Deflationary theory of truth
In philosophy and logic, a deflationary theory of truth is one of a family of theories that all have in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement.
Redundancy theory
was probably the first philosopher or logician to note that predicating truth or existence does not express anything above and beyond the statement to which it is attributed. He remarked:
It is worthy of notice that the sentence "I smell the scent of violets" has the same content as the sentence "it is true that I smell the scent of violets". So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth.
Nevertheless, the first serious attempt at the formulation of a theory of truth which attempted to systematically define the truth predicate out of existence is attributable to F. P. Ramsey. Ramsey argued, against the prevailing currents of the times, that not only was it not necessary to construct a theory of truth on the foundation of a prior theory of meaning but that once a theory of content had been successfully formulated, it would become obvious that there was no further need for a theory of truth, since the truth predicate would be demonstrated to be redundant. Hence, his particular version of deflationism is commonly referred to as the redundancy theory. Ramsey noted that in ordinary contexts in which we attribute truth to a proposition directly, as in "It is true that Caesar was murdered", the predicate "is true" does not seem to be doing any work. "It is true that Caesar was murdered" just means "Caesar was murdered" and "It is false that Caesar was murdered" just means that "Caesar was not murdered".
Ramsey recognized that the simple elimination of the truth-predicate from all statements in which it is used in ordinary language was not the way to go about attempting to construct a comprehensive theory of truth. For example, take the sentence Everything that John says is true. This can be easily translated into the formal sentence with variables ranging over propositions For all P, if John says P, then P is true. But attempting to directly eliminate "is true" from this sentence, on the standard first-order interpretation of quantification in terms of objects, would result in the ungrammatical formulation For all P, if John says P, then P. It is ungrammatical because P must, in that case, be replaced by the name of an object and not a proposition. Ramsey's approach was to suggest that such sentences as "He is always right" could be expressed in terms of relations: "For all a, R and b, if he asserts aRb, then aRb".
Ramsey also noticed that, although his paraphrasings and definitions could be easily rendered in logical symbolism, the more fundamental problem was that, in ordinary English, the elimination of the truth-predicate in a phrase such as Everything John says is true would result in something like "If John says something, then that". Ramsey attributed this to a defect in natural language, suggesting that such pro-sentences as "that" and "what" were being treated as if they were pronouns. This "gives rise to artificial problems as to the nature of truth, which disappear at once when they are expressed in logical symbolism..." According to Ramsey, it is only because natural languages lack, what he called, pro-sentences that the truth predicate cannot be defined away in all contexts.
A. J. Ayer took Ramsey's idea one step further by declaring that the redundancy of the truth predicate implies that there is no such property as truth.
There are sentences...in which the word "truth" seems to stand for something real; and this leads the speculative philosopher to enquire what this "something" is. Naturally he fails to obtain a satisfactory answer, since his question is illegitimate. For our analysis has shown that the word "truth" does not stand for anything, in the way which such a question requires.
This extreme version of deflationism has often been called the disappearance theory or the no truth theory of truth and it is easy to understand why, since Ayer seems here to be claiming both that the predicate "is true" is redundant and also that there is no such property as truth to speak of.
Performative theory
formulated a performative theory of truth in the 1950s. Like Ramsey, Strawson believed that there was no separate problem of truth apart from determining the semantic contents which give the words and sentences of language the meanings that they have. Once the questions of meaning and reference are resolved, there is no further question of truth. Strawson's view differs from Ramsey's, however, in that Strawson maintains that there is an important role for the expression "is true": specifically, it has a performative role similar to "I promise to clean the house". In asserting that p is true, we not only assert that p but also perform the "speech act" of confirming the truth of a statement in a context. We signal our agreement or approbation of a previously uttered assertion or confirm some commonly held belief or imply that what we are asserting is likely to be accepted by others in the same context.Tarski and deflationary theories
Some years before Strawson developed his account of the sentences which include the truth-predicate as performative utterances, Alfred Tarski had developed his so-called semantic theory of truth. Tarski's basic goal was to provide a rigorously logical definition of the expression "true sentence" within a specific formal language and to clarify the fundamental conditions of material adequacy that would have to be met by any definition of the truth-predicate. If all such conditions were met, then it would be possible to avoid semantic paradoxes such as the liar paradox Tarski's material adequacy condition, or Convention T, is: a definition of truth for an object language implies all instances of the sentential formwhere S is replaced by a name of a sentence and P is replaced by a translation of that sentence in the metalanguage. So, for example, "La neve è bianca is true if and only if snow is white" is a sentence which conforms to Convention T; the object language is Italian and the metalanguage is English. The predicate "true" does not appear in the object language, so no sentence of the object language can directly or indirectly assert truth or falsity of itself. Tarski thus formulated a two-tiered scheme that avoids semantic paradoxes such as Russell's paradox.
Tarski formulated his definition of truth indirectly through a recursive definition of the satisfaction of sentential functions and then by defining truth in terms of satisfaction. An example of a sentential function is "x defeated y in the 2004 US presidential elections"; this function is said to be satisfied when we replace the variables x and y with the names of objects such that they stand in the relation denoted by "defeated in the 2004 US presidential elections". In general, a1,..., an satisfy an n-ary predicate φ if and only if substitution of the names "a1",..., "an" for the variables of φ in the relevant order yields "φ", and φ. Given a method for establishing the satisfaction of every atomic sentence of the form A, the usual rules for truth-functional connectives and quantifiers yield a definition for the satisfaction condition of all sentences of the object language. For instance, for any two sentences A, B, the sentence A & B is satisfied if and only if A and B are satisfied, for any sentence A, ~A is satisfied if and only if A fails to be satisfied, and for any open sentence A where x is free in A, A is satisfied if and only if for every substitution of an item of the domain for x yielding A*, A* is satisfied. Whether any complex sentence is satisfied is seen to be determined by its structure. An interpretation is an assignment of denotation to all of the non-logical terms of the object language. A sentence A is true if and only if it is satisfied in I.
Tarski thought of his theory as a species of correspondence theory of truth, not a deflationary theory.
Disquotationalism
On the basis of Tarski's semantic conception, W. V. O. Quine developed what eventually came to be called the disquotational theory of truth or disquotationalism. Quine interpreted Tarski's theory as essentially deflationary. He accepted Tarski's treatment of sentences as the only truth-bearers. Consequently, Quine suggested that the truth-predicate could only be applied to sentences within individual languages. The basic principle of disquotationalism is that an attribution of truth to a sentence undoes the effects of the quotation marks that have been used to form sentences. Instead of above then, Quine's reformulation would be something like the following "Disquotation Schema":Disquotationalists are able to explain the existence and usefulness of the truth predicate in such contexts of generalization as "John believes everything that Mary says" by asserting, with Quine, that we cannot dispense with the truth predicate in these contexts because the convenient expression of such generalization is precisely the role of the truth predicate in language. In the case of "John believes everything that Mary says", if we try to capture the content of John's beliefs, we would need to form an infinite conjunction such as the following:
The disquotation schema, allows us to reformulate this as:
Since x is equivalent to "x" is true, for the disquotationalist, then the above infinite conjunctions are also equivalent. Consequently, we can form the generalization:
Since we could not express this statement without a truth-predicate along the lines of those defined by deflationary theories, it is the role of the truth predicate in forming such generalizations that characterizes all that needs to be characterized about the concept of truth.