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semantic theory of truth wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 origin 2 tarski s theory of truth 3 kripke s theory of truth 4 see also 5 references 6 further reading 7 external links toggle the table of contents semantic theory of truth 7 languages eesti français 日本語 português русский українська 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia theory of truth in the philosophy of language convention t redirects here not to be confused with t schema a semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences 1 origin edit the semantic conception of truth which is related in different ways to both the correspondence and deflationary conceptions is due to work by polish logician alfred tarski 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 the course of this he made several metamathematical discoveries most notably tarski s undefinability theorem using the same formal technique kurt gödel used in his incompleteness theorems roughly this states that a truth predicate satisfying convention t for the sentences of a given language cannot be defined within that language tarski s theory of truth edit to formulate linguistic theories 2 without semantic paradoxes such as the liar paradox 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 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 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 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 as tarski originally formulated it this theory applies only to formal languages cf also semantics of first order logic he gave a number of reasons for not extending his theory to natural languages 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 into an approach to theories of meaning for natural languages which involves treating truth as a primitive rather than a defined concept see truth conditional semantics tarski developed the theory to give an inductive definition of truth as follows see t schema 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 constituents the simplest constituents are atomic sentences 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 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 it is a rather controversial point whether tarski s semantic theory should be counted either as a correspondence theory or as a deflationary theory 3 kripke s theory of truth edit see also truth kripke s semantics kripke s theory of truth saul kripke 1975 is based on partial logic a logic of partially defined truth predicates instead of tarski s logic of totally defined truth predicates with the strong kleene evaluation scheme 4 see also edit disquotational principle semantics of logic t schema triune continuum paradigm references edit hale bob wright crispin miller alexander eds 18 february 2017 a companion to the philosophy of language west sussex england john wiley sons pp 309 330 doi 10 1111 b 9780631213260 1999 00015 x isbn 9780631213260 retrieved 28 february 2024 p 326 parts of section is adapted from kirkham 1992 kemp gary quine versus davidson truth reference and meaning oxford england oxford university press 2012 p 110 axiomatic theories of truth stanford encyclopedia of philosophy further reading edit simon blackburn and keith simmons eds 1999 truth oxford university press isbn 0 19 875250 4 michael k butler 2017 deflationism and semantic theories of truth pendlebury press isbn 0993594549 wilfrid hodges 2001 tarski s truth definitions in the stanford encyclopedia of philosophy richard kirkham 1992 theories of truth bradford books isbn 0 262 61108 2 saul kripke 1975 outline of a theory of truth journal of philosophy 72 690 716 alfred tarski 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 edit semantic theory of truth internet encyclopedia of philosophy tarski s truth definitions an entry of stanford encyclopedia of philosophy alfred tarski 1944 the semantic conception of truth and the foundations of semantics philosophy and phenomenological research 4 v t e truth general statement propositions truth bearer truth maker theories coherence consensus constructivist correspondence deflationary epistemic pluralist pragmatic redundancy semantic v t e mathematical logic general axiom list cardinality first order logic formal proof formal semantics foundations of mathematics information theory lemma logical consequence model theorem theory type theory theorems list paradoxes gödel s completeness incompleteness theorems tarski s undefinability banach tarski paradox cantor s theorem paradox diagonal argument compactness halting problem lindström s löwenheim skolem russell s paradox logics traditional classical logic logical truth tautology proposition inference logical equivalence consistency equiconsistency argument soundness validity syllogism square of opposition venn diagram propositional boolean algebra boolean functions logical connectives propositional calculus propositional formula truth tables many valued logic 3 finite predicate first order list second order monadic higher order fixed point free quantifiers predicate monadic predicate calculus set theory set hereditary class ur element ordinal number extensionality forcing relation equivalence partition set operations intersection union complement cartesian product power set identities types of sets countable uncountable empty inhabited singleton finite infinite transitive ultrafilter recursive fuzzy universal universe constructible grothendieck von neumann maps cardinality function map domain codomain image in sur bi jection schröder bernstein theorem isomorphism gödel numbering enumeration large cardinal inaccessible aleph number operation binary theories zermelo fraenkel axiom of choice continuum hypothesis general kripke platek morse kelley naive new foundations tarski grothendieck von neumann bernays gödel ackermann constructive formal systems list language syntax alphabet arity automata axiom schema expression ground extension by definition conservative relation formation rule grammar formula atomic closed ground open free bound variable language metalanguage logical connective predicate functional variable propositional variable proof quantifier rank sentence atomic spectrum signature string substitution symbol function logical constant non logical variable term theory list example axiomatic systems list of true arithmetic peano second order elementary function primitive recursive robinson skolem of the real numbers tarski s axiomatization of boolean algebras canonical minimal axioms of geometry euclidean elements hilbert s tarski s non euclidean principia mathematica proof theory formal proof natural deduction logical consequence rule of inference sequent calculus theorem systems axiomatic deductive hilbert list complete theory independence from zfc proof of impossibility ordinal analysis reverse mathematics self verifying theories model theory interpretation function of models model atomic equivalence finite prime saturated spectrum submodel non standard model of non standard arithmetic diagram elementary categorical theory model complete theory satisfiability semantics of logic strength theories of truth semantic tarski s kripke s t schema transfer principle truth predicate truth value type ultraproduct validity computability theory church encoding church turing thesis computably enumerable computable function computable set decision problem decidable undecidable p np p versus np problem kolmogorov complexity lambda calculus primitive recursive function recursion recursive set turing machine type theory related abstract logic algebraic logic automated theorem proving category theory concrete abstract category category of sets history of logic history of mathematical logic timeline logicism mathematical object philosophy of mathematics supertask mathematics portal retrieved from https en wikipedia org w index php title semantic_theory_of_truth oldid 1340137832 categories mathematical logic semantics theories of truth theories of deduction hidden categories articles with short description short description is different from wikidata this page was last edited on 24 february 2026 at 03 37 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia 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