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A semantic theory of truth is a theory of truth in the
philosophy of language In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the ...
which holds that truth is a property of sentences.


Origin

The
semantic Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
conception of truth, which is related in different ways to both the correspondence and
deflationary In economics, deflation is a decrease in the general price level of goods and services. Deflation occurs when the inflation rate falls below 0% (a negative inflation rate). Inflation reduces the value of currency over time, but sudden deflation ...
conceptions, is due to work by
Polish Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...
ian
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
. Tarski, in "On the Concept of Truth in Formal Languages" (1935), attempted to formulate a new theory of truth in order to resolve the
liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the trut ...
. In the course of this he made several metamathematical discoveries, most notably Tarski's undefinability theorem using the same formal technique
Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imm ...
used in his
incompleteness theorems Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...
. Roughly, this states that a truth-predicate satisfying
Convention T 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 deflati ...
for the sentences of a given language cannot be defined ''within'' that language.


Tarski's theory of truth

To formulate linguistic theories without semantic
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
es such as the
liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the trut ...
, it is generally necessary to distinguish the language that one is talking about (the ''object language'') from the language that one is using to do the talking (the ''
metalanguage In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quota ...
''). In the following, quoted text is use of the object language, while unquoted text is use of the metalanguage; a quoted sentence (such as "''P''") is always the metalanguage's ''name'' for a sentence, such that this name is simply the sentence ''P'' rendered in the object language. In this way, the metalanguage can be used to talk about the object language; Tarski's theory of truth (
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
1935) demanded that the object language be contained in the metalanguage. Tarski's material adequacy condition, also known as Convention T, holds that any viable theory of truth must entail, for every sentence "''P''", a sentence of the following form (known as "form (T)"): (1) "P" is true
if, and only if In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bic ...
, P. For example, (2) 'snow is white' is true if and only if snow is white. These sentences (1 and 2, etc.) have come to be called the "T-sentences". The reason they look trivial is that the object language and the metalanguage are both English; here is an example where the object language is German and the metalanguage is English: (3) 'Schnee ist weiß' is true if and only if snow is white. It is important to note that as Tarski originally formulated it, this theory applies only to
formal language In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of s ...
s. He gave a number of reasons for not extending his theory to
natural language In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languag ...
s, including the problem that there is no systematic way of deciding whether a given sentence of a natural language is well-formed, and that a natural language is ''closed'' (that is, it can describe the semantic characteristics of its own elements). But Tarski's approach was extended by
Davidson Davidson may refer to: * Davidson (name) * Clan Davidson, a Highland Scottish clan * Davidson Media Group * Davidson Seamount, undersea mountain southwest of Monterey, California, USA * Tyler Davidson Fountain, monument in Cincinnati, Ohio, USA ...
into an approach to theories of ''
meaning Meaning most commonly refers to: * Meaning (linguistics), meaning which is communicated through the use of language * Meaning (philosophy), definition, elements, and types of meaning discussed in philosophy * Meaning (non-linguistic), a general te ...
'' for natural languages, which involves treating "truth" as a primitive, rather than a defined, concept. (See
truth-conditional semantics Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associate ...
.) Tarski developed the theory to give an
inductive definition In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set ( Aczel 1977:740ff). Some examples of recursively-definable objects include fact ...
of truth as follows. (See
T-schema The T-schema ("truth schema", not to be confused with "Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it a ...
) For a language ''L'' containing ¬ ("not"), ∧ ("and"), ∨ ("or"), ∀ ("for all"), and ∃ ("there exists"), Tarski's inductive definition of truth looks like this: * (1) A primitive statement "''A''" is true if, and only if, ''A''. * (2) "¬''A''" is true if, and only if, "''A"'' is not true. * (3) "''A''∧''B''" is true if, and only if, "''A" is true'' and "''B" is true''. * (4) "''A''∨''B''" is true if, and only if, "''A" is true'' or "''B" is true'' or ("''A" is true'' and "''B" is true''). * (5) "∀''x''(''Fx'')" is true if, and only if, for all objects x; "Fx" is true. * (6) "∃''x''(''Fx'')" is true if, and only if, there is an object ''x'' for which "Fx" is true. These explain how the truth conditions of ''complex'' sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their
constituent Constituent or constituency may refer to: Politics * An individual voter within an electoral district, state, community, or organization * Advocacy group or constituency * Constituent assembly * Constituencies of Namibia Other meanings * Cons ...
s. The simplest constituents are
atomic sentence In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. ...
s. A contemporary semantic definition of truth would define truth for the atomic sentences as follows: * An atomic sentence ''F''(''x''1,...,''x''''n'') is true (relative to an assignment of values to the variables ''x''1, ..., ''x''''n'')) if the corresponding values of variables bear the relation expressed by the
predicate Predicate or predication may refer to: * Predicate (grammar), in linguistics * Predication (philosophy) * several closely related uses in mathematics and formal logic: **Predicate (mathematical logic) **Propositional function **Finitary relation, ...
''F''. Tarski himself defined truth for atomic sentences in a variant way that does not use any technical terms from semantics, such as the "expressed by" above. This is because he wanted to define these semantic terms in the context of truth. Therefore it would be circular to use one of them in the definition of truth itself. Tarski's semantic conception of truth plays an important role in modern logic and also in contemporary
philosophy of language In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the ...
. It is a rather controversial point whether Tarski's semantic theory should be counted either as a correspondence theory or as a deflationary theory.


Kripke's theory of truth

Kripke's theory of truth (
Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and eme ...
1975) is based on partial logic (a logic of partially defined
truth predicate In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or i ...
s instead of Tarski's logic of totally defined truth predicates) with the strong Kleene evaluation scheme.Axiomatic Theories of Truth (Stanford Encyclopedia of Philosophy)
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See also

*
Disquotational principle The disquotational principle is a philosophical principle which holds that a rational speaker will accept "''p''" if and only if he or she believes ''p''. The quotes indicate that the statement ''p'' is being treated as a sentence, and not as a ...
*
Semantics of logic In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment. Overview The truth cond ...
*
T-schema The T-schema ("truth schema", not to be confused with "Convention T") is used to check if an inductive definition of truth is valid, which lies at the heart of any realisation of Alfred Tarski's semantic theory of truth. Some authors refer to it a ...
*
Triune continuum paradigm The Triune Continuum Paradigm is a paradigm for general system modeling published in 2002.A. Naumenko''Triune Continuum Paradigm: a paradigm for general system modeling and its applications for UML and RM-ODP'' Doctoral thesis 2581, Swiss Federal I ...


References


Further reading

*
Simon Blackburn Simon Blackburn (born 12 July 1944) is an English academic philosopher known for his work in metaethics, where he defends quasi-realism, and in the philosophy of language; more recently, he has gained a large general audience from his effort ...
and Keith Simmons, eds., 1999. ''Truth''. Oxford University Press, . * Michael K Butler, 2017. ''Deflationism and Semantic Theories of Truth''. Pendlebury Press, . * Wilfrid Hodges, 2001
Tarski's truth definitions
In the
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. E ...
. *
Richard Kirkham Richard Ladd Kirkham (born June 18, 1955) is an American philosopher. Among his published works are ''Theories of Truth'' (his most-cited work, published by MIT Press in 1992), "Does the Gettier Problem Rest on a Mistake?" ''Mind'' (1984. Vol. 93 ...
, 1992. ''Theories of Truth''. Bradford Books, . *
Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American philosopher and logician in the analytic tradition. He was a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and eme ...
, 1975. "Outline of a Theory of Truth". ''Journal of Philosophy'', 72: 690–716. *
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
, 1935. "The Concept of Truth in Formalized Languages". ''Logic, Semantics, Metamathematics'', Indianapolis: Hackett 1983, 2nd edition, 152–278. * Alfred Tarski, 1944
The Semantic Conception of Truth and the Foundations of Semantics
''Philosophy and Phenomenological Research'' 4.


External links


Semantic Theory of Truth
''Internet Encyclopedia of Philosophy''
Tarski's Truth Definitions
(an entry o
Stanford Encyclopedia of Philosophy
*
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
, 1944.
The Semantic Conception of Truth and the Foundations of Semantics
''Philosophy and Phenomenological Research'' 4. {{Mathematical logic Mathematical logic Semantics Theories of truth Theories of deduction