{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T16:17:52Z","timestamp":1751473072235},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":3973,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:p>The fact that G\u00f6del's famous incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of the community of logicians. Indeed, almost every more or less formal treatment of the theorem makes a reference to this connection. G\u00f6del himself remarked in the paper announcing his celebrated result (cf. [7]):<\/jats:p><jats:p>The analogy between this result and Richard's antinomy leaps to the eye;<\/jats:p><jats:p>there is also a close relationship with the \u2018liar\u2019 antinomy, since \u2026 we are<\/jats:p><jats:p>\u2026 confronted with a proposition which asserts its own unprovability.<\/jats:p><jats:p>In the light of the fact that the existence of this connection is commonplace it is all the more surprising that very little can be learnt about its exact nature except perhaps that it is some kind of similarity or analogy. There is, however, a lot more to it than that. Indeed, as we shall try to show below, the general ideas underlying the three central theorems concerning internal limitations of formal deductive systems can be taken as different ways to resolve the Liar paradox. More precisely, it will turn out that an abstract formal variant of the Liar paradox, which can almost straightforwardly inferred from its original ordinary language version, is a possible common generalization of (both the syntactic and semantic versions of) G\u00f6del's incompleteness theorem, the theorem of Tarski on the undefinability of truth, and that of Church concerning the undecidability of provability.<\/jats:p>","DOI":"10.2178\/bsl\/1046288723","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T20:14:15Z","timestamp":1109794455000},"page":"3-25","source":"Crossref","is-referenced-by-count":6,"title":["G\u00f6del, Tarski, Church, and The Liar"],"prefix":"10.1017","volume":"9","author":[{"given":"Gy\u00f6rgy","family":"Ser\u00e9ny","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600004704_ref016","volume-title":"Mathematical logic","author":"Shoenfield","year":"1967"},{"key":"S1079898600004704_ref011","doi-asserted-by":"crossref","first-page":"190","DOI":"10.4064\/fm-37-1-190-192","article-title":"A system which can define its own truth","volume":"37","author":"Myhill","year":"1950","journal-title":"Fundamenta Mathematicae"},{"key":"S1079898600004704_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1973-0432416-X"},{"key":"S1079898600004704_ref013","doi-asserted-by":"crossref","DOI":"10.4159\/9780674042469","volume-title":"Mathematical logic","author":"Quine","year":"1951"},{"key":"S1079898600004704_ref015","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/11.3.61"},{"key":"S1079898600004704_ref007","volume-title":"On formally undecidable propositions of Principia Mathematica and related systems","author":"G\u00f6del","year":"1962"},{"key":"S1079898600004704_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4489-7"},{"key":"S1079898600004704_ref005","volume-title":"Model theory","author":"Chang","year":"1973"},{"key":"S1079898600004704_ref019","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195046724.001.0001","volume-title":"G\u00f6del's incompleteness theorems","author":"Smullyan","year":"1992"},{"key":"S1079898600004704_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2964058"},{"key":"S1079898600004704_ref014","volume-title":"The Ways of Paradox and other essays","author":"Quine","year":"1979"},{"key":"S1079898600004704_ref006","doi-asserted-by":"publisher","DOI":"10.1093\/mind\/LI.203.259"},{"key":"S1079898600004704_ref004","volume-title":"Computability and logic","author":"Boolos","year":"1992"},{"key":"S1079898600004704_ref017","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71123-6"},{"key":"S1079898600004704_ref021","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican0669-63"},{"key":"S1079898600004704_ref008","volume-title":"Advanced logic for applications","author":"Grandy","year":"1979"},{"key":"S1079898600004704_ref003","volume-title":"The logic of provability","author":"Boolos","year":"1995"},{"key":"S1079898600004704_ref009","first-page":"300","article-title":"Bemerkungen zu den Paradoxien von Russell und Burali\u2013Forti","volume":"2","author":"Grelling","year":"1907","journal-title":"Abhandlungen der Fries'schen Schule"},{"key":"S1079898600004704_ref020","doi-asserted-by":"publisher","DOI":"10.2307\/2102968"},{"key":"S1079898600004704_ref001","first-page":"30","volume-title":"Arithmetic, proof theory, and computational complexity","author":"Baaz","year":"1993"},{"key":"S1079898600004704_ref010","volume-title":"Introduction to mathematical logic","author":"Mendelson","year":"1965"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600004704","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,2]],"date-time":"2023-05-02T14:46:59Z","timestamp":1683038819000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600004704\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["S1079898600004704"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1046288723","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}