Deflationary theory of truth
Encyclopedia
A deflationary theory of truth is one of a family of theories which all have in common the claim that assertions that predicate truth
Truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

 of a statement do not attribute a property called truth to such a statement.

Redundancy theory

Gottlob Frege
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...

 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 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".

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
Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...

 of quantification
Quantification
Quantification has several distinct senses. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method.In logic,...

 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 (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 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 therefore unnecessary) AND that there is no such property as truth to speak of.

Performative theory

Peter Strawson 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 (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 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
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...

 had developed his so-called semantic theory of truth
Semantic theory of truth
A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.-Origin:The semantic conception of truth, which is related in different ways to both the correspondence and deflationary conceptions, is due to work published by Polish...

. 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
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...

 (i.e. "This sentence is false.") Tarski's material adequacy condition, or Convention T, is: a definition of truth for an object language implies all instances of the sentential form
S is true if and only if P

where S is replaced by a name of a sentence (in the metalanguage
Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined. In logic and linguistics, a metalanguage is a language used to make statements about statements in another language...

) 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
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...

.

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 the case just mentioned, replacing x with "George W. Bush" and y with "John Kerry" would satisfy the function, resulting in a true sentence). In general, a1, ..., an satisfy n-adic
Arity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes. The arity of a relation is the dimension of the domain in the corresponding Cartesian product...

 predicate φ(x1. ..., xn) just in case substitution of the names 'a1', ..., 'an' for the variables of φ in the relevant order yields "φ(a1, ..., an)", and φ(a1, ..., an). Given a method for establishing the satisfaction (or not) of every atomic sentence
Atomic sentence
In logic, an atomic sentence is a type of declarative sentence which is either true or false and which cannot be broken down into other simpler sentences...

 of the form A(...xk...), the usual rules for truth-functional connectives
Logical connective
In logic, a logical connective is a symbol or word used to connect two or more sentences in a grammatically valid way, such that the compound sentence produced has a truth value dependent on the respective truth values of the original sentences.Each logical connective can be expressed as a...

 and quantifiers yield a definition for the satisfaction condition of all sentences of the object language. For instance, for any two sentences A, B, A&B is satisfied if and only if A and B are satisfied (where '&' stands for conjunction
Logical conjunction
In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false....

), 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, (x)A is satisfied if and only if for every substitution of an item of the domain
Domain of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse , is the set of entities over which certain variables of interest in some formal treatment may range...

 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
Denotation
This word has distinct meanings in other fields: see denotation . For the opposite of Denotation see Connotation.*In logic, linguistics and semiotics, the denotation of a word or phrase is a part of its meaning; however, the part referred to varies by context:** In grammar and literary theory, the...

 to all of the non-logical terms of the object language. A sentence A is true (under an interpretation I) if and only if it is satisfied in I.

Tarski thought of his theory as a species of correspondence theory of truth
Correspondence theory of truth
The correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world, and whether it accurately describes that world...

, 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. 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 (T) above then, Quine's reformulation would be something like the following "Disquotation Schema":
Sentence "S" is true if and only if S.

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.

Prosententialism

Prosententialism asserts that 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." By analogy, 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 reject the idea that truth is a property of some sort.

Horwich's minimalism

Paul Horwich
Paul Horwich
Paul Horwich is a British analytic philosopher at New York University, whose work includes writings on causality, the philosophy of language and Wittgenstein's later philosophy. Horwich earned his PhD from Cornell University; his thesis advisor was Richard Boyd...

's theory of truth, known as the Minimalist Theory, takes the primary truth-bearing entities to be propositions, rather than sentences. 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 if and only if 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 of nothing more than a disposition to assent to all of the instances of the above schema when we encounter them.

Objections to deflationism

One of the main objections to deflationary theories of all flavors was formulated by Jackson, Oppy and Smith in 1994 (following Kirkham 1992). According to the objection, if deflationism is interpreted as a sentential theory (that is, one where truth is predicated of sentences on the left hand side of the biconditionals such as (T) 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 if and only if grass is green.


the objection is just that, if the italicized words are 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; i.e. propositions.

Normativity of assertions

Michael Dummett
Michael Dummett
Sir Michael Anthony Eardley Dummett FBA D.Litt is a British philosopher. He was, until 1992, Wykeham Professor of Logic at the University of Oxford...

, 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 response 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 convenient way of expressing this otherwise inexpressible generalization.

See also

  • Truth
    Truth
    Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

  • Truth theory

  • Coherentism
    Coherentism
    There are two distinct types of coherentism. One refers to the coherence theory of truth. The other refers to the coherence theory of justification. The coherentist theory of justification characterizes epistemic justification as a property of a belief only if that belief is a member of a coherent...

  • Confirmation holism
    Confirmation holism
    Confirmation holism, also called epistemological holism is the claim that a single scientific theory cannot be tested in isolation; a test of one theory always depends on other theories and hypotheses....



Related topics

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    Belief
    Belief is the psychological state in which an individual holds a proposition or premise to be true.-Belief, knowledge and epistemology:The terms belief and knowledge are used differently in philosophy....

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    Information
    Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

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    An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...


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    Knowledge
    Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

  • Pragmatism
    Pragmatism
    Pragmatism is a philosophical tradition centered on the linking of practice and theory. It describes a process where theory is extracted from practice, and applied back to practice to form what is called intelligent practice...

  • Pragmaticism
    Pragmaticism
    Pragmaticism is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary journals"...

  • Pragmatic maxim
    Pragmatic maxim
    The pragmatic maxim, also known as the maxim of pragmatism or the maxim of pragmaticism, is a maxim of logic formulated by Charles Sanders Peirce...


  • Reproducibility
    Reproducibility
    Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...

  • Scientific method
    Scientific method
    Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...

  • Testability
    Testability
    Testability, a property applying to an empirical hypothesis, involves two components: the logical property that is variously described as contingency, defeasibility, or falsifiability, which means that counterexamples to the hypothesis are logically possible, and the practical feasibility of...

  • Verificationism


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