Deflationary theory of truth

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The deflationary theory of truth is a family of theories which all have in common the belief that assertions that predicate truth of a statement do not provide any substantive information or insight into the nature of truth.

Deflationary theories need to be carefully distinguished from so-called primitivist theories of truth, which claim that truth is a fundamental, indefinable, irreducible property of propositions, on the one hand, and from currently fashionable identity theories of truth, which claim that truth is a relation of identity between truth-bearers and truthmakers on the other.

The redundancy theoryEdit

Gottlob Frege was probably the first philosophical logician to express something very close to the idea that the predicate "is true" does not express anything above and beyond the statement to which it is attributed.

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. (Frege, 1918).

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 (or mental content) 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 Ceaser 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".

Of course, Ramsey was a rather careful thinker and recognized immediately 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. This is not a problem if we have the necessary tools at our disposition, namely higher-order quantification over propositions or substitutional quantification, but these were not available to Ramsey. 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". But, again, since the only sort of quantification that had been fully developed and understood at the time was first-order quantification over names of objects, this approach could not work. The only possibilities are to take aRb as the name of some object and wind up with an ungrammatical conditional statement that has a name in place of a proposition in the consequent, or we can take each one of a, R and b as names for objects, in which case we end up with collections of objects as replacements for 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 (expressions that stand in relation to sentences as pronouns stand to nouns) 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 disapperance 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 therefore unnecessary) AND that there is no such property as truth to speak of.

This naturally leads us to the question whether deflationary theories necessarily entail such extreme commitments. It has recently been maintained (Nic Damjanovich 2002) that these two positions (that the truth-predicate is redundant and that truth is not a property) are, in fact, incompatible. The argument runs as follows: it would seem that any attempt to define away the truth predicate in those awkward contexts of generalization such as Harry always tells the truth requires, in order to work, the use of the tools of higher-order quantification. But once this formal apparatus is avalaible, it becomes possible to formulate statements that describe precisely the property that all truth-bearing sentences share in common. This applies to both sentential and propositional versions of redundance theories. In the first case, such a statement can be formulated as follows:

$\forall x (T(x) \leftrightarrow \exists p ((x=p) \land p)))$

where x stands for any object, T is the truth-predicate and the bound varaible p ranges over propositions. In the second case, the following statement can be formed:

$\forall x (T(x) \leftrightarrow \exists s ((x='s') \land s)))$

where s ranges over sentences. Both statements assert the existence of a common property which all truthbearers bear. However, this property just consists in the fact that assertions of the truth of a statement and assertions of the statement itself are equivalent. This is just the sort of property that many other deflationists welcome.

The performative theoryEdit

Peter Strawson formulated a performative theory of truth in the 1950's which was based on the idea of emotivism in moral philosophy. Like Ramsey, Strawson believed that there was no separate problem of truth apart from determining the semantic contents (or facts of the world) 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 perfom 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 theoriesEdit

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. (Material adequacy is the criterion that a definition of truth must satisfy our intuitions about the term in question; here it is 'true'.) If all such conditions were met, then it would be possible to avoid semantic paradoxes such as the liar paradox (i.e. "This sentence is false.") Tarski defined his material adequacy condition, or Convention T, in the following way:

(Eq) X is true if and only if P.

where X is replaced by a name of a sentence and p is replaced by the sentence itself or a translation of it in the metalanguage. The left hand side of this biconditional expression must, according to Tarski, consist exclusively of syntactic terms (or "objects") from the object language and the right hand side may consist of semantic or syntactic concepts exclusively from the metalangauge. Tarski thus formulated a two-tiered schema that avoids semantic paradoxes by keeping the truth-predicate out of the lower-level object language. So, for example, "La neve è bianca is true iff snow is white" is a sentence which conforms to Convention T: the object-language is Italian and the metalanguage is English. It is to be noted that, although Tarski defined himself, and others have defined him, as a correspondence theorist, the basic intuition behind (Eq) is the same one that inspired Frege, Ramsey, Ayer and Strawson to adopt deflationary theories of truth: there is some sort of equivalence between assertions of the truth of a statement and assertions of the statement itself.

Based on this equivalence schema, 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". Such a function is said to be satisfied when we replace the variables X and Y with the names of objects such that the result is a true sentence (in the case just mentioned, replacing X with George W. Bush and Y with John Kerry would satisfy the function, resulting in a true sentence). Satisfaction is defined by Tarski as sequences of ordered pairs <variable, object> such that when each object in the sequence of objects satisfies each variable, the result is a true sentence. It then becomes straightforward to define truth. Since there are no free variables in closed sentences, either every sequence will satisfy the sentence or none will. True sentences are the those that are satisfied by all sequences, false sentences are those that are satisfied by none.

DisquotationalismEdit

On the basis of Tarski's semantic conception, W.V.O. Quine developed what eventually came to be called the disquotational theory of truth. Quine interpreted Tarksi's theory as essentially deflationary. He accepted Tarski's treatment of sentences as the only truth-bearers, since it follows as a logical consequence of his semantic holism that such universal entities as propositions do not exist and interlinguistic synonymy is impossible. 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 (EQ) above then, Quine's reformulation would be something like the following "Disquotation Schema:

(DS) Sentence "S" is true iff S.

Contrary to (EQ), (DS) requires that any name of a sentence must be formed by quotation marks, and that instances of the schema must be homophonic.

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:

If Mary says that lemons are yellow, then lemons are yellow, and if Mary says that lemons are green, then lemons are green, and...

The disquotation schema (DS), allows us to reformulate this as:

If Mary says that lemons are yellow, then the sentence "lemons are yellow" is true, and if Mary says that lemons are green, then the sentence "lemons are green" is true, and..."

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:

For all sentences "S", if Mary said S, then "S" is true.

Since we could not express this statement without a truth-predicate along the lines of the 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.

ProsententialismEdit

Prosententialism asserts that, just as there are other so-called proforms which stand in for and are anaphorically dependent on the forms of expression that they stand in for (e.g. pronouns are proforms of nouns), so there are prosentences which stand in for and derive their meanings from the sentences which they substitute. In the statement:

Bill is tired and he is hungry.

the pronoun "he" takes its reference from the noun "Bill." In the statement:

He explained that he was in financial straits, said that this is how things were, and that therefore he needed an advance.

the clause "this is how things were" receives its reference from the previously occurring sentential clause "he was in financial straits", according to a prosententialist account.

How does this relate to truth? Prosententialists view the statements that contain "is true" as sentences which do not contain a truth-predicate but rather contain some form of prosentence; the truth-predicate itself is part of an anaphoric or prosentential construction. Prosententialists point out the many parallels which exist between pronouns and prosentences. Pronouns are often used out of "laziness", as in:

Bill is tired and he is hungry

or they can be used in quantificational contexts, such as:

Someone is in the room and he is armed with a rifle.

In a similar manner, "it is true" can be used as a prosentence of laziness, as in:

Fred believes that it is raining and it is true.

and as a quantificational prosentence, such as:

Whatever Alice believes is true.

Prosententialists therefore differ from redundantists, because they do not see the truth-predicate as being redundant but as a very important part of an anaphoric clause. They also differ from disquotationalists in maintaining that there is no truth predicate. They also reject the idea that truth is a property of some sort.

Horwich's minimalismEdit

It was noted in passing above that one of the essential defects of simple redundancy theories, such as that of Ramsey, is that they require, in order to deal with those contexts of generalization such as "Everything Socrates says is true", the use of higher-order quantification over properties or subsitutional quantification. However, if these tools are made available, then it becomes possible to formulate a certain property which all of these properties or sentences share in common. Paul Horwich's theory of truth, known as the minimalist theory, accepts precisely this latter consequence, while still remaining fundamentally a deflationary theory of truth. Horwich takes the primary truth-bearing entities to be propositions rather than sentences and claims that these propositions all share a common property which was defined earlier but which will be stated again here for convenience:

$\forall x (T(x) \leftrightarrow \exists p ((x=p) \land p)))$

where p ranges over propositions. The statement asserts the existence of a common property which all truthbearers bear. However, this property just consists in the fact that assertions of the truth of a proposition and assertions of the propositions itself are equivalent. According to the minimalist view then, truth is indeed a property of propositions (or sentences, as the case may be) but it is so minimal and anomalous a property that it cannot be said to provide us with any useful information about or insight into the nature of truth. It is fundamentally nothing more than a sort of metalinguistic property.

Another way of formulating the minimalist thesis is to assert that the conjunction of all of the instances of the following schema:

The proposition that P is true iff P.

provides an implicit definition of the property of truth. Each such instance is an axiom of the theory and there are an infinite number of such instances (one for every actual or possible proposition in the universe). Our concept of truth consists in nothing more than a disposition to assent to all of the instances of the above schema when we encounter them.

Objections to DeflationismEdit

One of the main objections to deflationary theories of all flavors was formulated by Jackson, Oppy and Smith in 1994. According to the objection, if deflationism is interpreted as a sentential theory (that is, one where sentences fill in the left hand side of the biconditionals such as (EQ) above), then deflationism is false; on the other hand, if it is interpreted as a propositional theory, then it is trivial. Examining another simple instance of the standard equivalence schema:

Grass is green is true iff grass is green.

the objection is just that, if the part on the left-hand side of the biconditional is taken as a sentence, then it is false, because something more is required for the whole statement to be true than merely the fact that "grass is green" is true. It is also necessary that the sentence "grass is green" means that grass is green and this further linguistic fact is not dealt with in the equivalence schema. However, if we now assume that grass is green on the left-hand side refers to a proposition, then the theory seems trivial since snow is white is defined as true if and only if snow is white. Note that the triviality involved here is not caused by the concept of truth but by that of proposition. In any case, simply accepting the triviality of the propositional version implies that there can be no explanation of the connection between sentences and the things that they express (presumably propositions!!). Consequently, there can be no theory of meaning, for this version of deflationism. This does not refute deflationism about truth, but it makes the theory less than appealing to those who are interested in trying to formulate meaning theories.

Another alternative is to accept that deflationism applies to "interpreted sentences", rather than propositions. The difficulty here is that, since interpreted sentences already have meaning, some other account of what such meaning consists in must be provided and it cannot appeal to the concept of truth, on pain of circularity. For this reason, it has become popular among deflationists to attempt to develop theories of meaning as use.

Correspondence intuitionEdit

Another very common objection to deflationism is the complaint that it does not account for something called the correspondence intuition. This is just the general intuitive sense that people supposedly have that true sentences or thoughts correspond to the facts, where facts are a separate ontological class of entities from truth-bearers, such as propositions, and whose existence makes truth-bearers true by "standing in a relation of correspondence with them". A simple response to this objection is that deflationism neither denies nor affirms the existence of any such facts and relations. The claim that the truth-predicate is redundant, for example, does not imply anything about facts, states of affairs or other ontological matters.

Normativity of assertionsEdit

Michael Dummett,among others, has argued that deflationism cannot account for the fact that truth should be a normative goal of assertion. The idea is that truth plays a central role in the activity of stating facts. The deflationist reponse is that the assertion that truth is a norm of assertion can be stated only in the form of the following infinite conjunction:

One should assert the proposition that grass is green only if grass is green and one should assert the proposition that lemons are yellow only if lemons are yellow and one should assert the proposition that a square circle is impossible only if a squared circle is impossible and...

This, in turn, can be reformulated as:

For all propositions P, speakers should assert the propositions that P only if the proposition that P is true.

It may be the case that we use the truth-predicate to express this norm, not because it has anything to do with the nature of truth in some inflationary sense, but because it is a conventient way of expressing this otherwise inexpressible generalization.

References Edit

• Frege, G. (1918) Ricerche Logiche. M. di Francesco (ed.). tr: R. Casati. Milan: Guerini. 1998.
• Kirkham, Richard. (1992) Theories of Truth, MIT Press.
• Horwich. P. (1998) Truth. Oxford:Clarendon Press:
• Ayer, A.J. (1952). Language, Truth and Logic. New York: Dover Publications. ISBN 486200108
• Quine, W.V.O. (1970) Philosophy of Logic (Englewood Cliffs, NJ: Prentice Hall)
• Tarski, A. (1944)The Semantic Conception of Truth, in Philosophy and Phenomenologcial Research. 4: 341-76.
• Strawson, P.F. (1949) "Truth", Analysis, 9: 83-97.
• Damnyanovic, Nic. A Short History of Deflationism ((online))
• Beeb, James R. The Pro-sentential theory of truth in The Internet Encyclopedia of Philosophy ((online))