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- Nuel Belnap (2006). Presentence, Revision, Truth, and Paradox. Philosophy and Phenomenological Research 73 (3):705–712.Tim Maudiin’s Truth and Paradox (Maudlin 2004, cited here as T&P), a book that is richly endowed with interesting analyses and original theses, chooses to ignore both the prosentential theory of truth from Grover, Camp and Belnap 1975 and the revision theory in its book form, Gupta and Belnap 1993 (The Revision Theory of Truth, henceforth RTT).1 There is no discussion of either theory, nor even any mention of them in the list of references. I offer a pair of quotes chosen from among a number of T&P generalizations that Maudlin would doubtless have modified if RTT had been on his mind at the time of composition of T&P. (1) "...every acceptable account of truth seems to imply that the Tlnferences must be valid" (p. 15). My response is that the revision theory of truth is built on an explicit denial of this. Rather than taking them as "valid," RTT takes the T—Inferences as stage-of-revision—shifting revision principles in the context of a definitional account of truth. (2) "...most discussions of the Liar paradox and related paradoxes...do not address [such questions as]...where ['l`&P’s] Proof Lambda and Proof Gamma go wrong" (p. 20). In fact, RTT is not open to this criticism. It’s simple natural-deduction calculus C0 addresses exactly such questions.Reading list | Discuss | Edit | Categorize |My bibliography
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The Revision Theory of Truth (Gupta/Belnap 93) has been challenged in A. M. Yaqb's recent book The Liar Speaks the Truth. Yaqb suggests some non-trivial changes in the original theory — changing the limit rule — to avoid certain artifacts. In this paper it is shown that the proposed changes are not sufficient, i.e., Yaqb's system also produces artifacts. An alternative solution is proposed and the relation between it and Yaqb's solution is explored.
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| | Other links: jstor.org | Scholar | At my library | More options ... In The Revision Theory of Truth (MIT Press, 1993), Gupta and Belnap claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions—conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological models in which truth behaves like a classical concept, and investigate conditions under which a model is Thomason: they argue that a model is Thomason when there is no vicious reference in it. We extend their investigation, considering notions of nonpathologicality and senses of “no vicious reference” generated both by revision theories of truth and by fixedpoint theories of truth. We show that some of the fixed-point theories have an advantage analogous to that which Gupta and Belnap claim for their approach, and that at least one revision theory does not. This calls into question the claim that the revision theories have a distinctive advantage in this regard.
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| | Scholar | More options ... We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as "revision operations". More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure: (ii) show that the categorical truth set of Belnap and Gupta's theory of truth over arithmetic using fully varied revision sequences yields a complete $\Pi_3^1$ set of integers: (iii) the set of stably categorical sentences using their revision operator ψ is similarly $\Pi_3^1$ and which is complete in $G\ddot{o}del's$ universe of constructible sets L: (iv) give an alternative account of a theory of truth-realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points.
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| | Other links: jstor.org projecteuclid.org dx.doi.org | Scholar | At my library | More options ... In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological ...
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| | Scholar | At my library | More options ... In (2002) I argued that Gupta and Belnap’s Revision Theory of Truth (1993) has counterintuitive consequences. In particular, the pair of sentences: (S1) At least one of S1 and S2 is false. (S2) Both of S1 and S2 are false.1 is pathological on the Revision account. There is one, and only one, assignment of truth values to {(S1), (S2)} that make the corresponding Tarski..
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| | Other links: blackwell-synergy.com analysis.oxfordjournals.org jstor.org dx.doi.org | Scholar | At my library | More options ... Minimalists about truth say that the important properties of the truth predicate are revealed in the class of T -biconditionals. Most minimalists demur from taking all of the T -biconditionals of the form “ p is true if and only if p”, to be true, because to do so leads to paradox. But exactly which biconditionals turn out to be true? I take a leaf out of the epistemic account of vagueness to show how the minimalist can avoid giving a comprehensive answer to that question. I also show that this response is entailed by taking minimalism seriously, and that objections to this position may be usefully aided and abetted by Gupta and Belnap’s revision theory of truth.
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| | Scholar | More options ... We are grateful to Professor Robert Koons for his excellent, and generous, review (henceforth KR) of our book The Revision Theory of Truth (henceforth RTT). Koons provides in KR a welcome guide to our RTT, and he puts forward objections that deserve serious consideration. In this note we shall respond only to his principal objection.' This objection, which is developed on pp. 625 ââ¬â 628 of KR, calls into question our main thesis. As we argue below, however, the objection is not successful. We should forewarn the reader that this note is not self-contained. It presupposes familiarity with RTT (primarily, Chapter 4) and with KR. The main thesis of RTT is that truth is a circular concept. We argued that the Tarski biconditionals, read as partial definitions, constitute an intensionally adequate definition of truth. In other words, if T is a predicate defined by the Tarski-style infinitistic definition (I).
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| | Other links: pitt.edu dx.doi.org | Scholar | At my library | More options ... In this book, Yaqub describes a simple conception of truth and shows that it yields a semantical theory that accommodates the whole range of our seemingly conflicting intuitions about truth. This conception takes the Tarskian biconditionals (such as "The sentence 'Johannes loved Clara' is true if and only if Johannes loved Clara") as correctly and completely defining the notion of truth. The semantical theory, which is called the revision theory, that emerges from this conception paints a metaphysical picture of truth as a property whose applicability is given by a revision process rather than by a fixed extension. The main advantage of this revision process is its ability to explain why truth seems in many cases almost redundant, in others substantial, and yet in others paradoxical (as in the famous Liar). Yaub offers a comprehensive defense of the revision theory of truth by developing consistent and adequate formal semantics for languages in which all sorts of problematic sentences (Liar and company) can be constructed. Yaqub concludes by introducing a logic of truth that further demonstrates the adequacy of the revision theory.
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| | Scholar | At my library | More options ... We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified (in terms of definitional complexity) account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.
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| | Other links: jstor.org | Scholar | At my library | More options ... Gupta’s Rule of Revision theory of truth builds on insights to be found in Martin and Woodruff (1975) and Kripke (1975) (who in turn build on Tarski) in order to permanently deepen our understanding of truth, of paradox (and of the absence of it), and of how we work our language while our language is working us. His concept of a predicate deriving its meaning by way of a Rule of Revision ought to impact significantly on the philosophy of language. Still, fortunately, he has left me something to..
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| | Other links: springerlink.com | Scholar | At my library | More options ... Discussion of Nuel Belnap, Presentence, revision, truth, and paradox
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