Issue #08. June 1997. Pp. 15-23.
«Truth in Pure Semantics: A Reply to Putnam»
Copyright © by SORITES and Luis Fernández Moreno
Luis Fernández Moreno
§1. Introduction
One of the most important explications of the notion of truth is the semantical conception of truth. It was originally put forward by Alfred Tarski in the thirties and it rapidly gained important followers, notably Rudolf Carnap, but was not without critics, e.g. Otto Neurath. In recent years Hilary Putnam has become one of the most important opponents of the semantical conception of truth.
In his book Representation and Reality<11>Foot note 2_1 Putnam raises a number of objections against the semantical conception of truth, two of which are the following. Firstly, he finds it objectionable that according to the semantical conception of truth the equivalences of the form (T) -- for instance, the equivalence «the sentence `Schnee ist weiss' is true in German if and only if snow is white» -- are logically necessary. Let us recall that the equivalences of the form (T), or for short the T-equivalences, are obtained from the schema «S is true in L if and only if p» by substituting «L» for the metalinguistic name of an object language, «S» for the metalinguistic name of a sentence of the object language and «p» for the metalinguistic translation of this sentence. Tarski lays down as the condition for the extensional adequacy of a truth definition for an object language that every T-equivalence formed with the sentences of the object language should follow from this definition. The fulfillment of this adequacy condition is a very important desideratum for a truth definition and hence for a theory of truth, as it uniquely determines the extension of the intuitive use of the term «true» when applied to sentences.
Secondly, Putnam claims that according to the semantical conception of truth the truth of a sentence depends only on its syntactic structure and on the way the world is, and not on the meaning of the sentence. This second objection, if correct, would be a very strong objection against the semantical conception of truth, since it is undeniable that the truth of a sentence depends on its meaning.
It is worth noting that Putnam's argument against the semantical conception of truth in his book Representation and Reality is addressed at Carnap's rather than against Tarski's formulation of it. In the following pages I shall examine Putnam's two objections against Carnap's formulation of the semantical conception of truth.
Before presenting Putnam's argument it is advisable to remind ourselves briefly Carnap's distinction between descriptive and pure semantics. Descriptive semantics deals with the semantical properties of natural languages, and so of languages which are given by historical facts; the description of those languages is based on empirical investigation. In contrast, an artificial language is given by setting up a system of rules. Carnap formulates the interpretation of an artificial language by means of a semantical system and characterizes pure semantics as the analysis of semantical systems.<12>Foot note 2_2 A semantical system is a system of rules formulated in a metalanguage and referring to an object language so that those rules provide necessary and sufficient truth conditions for every sentence of the object language. Accordingly those rules provide an interpretation for the sentences of the object language. In particular, the truth rules for an object language not only provide the interpretation of the sentences of this language, but also constitute a truth definition for the language.
§2. Putnam's Argument
Let us consider a language, L1, a fragment of the German language which contains only two sentences, «Schnee ist weiss» und «Der Mond ist blau». The truth rules for L1 are the following: The sentence «Der Mond ist blau» is true in L1 if and only if the moon is blue, and the sentence «Schnee ist weiss» is true in L1 if and only if snow is white. Therefore the sentence «Der Mond ist blau» means in L1 that the moon is blue, and the sentence «Schnee ist weiss» means in L1 that snow is white.
Let «S» be a metalinguistic variable for sentences; then the truth rules and the truth definition for L1 can be formulated thus:
S is true in L1 if and only if (S = «Der Mond ist blau» andthe moon is blue) or (S = «Schnee ist weiss» and snow iswhite).<13>Foot note 2_3
Carnap and Tarski have indeed accepted such a truth definition for languages with only a finite number of sentences. Putnam formulates his objections to the semantical conception of truth precisely on the basis of the language L1 and of the truth definition for L1. Putnam claims that a consequence of this definition is that the truth of a sentence depends only on its syntactic structure and on the way the world is, but not on the meaning of the sentence, because, Putnam says, whether a sentence S has the property «S is spelled `Schnee ist weiss' and snow is white» (i.e. the property that the sentence is spelled S-c-h-n-e-e-space-i-s-t-space-w-e-i-s-s and snow is white) does not depend at all on the meaning of the sentence, and truth in L1 has been defined as the disjunction of this property and another of the same kind.<14>Foot note 2_4 Putnam also asserts: Because the equivalence «the sentence `Schnee ist weiss' is true in L1 if and only if snow is white» is a logical consequence of the truth definition, that equivalence is logically necessary given this definition of «true in L1».<15>Foot note 2_5
Putnam refers to a talk with Carnap in the fifties, in which Putnam argued against Carnap's thesis that the T-equivalences are logically necessary<16>Foot note 2_6 thus: The fact that the sentence «Schnee ist weiss» is true in German if and only if snow is white is quite an empirical and contingent one. If the German language had developed differently, then the expression «Schnee» might have denoted not snow but water and then the truth conditions for the sentence «Schnee ist weiss» in German would not have been given by the sentence «snow is white», but by the sentence «water is white». Carnap replied to Putnam by means of the distinction between descriptive and pure semantics; the latter considers only languages taken as abstract objects and defined by semantical rules. Putnam puts Carnap's answer as follows:
«When `German' is defined as `the language with such and such semantical rules' it is logically necessary that the truth condition for the sentence `Schnee ist weiss' in German is that snow is white.»<17>Foot note 2_7
In Representation and Reality Putnam addresses an objection to Carnap's answer, an objection which he did not formulate at the time of his talk with Carnap, although he says that he had already thought of it. Let us consider the following definition of the language L1 by truth rules and syntactic rules. Let «L» be a metalinguistic variable for languages and «S» a metalinguistic variable for sentences. Then the language L1 can be defined thus:
L1=df the language L such that, for any sentence S, S is true in L1 if and only if (S is spelled «Der Mond ist blau» and the moon is blue) or (S is spelled «Schnee ist weiss» and snow is white); and (syntactic restriction) no inscription with any other spelling is a well-formed formula of L.
At first sight one could perhaps think that this definition of L1 is circular, because the term «L1» occurs itself as a part of the definiens of «L1» (namely as part of the predicate «true in L1»). On this point Putnam correctly asserts that the definition of L1 is not circular, because the expression «L1» does not occur in the definiens of the expression «true in L1». But, Putnam says, if in the last characterization of L1 one substitutes the expression «true in L1» for its definiens in order to show clearly that the definition of L1 is not circular, then one obtains the following definition of L1:
L1=df the language L such that, for any sentence S, (S is spelled «Der Mond ist blau» and the moon is blue) or (S is spelled «Schnee ist weiss» and snow is white) if and only if (S is spelled «Der Mond ist blau» and the moon is blue) or (S is spelled «Schnee ist weiss» and snow is white); and (syntactic restriction) no inscription with any other spelling is a well-formed formula of L.
Putnam concludes that:
«Apart from the syntactic restriction, this is now an empty (tautological) condition. Every language which satisfies the syntactic restriction satisfies this!»<18>Foot note 2_8
In other words: another language Lj, whose sentences have the same syntactic structure as the sentences of L1, but with a different meaning, satisfies the definition of L1 too. Therefore Carnap's definition of a language by semantical rules is empty («tautological» in a broad sense) -- apart from the syntactic restriction.
Putnam therefore claims to have shown that the sense in which Carnap maintains that the T-equivalences are logically necessary is unacceptable: Since Carnap's thesis that the T-equivalences are logically necessary is based on his definition of a language -- a language defined by semantical rules -- and this definition is untenable because it is empty, Carnap's thesis turns out to be unacceptable.
§3. Carnap's Definition of an Interpreted Language is not Empty
However, I do not agree with Putnam's objection. Against his claim I shall argue that Carnap's definition of an interpreted language is not empty.
First it must be pointed out how Putnam arrives at that empty description of a language. The procedure is absolutely trivial. If in an explicit definition one substitutes the definiendum for the definiens, then one arrives at a logically true statement, namely the identity or the equivalence of the definiens with itself. This is the procedure that Putnam applies to the definition of truth in L1 which is part of the definition aforementioned of L1.
But that definition of L1 contains not only the term «true in L1» but also the definiens of «true in L1». Therefore the definition of L1 one arrives at, if one leaves out the expression «true in L1» to show clearly that the definition of L1 is not circular, is not the definition Putnam claims, but the following:
L1=df the language L such that for any sentence S, (S is spelled «der Mond ist blau» and the moon is blue) or (S is spelled «Schnee ist weiss» and snow is white); and (syntactic restriction) no inscription with any other spelling is a well-formed formula of L.
This definition of L1 is not empty. One must stress here that the sentences of the metalanguage «the moon is blue» and «snow is white» which appear in the definition of L1 state the truth conditions for the sentences «Der Mond ist blau» and «Schnee ist weiss», and hence they give us the meaning of those sentences of L1. The object language L1 we are considering then fulfills this definition, because L1 is a fragment of the German language consisting only of the sentences «Der Mond ist blau» and «Schnee ist weiss» and the translations of these German sentences into the metalanguage -- i.e. into English -- are the sentences «the moon is blue» and «snow is white». Thus the fulfillment of the definition of L1 by a language depends not only on the syntactic restriction but also on the meaning of the sentences of the language.
If Carnap's definition of a language by semantical rules is not empty, as I have just argued, then it can be claimed that there is an acceptable sense in which the T-equivalences are to be regarded as logically necessary. Let us remember Tarski's condition for the adequacy of a truth definition, which Carnap assumes and which is intuitively satisfactory, as it uniquely determines the extension of the intuitive use of the term «true» applied to sentences: a truth definition for an object language is extensionally adequate if every T-equivalence formed with the sentences of the object language follows from this definition. So an extensionally adequate truth definition must have the T-equivalences as logical consequences and hence these equivalences are logically necessary on the basis of the truth definition.<19>Foot note 2_9
Now, Putnam admits that the fulfillment of Tarski's condition guarantees the extensional adequacy of a truth definition and he has not offered an alternative criterion for this purpose. Thus, Putnam would also employ Tarski's criterion to test the extensional correctness of a truth definition. But then, if as a result of this test Putnam concludes that a truth definition is extensionally adequate, he will have also to agree that the T-equivalences are logically necessary given that truth definition. Since in the framework of a truth definition and hence of a theory of truth which fulfills Tarski's adequacy condition the T-equivalences must be regarded as logically necessary.<20>Foot note 2_10
In short, once we have rejected Putnam's objection against Carnap's definition of an interpreted language, and if Tarski's adequacy condition for a truth definition is accepted, then it turns out to be admissible to regard the T-equivalences -- as they are in Carnap's pure semantics -- as logically necessary. If Putnam wants to reject this conclusion, he needs to question Tarski's adequacy condition for a truth definition, but this is something he is not willing to do.
§4. The Dependence of Truth on Meaning in Carnap's Semantics
My reply to Putnam's objection against Carnap's definition of an interpreted language also contains the reply to his second objection against Carnap's truth definition by semantical rules, i.e. to the objection that according to this definition the truth of a sentence depends only on its syntactic structure and on the way the world is, but not on its meaning, because, Putnam claims, whether a sentence has the property «S is spelled `Schnee ist weiss' and snow is white» does not depend on the meaning of the sentence.
To prove that this objection is incorrect let us recall that the second member of this conjunction, i.e. the sentence «snow is white», gives us the interpretation of the sentence «Schnee ist weiss». If one changes the meaning of the predicate «ist weiss» so that it no longer means the property of being white but the property of being red, then one has changed the language, one has defined another language, let us say L2, and one shall hence have the following clause in the truth definition: S is true in L2 if and only if S is spelled «Schnee ist weiss» and snow is red.
Putnam seems to see this way out from his objection. As mentioned, he claims that whether a sentence has the property «S is spelled `Schnee ist weiss' and snow is white» does not depend on the meaning of the sentence and he adds:
«But to be `true in L1' was defined as to have the disjunction of this property and another similar property. Occasionally a philosopher of a Tarskian bent seems to be dimly aware of this problem, and then the philosopher is likely to say, `Well, if you change the meaning of the words, then you are changing the language. Then of course you have to give a different truth definition.'(Note that this is just what Carnap said, in a less formal guise.) But what is `the language'?»<21>Foot note 2_11
Here Putnams asks the question «what is `the language'?» because he thinks that he has refuted Carnap's definition of an interpreted language. An advocate of the semantical conception of truth should therefore formulate a definition of an interpreted language which is not empty and according to which the truth of the sentences of this language does not depend only on their syntactic structure and on the way the world is, but also on their meaning. However, I have argued that Carnap's definition of a language has that property. We have seen that according to his definition (and hence to the truth definition which is part of that definition) the truth of a sentence of the object language depends also on its meaning, since the sentence of the metalanguage which says how the world is to be for the sentence of the object language being true is the translation into the metalanguage of the sentence of the object language. A change in the meaning of a sentence of the object language implies a change of language (i.e. of the object language), and as a result of this change the sentence of the metalanguage that gave the truth conditions of the sentence of the old object language must be replaced by the sentence of the metalanguage which is synonymous with the sentence of the new object language. It is indeed a similar answer as Carnap's -- Putnam himself admits.
In any case Putnam would still lodge the objection to Carnap's truth definition that it does not take into account many factors which are relevant to the meaning -- and therefore to the truth or falsehood -- of a sentence. So Putnam says:
«What is bizarre about these Tarskian `truth definitions' is that so many factors which are obviously relevant to the meaning of a sentence (and hence to whether the sentence is true or false) do not appear in the definition at all: under what circumstances it is considered correct to assert the sentence; what typically causes experts and/or ordinary speakers to utter the sentence; how the sentence came into the language; how a speaker typically acquires the use of these words; etc.»<22>Foot note 2_12
However, it is not at all bizarre that these factors do not appear in Carnap's truth definition. On the contrary, it is obvious that they are not going to appear in pure semantics as Carnap conceived it.
In the definition of an interpreted language -- of a language whose expressions have meaning -- in Carnap's pure semantics one abstracts away from the speakers. The assignment of meanings to the primitive descriptive signs of the language proceeds by stipulation, although the definitions of the semantical terms must fulfill conditions of adequacy which guarantee at least a partial correspondence between the thus defined concepts and the intuitive semantical concepts. The circumstance that in pure semantics one abstracts away from the speakers in the sense just mentioned implies that, in this context, the questions which Putnam asks above do not have an answer or can only have a trivial one. But this does not constitute in itself an objection to Carnap's theory in the field for which he formulated it -- the field of pure semantics.
Luis Fernández Moreno
Institute of Philosophy
CSIC [Spanish Institute for Advanced Study]
Madrid, Spain
<flvfm16@ifs.csic.es>