Iranian Association of Logic
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Iranian Association of Logic (IAL) is the owner of Logical Letter.
Volume 1, Issue 1 (2026)
3 2026, 1(1): 29-35 |
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Request Type: Original Research |
Received: 2026/10/21 | Accepted: 2027/01/2 | Published: 2027/01/2
Received: 2026/10/21 | Accepted: 2027/01/2 | Published: 2027/01/2
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Bastin H. Paradoxes of Truth: The Liar and Its Modern Solutions. 3 2026; 1 (1) :29-35
URL: http://daneshafarand.org/article-9-87271-en.html
URL: http://daneshafarand.org/article-9-87271-en.html
Independent Researcher
Abstract: (2 Views)
Aims This article surveys the Liar paradox and the main families of solutions proposed since the 1930s, and assesses what each solution costs.
Approach After a brief history of the paradox, including its treatment by logicians in Shiraz in the fifteenth century, the article presents Tarski's undefinability theorem and hierarchy of languages, Kripke's fixed-point theory of truth, contextualist and revision-theoretic approaches, and paraconsistent and paracomplete logics. The problem of ``revenge'' paradoxes is used as a common test.
Main Points The Liar shows that three natural assumptions cannot all be kept: that a language can talk about the truth of its own sentences, that truth obeys the equivalence ``? is true if and only if ?'', and that classical logic holds without restriction. Each solution gives up one of these assumptions or restricts it. Every solution so far proposed faces some form of revenge.
Conclusion There is no consensus solution to the Liar. The paradox remains a productive test for theories of truth, meaning and logical consequence, and its study has led to some of the most important technical work in philosophical logic.
Approach After a brief history of the paradox, including its treatment by logicians in Shiraz in the fifteenth century, the article presents Tarski's undefinability theorem and hierarchy of languages, Kripke's fixed-point theory of truth, contextualist and revision-theoretic approaches, and paraconsistent and paracomplete logics. The problem of ``revenge'' paradoxes is used as a common test.
Main Points The Liar shows that three natural assumptions cannot all be kept: that a language can talk about the truth of its own sentences, that truth obeys the equivalence ``? is true if and only if ?'', and that classical logic holds without restriction. Each solution gives up one of these assumptions or restricts it. Every solution so far proposed faces some form of revenge.
Conclusion There is no consensus solution to the Liar. The paradox remains a productive test for theories of truth, meaning and logical consequence, and its study has led to some of the most important technical work in philosophical logic.
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