Black vs. Tarski en el "Problema filosófico de la verdad"

Abstract

What is the philosophical problem of truth? When Tarski attempted to define a true proposition in certain languages, he thereby admitted that the problem formed part of the theory of knowledge, thus establishing, at least pragmatically, a link with traditional philosophy. On the basis of this link Black points out that Tarski's conclusions were of little or no help in "clarifying the philosophical problem of truth".

Black's criticism should be analysed in order not to confuse two theses: (A) the formalistic position (Tarski and, in part, Carnap) and (B) the naturalistic position, represented by Black, though not exclusively so. The former maintains that one can only speak: of 'truth (or falsity)' in formalized language; the latter asks whether the predicate 'true (false)' can be validly used in 'natural' language and doubts whether the formalized definition of 'truth' can be adapted to ordinary languages.

According to Tarski such an application is impossible owing to the fact that in ordinary language there are no coherent and well defined levels (object-language, meta-language) which will allow one to avoid the use on the same level, of expressions descriptive of the language and of the names of such expressions; according to Tarski such a language as uses the term 'true (false)' in reference to its own expressions is a 'semantically closed' language. A language of this type permits of the formation of paradoxes. Thus stated, it would seem that the difficulty of those who wish to handle logically the term 'truth' in natural language would be to pass from a 'semantically closed' language to an 'open' one that, thanks to the distinction of levels, would prevent the formation of par. adoxes. Tarski rejects this approach. In view of the lack of formal structure in ordinary language there is no sense even in speaking in it of 'logical incoherence'; one would need first to show the conditions of possible incoherence in ordinary language in order afterwards to establish the possibility of dealing with the terms 'truth', 'true' and their opposites. The author points out that in this context Tarski falls into a certain contradiction: on the one hand he uses ordinary language to consider the formation of paradoxes, and on the other he asserts that it is impossible to determine the property of coherence in that same language. If it is senseless to characterize ordinary language as 'incoherent', why should one start out from the paradoxes that occur in it when the term 'true' is applied to the expressions of that same language?

All the same it is unreasonable to ask Tarski (as Black does) to adapt the formalistic theses to ordinary language. It would be different if one were trying to solve the so-called 'philosophical problem of truth'. Which means that if the difference between formalized and non-formalized language is accepted and if natural language is assigned to the latter class of languages the logical status of the terms 'truth' and 'true' is not transferable from the first class to the second. In other words, the meta-language used in forming the proposition 'X is true' must be richer than the object-language; it has to include variables of a higher logical type. Hence one may infer that the 'philosophical problem of truth' is different from the 'logical problem of truth'.

Black agrees in separating logical from philosophical treatment. But this introduces a question: Why should one insist that formalistic conclusions should be applied to natural language? If the validity of formalistic theses in deductive systems in general is accepted, one cannot expect this validity to be transferred to non-formalized language: the use of the term 'truth' is established only by strictly logical means. To expect to continue employing the terms 'truth', 'true', etc., in ordinary language is only possible if one postulates an area of specific problems for these terms, that is to say, if one accepts the existence of the 'philosophical problem of truth'.

The 'naturalistic' theses themselves establish this lock of communication between the two kinds of language; Black, for example, observes that we must either resign ourselves to the "transitory and fluctuating nature of the 'concept' truth, or look for some other way of defining it". But there exists a third possibility not envisaged by Black: the elimination of the term 'truth' from ordinary language as redundant and equivocal, thus avoiding the formation of paradoxes. But then this would be equivalent to accepting the principal outcome of Tarski's thesis: to assert that a proposition is true is logically equivalent to asserting that proposition.

What, then, is the philosophical problem of truth? This expression hides a substantialist thesis which might go so far as to hypostatize the term 'truth'. On these lines one might speak of the 'nature' of truth, and even of its 'natural essence'; if truth is an entity to which it is reasonable to attribute properties ('essence', 'nature', 'root') the doors are thrown open to the most exaggerated realism. This seems to be Black's position when he asks for 'a satisfactory general description of usage' or demands 'a direct solution'; the words general and direct point towards essences. What difference is there in effect between asking for 'a certain eidos' in order to arrive at a general definition of areté and seeking that 'general property of the designata'?

In the first place the semantic definition establishes a relation between a certain type of expressions (factual) and the fact or state of affairs to which the expression refers; in the second place it requires that this relation should be one of equivalence if the expressions are to be classified in the set of the true ones. Taken in this way, of course, the semantic definition will provide no more than an indicative criterion restricted to the factual propositional type of expressions. Otherwise one would have to assume the existence of a pragmatic kind of general disposition which would 'enable us' to utter expressions such as 'It's snowing' or any other and determine beforehand the correctness of the expression with respect to the designatum. This leads to a very dangerous muddle; on the one hand we look for a 'general property', but this will transfer the problem in toto to the class of abstract entities (Platonic realism) while on the other we ask for a 'general disposition' of the user of the expressions, which brings up again the problem of the criterion of truth on the level of the Cartesian cogito.

It is to be feared that the expression 'philosophical problem of truth' is definitely referring to the historical catalogue of the various attempts to arrive at a general and comprehensive characterization of all the expressions which aim at establishing a certain cognoscitive relation. That is to say, that if as a result of this critical revision of the so-called 'problem of truth' one reached the conclusion that it was a case of the repeated postulation of a problem that was irresolvable because it lacked meaning (pseudo-problem), it would then be permissible to speak of the 'philosophical problem of truth' only in order to refer to the lack of meaning in the problem on the one hand, and to the very fact of its formulation on the other.

Furthermore, it is incorrect to use the expression 'semantic definition of truth' to characterize Tarski's formula to the effect that: 'X is true if and only if p' (where 'X' = def. symbol for the descriptive name of one proposition, and p = def. symbol to designate any proposition.) It is, in fact, doubly unsuitable: (1) because in itself this formula is not a definition, and (2) because its author never regarded it as such. The results that Tarski arrived at in studying the use of the terms 'truth' and 'true' in so-called colloquial language are completely negative, as has been shown supra. As a matter of fact the formula 'X is a true proposition if and only if p' is used to show how impossible it is to formalize the semantics of natural language. It is possible to use this formula to construct paradoxes, which demonstrate the logical incoherence of ordinary language when the terms in question are introduced into it. So Tarski could hardly arrive at a semantic 'definition' of truth by means of a formula that merely gives rise to logical difficulties. For this reason, either the problem must be stated on another level (for instance that suitable for formalized language such as calculus of classes or finite language of the first order) or it must be left open on the level of ordinary language, but then with the consequences already pointed out.