theories which give intuitively acceptable transla- tions in their T-sentences (see, e.g. “In Defense of Convention T”, p. 74). It is because an infinite number of true T-sentences must be produced from a finite number of axioms, Davidson thinks, that this confidence is justified, for it is implausible that any theory which did not, in effect, give translations, would be able to systematically pair truth conditions with sentences in such a way that a true T-sentence could be proven for each sentence of a language.

(b) the sentence ‘for any x, if x is Tr then x is S’.

Tarski, Davidson, and Theories of Truth 9

Consider now, in the light of T’, the following remarks Davidson makes in “Reality without Reference” :

A general and pre-analytic notion of truth is presupposed by the theory. It is because we have this notion that we can tell what counts as evidence for the truth of a T- sentence. But the same is not required of the concepts of satisfaction and reference. Their role is theoretical, and so we know all there is to know about them when we know how they operate to characterize truth. We don’t need a general concept of reference in the construction of an adequate theory. (p. 223)

Davidson would have the interpreter empirically test theories of truth by applying Convention T’. Why does the interpreter need a general notion of truth in order to do this? Although he does not need to be able to translate from the one language to the other, as he would if he were applying Tarski’s convention, he does need to be able to discover the conditions under which the predicate ‘Tr’ applies to object language sentences. This is something he can- not do so long as the predicate is purely formal, that is, without interpreta- tion. For Tarski this formality does not matter, because Tarski’s convention can be applied without giving an interpretation to ‘Tr’. Davidson’s inter- preter, however, must give some meaning to ‘Tr’ before he can test his T-theory to determine whether or not it is adequate as a theory of truth.

We have not yet discovered Davidson’s reason for thinking that the inter- preter needs the general concept of truth in order to apply Convention T’. We have only discovered a reason for thinking that the predicate formally defined must be given some interpretation before Convention T’ can be applied. I wish now to postpone for a time any further consideration of the function of a theory of truth in the empirical task of interpretation in order to discuss the implications, for the form of the theory of truth itself, of Davidson’s second, material departure from Tarski. In the course of this discussion I will reject one way of characterizing Davidson’s representation of the interpreter’s pre- theoretical understanding of the truth predicate. I will wait to more positively describe this understanding until I return to the role of theories of truth in interpretation.

111.

I have been arguing that the truth predicate must be understood indepen- dently of any theory of truth because of Davidson’s second departure from Tarski, namely, his elimination from the convention of the notion of transla- tion. Earlier I argued that Davidson has a quite different motivation for allowing semantic predicates to occur primitively in theories of truth: he needs

10 David Larson

to avoid the antinomies caused by the universality of natural language. Have we now found a second reason for allowing semantic primitives? Does the need for an independent understanding of the truth predicate require any changes in the form of T-theories, or only a change in the way in which those theories are understood? In “Reality without reference,” Davidson distin- guishes explanation within a theory and explanation of a theory (see p. 221). Within a theory of truth, truth is defined or explained in terms of satisfaction. It is the theoretical characterization of a predicate which constitutes explana- tion within a theory, but the explanation of a theory is its interpretation. A theory of truth in particular is explained when it is shown to satisfy Conven- tion T. In these terms, our question is whether the modification of Conven- tion T formally changes explanation within T-theories or only explanation of T-theories.

John Foster, in pressing the point that Davidson must presuppose a notion of truth if he is to explain meaning, concludes that his modification of Convention T has implications for the formal structure of T-theories them- selves; implications, that is, for the form of explanation within a theory. Here is what Foster says:

If the characterization of the truth predicate for L serves to explicate its sense, to say exactly what is meant by ‘is true in L’, it cannot also serve to interpret the expressions of L. The characterization can only serve as a theory of meaning if the truth predicate, thus employed, is already understood; for although the characterization tells us how in L truth applies, it is only by knowing that it is truth which thus applies that we can hope to gain an understanding of L. . . . Davidson is seeking to construct an interpretative theory of meaning, and this requires using the concept of truth as formally primitive. (Foster, p. 9)

Perhaps Foster’s point is simply that no theory can simultaneously explain truth and meaning. Either meaning must be assumed and truth explained, or truth assumed and meaning explained. This much is correct enough, but it concerns conventions T and T’, and does not directly support any conclusions about the form of T-theories. It is in Convention T that Tarski assumes a notion of meaning (translation), and in Convention T’ that Davidson assumes an understanding of truth (‘Tr’). In neither case does the concept of meaning play any role within T-theories.

Davidson accepts as basic and unanalyzed an intuitive notion of truth in order to give an explanation of the significance of T-theories, but this is quite different from taking any truth-predicate as formally primitive within the theory. In fact, such semantic predicates as Davidson is willing to take as formally primitive, for example ‘satisfies’ and ‘refers’, are expressly described as purely theoretical and irrelevant to the explanation, or test by Convention

Tarski, Davidson, and Theories of Truth 1 1

T’, of the theory (see “Reality without reference,” pp. 222-3). If it is necessary for an interpreter to know, not only a theory of truth, but also that it is a theory of truth, then it is necessary for the interpreter to have a general concept of truth under which he may recognize the particular conception of truth characterized in the theory to fall. It is not necessary for him to have a general concept either of satisfaction or of reference in spite of the fact that these terms may occur primitively in explanations within the theory; and the general concept of truth, though needed by the interpreter to explain the theory, plays no role within the theory itself.

A response in defense of Foster’s position could be made as follows: The argument just given does not consider how the interpreter is to recognize that a given theory is a theory specifically of truth. While it is true that recognizing a theory as being about truth is a matter of explaining the theory, not a matter of explanation within it, it is in this case also true that there are implications for the form of the theory itself. How might an interpreter recognize a theory as a theory about truth? The Tarskian answer is that a theory is recognized as a theory of truth when it is seen to satisfy Convention T; this answer, how- ever, will not do for Davidson because an interpreter cannot tell whether or not a theory satisfies Convention T’ until he understands the truth predicate at least to the extent of knowing the conditions under which it applies. Since the predicate he must understand is the very predicate characterized by the theory, and since he cannot rely on Convention T’ for that understanding, the truth predicate must be a previously understood predicate occurring primi- tively within the theory. Were the predicate to occur not primitively, but eli- minably (i.e. be defined) in the theory, there would be no reason for thinking that it had anything to do with truth. Thus, without confusing explanation within the theory and explanation of the theory it is still possible to argue that the truth predicate must occur primitively by showing that, unless it does, there is no way to recognize (explain) the theory as a theory of truth. To say that the truth predicate must already be understood is to say that it functions in some larger, containing theory as well as in the T-theory. The larger theory is no doubt unformalized, nevertheless truth can be thought of as defined outside the T-theory. The T-theory itself is not free to redefine truth, but must rather take it as a primitive concept.

This response does not establish Foster’s point. A theory can be explained (interpreted, or given empirical application) either at its axioms or at its theorems. Suppose a certain theory contains, either primitively or eliminably, a predicate P. On the one hand, P might be interpreted as a truth predicate because its axiomatic or definitional characterization were intuitively acceptable as a characterization of truth. Whether axiomatic or definitional

12 David Larson

makes no difference; the predicate is still understood by way of the axioms. Since the axioms describe the elements of which sentences are composed and on the basis of which they have their semantic content, to understand a theory of truth as a theory of truth by way of its axioms is to adopt what Davidson calls a Building Block approach to truth and meaning (see “Reality without reference”, p. 219-21). On the other hand, P might be interpreted as a truth predicate because its theorems were understood to use the notion in a manner correct according to some independent criterion such as Convention T. Davidson remains with Tarski on this point, holding that the only connection with truth is by way of the T-sentences. The axioms are not independently understood.

Foster’s claim that the truth predicate must occur primitively in a David- sonian theory falsely supposes that a theory of truth can be recognized as being about truth just in case the truth predicate occurs primitively. The sup- position is false because no theory, of course, would count as being about truth simply because it used a certain predicate, regardless of where that pre- dicate occurred; its use of that predicate must be correct, recognizable as giv- ing a notion of truth. If what Foster actually means, when he says that the truth predicate must occur primitively, is that the theory must be interpreted by way of its axioms; then his claim, though more defensible, is still wrong for all the reasons that the Building Block approach is wrong, that is, because it treats words rather than sentences as the units of meaning.

Contrary to Foster, the recognition of a theory of truth as a theory of truth is possible without supposing either that ‘Tr’ appear primitively or that the axioms are understood independently, and this is possible in spite of the fact that Convention T’ cannot be applied until ‘Tr’ is understood. All that is necessary is that ‘Tr’ be given some empirical application such that some cha- racterization of ‘Tr’ will count as satisfying Convention T’ . The satisfaction of Convention T’ is all that materially matters. The understanding of ‘Tr’ does not need to be anything more than an assumption identifying empirically discernable conditions for the application of ‘Tr’ . Any assumption made is justified if, on it, a theory of truth can be found which satisfies Convention T’. All that matters to the successful completion of the task of interpretation is that a theory of truth be found which yields, on some understanding of ‘Tr’, overwhelmingly more true than false T-sentences. It is the theoretical produc- tion of those T-sentences that is important, not what the T-sentences are, in their use of ‘Tr’, taken to state. Any predicate which is extensionally equiva- lent to the truth predicate - i.e. any interpretation of ‘Tr’ which makes pos- sible the satisfaction of Convention T’ - is equally acceptable. As I read him, Davidson recommends to the interpreter a specific understanding of ‘Tr’

Tarski, Davidson, and Theories of Truth 13

which makes its application an empirical matter. Before describing this recommendation further, however, I want to conclude my discussion of the formal differences between Tarski and Davidson by sketching the form of a Davidsonian theory of truth, something we are in a position to do only now that the formal implications of Davidson’s departures from Tarski have been discussed.

On Davidson’s account, a theory of truth has four sorts of axioms: (1) axioms of a general logical character, (2) axioms which, intuitively, are the translations of axioms of the object language theory, (3) axioms descriptive of object language syntax, and (4) axioms descriptive of object language semantics. As in the theory Tarski described, axioms of the first two sorts have nothing especially to do with linguistics. They introduce into the theory a wide variety of ordinary terms and give the theory the expressive power necessary to state interpretations of object language sentences. I take it that Quine’s observation sentences are among the second sort. Axioms of the third sort resemble those expressly stated by Tarski for the calculus of classes in providing notions of expression and concatenation, but are much more com- plex in that they treat a huge number of object language elements as primitive. The fourth sort of axioms replace what were, in Tarski’s theory, genuine definitions. They include an axiom which recursively characterizes satisfac- tion and possibly, but not necessarily, another which connects satisfaction and truth. The satisfaction axiom has a tremendous number of clauses corresponding to the large number of object language atomic sentences, as well as clauses for each primitive operator of the language. Together, these four sorts of axioms must suffice to entail, for each object language sentence, a true T-sentence.

IV

Davidson speaks of interpretation where Quine speaks of translation. For Quine, a theory of translation is an empirically constrained, though not empi- rically determined, mapping of one language onto another. The evidence rele- vant to translation is purely behavioral and yields conclusions of the form ‘x translates y’, where ‘x’ and ‘y’ name, respectively, an expression of the target language and an expression of the source language. Davidson prefers to speak of interpretation because on his account the target language is always used, never described, by the linguist. It is misleading to say that Davidson sub- stitutes descriptions of possible theories of interpretation for Quine’s descrip- tions of possible theories of translation, since for Davidson there are no

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conclusions of the form ‘x interprets y’. I shall therefore speak simply of the “task of interpretation” when I have in mind the empirical investigation, for purposes of understanding, of another’s speech as that investigation is described by Davidson. The task includes both the construction of a theory of truth and the testing, by the criterion provided by Convention T’, of that theory for adequacy.

Davidson’s claim that a theory satisfying Convention T’ will adequately model the product of interpretation is customarily expressed by saying that a theory of truth is a theory of meaning. Though convenient, this way of putting the matter has the unfortunate consequence of encouraging the prevalent mis- conception that on Davidson’s account the T-sentences produced by a theory of truth themselves model understanding. This is a misconception because it places undue importance on the theorems of the theory as compared to the axioms, and it is encouraged by calling the theory a theory of meaning because this suggests that it is the knowledge of statements of meaning produced by the theory which is important. Actually, in principle though not in practice, knowledge of the T-sentences must precede knowledge of the theory and understanding of the language.

Convention T’ requires that adequate theories of truth entail true sentences of the form ‘s is Tr if and only if p’. The convention functions as an assumption on the part of the prospective interpreter. He assumes that he will be in possession of an adequate theory of truth if he has a theory which entails true sentences of a particular form. While he has no problem deciding whe- ther a sentence has the right form, the interpreter cannot determine whether such a sentence is true or false until he understands the predicate ‘Tr’. He can of course understand Convention T’ without understanding ‘Tr’, for the pre- dicate is only mentioned by the convention, but he cannot apply the conven- tion until he knows the truth value of the mentioned sentence, and to do this he must have some understanding of ‘Tr’. To note this relationship between the truth predicate and Convention T’ is simply to remind ourselves of the metalinguistic status of the convention relative to any theory of truth.

According to Davidson, interpreters necessarily follow a principle of char- ity according to which speakers are to be presumed to hold a given sentence true just in case it actually is true (see, e.g., “Radical Interpretation”, p. 137). This principle is best taken as an expression of the interpreter’s pre-theoretical understanding of ‘Tr’ . We should describe the successful interpreter as assum- ing, prior to his acceptance of a theory of truth, that native speakers hold sentences true just in case the predicate ‘Tr’ applies to those sentences. Here is a formulation of this principle of charity: (PC) x is Tr iff (y) y holds true x

Tarski, Davidson, and Theories of Truth 15

where ‘x’ describes an object language sentence and ‘y’ ranges over speakers of the language. It is this assumption which is the crucial step in making the construction of a Tarskian theory of truth part of the empirical task of inter- pretation. Convention T’ does not provide an empirical criterion until this assumption is made, that is, until ‘Tr’ is empirically understood. This obviously depends on ‘holds true’ being attributable on behavioral grounds, but Davidson thinks this can be managed. At any rate, the point is that (PC) represents the interpreter’s assumption of an interpretation of ‘Tr’, and that this assumption, together with Convention T’, provides him with an empirical criterion of the adequacy of proposed theories of truth. The interpreter will no doubt find it necessary to attribute some false beliefs to his subjects, and these attributions certainly go against (PC); nevertheless, (PC) provides the sole connection between evidence and theory, and the interpreter can do no better than to choose a theory which violates it in as few instances as possible.

To see the interpreter’s need for (PC) is to see his need for a general and pre-analytic notion of truth. In order to apply Convention T’ the interpreter must give an interpretation to the formally defined truth predicate. This he does when he assumes (PC). Because (PC) uses the everyday concept of hold- ing true, or belief, the interpreter depends on his own general and pre-analytic concept of truth in testing theories of truth for adequacy.

Note that both assumptions which have, on this account, been attributed to the interpreter concern the characterization of a truth predicate and do not address the question of the relevance of theories of truth to the task of inter- pretation. These are assumptions about truth made in the course of interpret- ing, not assumptions about meaning or interpretation as such. It is not the inter- preter but the philosopher who argues that to both have a theory of truth and know that it is a theory of truth is to be able to interpret the speakers in question.

Given Convention T’ and the principle of charity(PC), the adequacy of a given theory of truth is empirically supported by generalizations giving the conditions under which a sentence is held true, provided that the theory assigns those same conditions to the sentence as its truth conditions. That is, the evidence relevant to the choice of a theory of truth for a language, when generalized, has the following form: (E)

(see “Radical Interpretation”, p. 135) The task of interpretation involves the discovery, for as many sentences as possible, of such a generalization as well as finding a theory of truth whose adequacy is, to the greatest extent possible, supported by these generaliza- tions. The interpreter seeks the best possible fit betweeen this evidence and the T-sentences of a theory of truth.

(y) (y holds true x if and only if p).

16 David Larson

Tarski’s definition of truth is materially constrained only by the need for theorems which satisfy Convention T. Likewise, Davidson’s axioms concerning truth and satisfaction are materially constrained only by way of resulting theorems. In spite of the fact that satisfaction is now axiomatically rather than definitionally characterized, any recursion on satisfaction is acceptable so long as true T-sentences result. The semantic axioms have no direct empirical content. This is immediately connected with the fact that Convention T’ is both meta-theoretical with respect to any theory of truth and itself a part of the task of interpretation. A theory of truth is able to play a role in the empirical task of interpretation in spite of the fact that its axioms are not empirical because Convention T’, supplemented with the principle of charity, makes the choice of a theory of truth an empirical matter.

BIBLIOGRAPHY

DAVIDSON Donald. “In Defense of Convention T.” In Inquiries into Truth and Interpretation.

DAVIDSON Donald. “Radical Interpretation.” In Inquiries into Truth and Interpretation. DAVIDSON Donald. “Reality without Reference.” In Inquiries into Truth and Interpretation. FOSTER J.A.; “Meaning and Truth Theory.” In Gareth Evans and John McDowell (eds.), Truth

PLATTS Mark. Ways of Meaning. London: Routledge and Kegan Paul, 1979. TARSKI Alfred. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Meta-

Oxford: Clarendon, 1983.

and Meaning. Oxford: Clarendon, 1976.

mathematics. Oxford: Clarendon, 1956.

Dialectica Vol. 42, No 1 (1988)