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- Patrick Greenough (2011). Truthmaker Gaps and the No-No Paradox. Philosophy and Phenomenological Research 82 (3):547-563.Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S says that p then S is false iff not-p—and given what they say, they are both true, and so not false. Contradiction! Conclude: they are not both false. Thus, despite their symmetry, the no-no sentences must differ in truth-value. Such is the no-no paradox.[1] Sorensen (2001, 2005a, 2005b) has argued that: (1) The no-no paradox is not a version of the liar but rather a cousin of the truth-teller paradox. (2) Even so, the no-no paradox is more paradoxical than the truth-teller. (3) The no-no and truth-teller sentences have groundless truthvalues—they are bivalent but give rise to “truthmaker gaps”. (4) It is metaphysically impossible to know these truth-values. (5) A truthmaker gap response to the no-no paradox provides reason to accept a version of epistemicism. In this paper it is shown that a truthmaker gap solution to the no-no and truth-teller paradoxes runs afoul of the dunno-dunno paradox, the strengthened no-no paradox, and the strengthened truth-teller paradox. In consequence, the no-no paradox is best seen as a form of the liar paradox. As such, it cannot provide a case for epistemicism.Reading list | Discuss | Edit | Categorize |My bibliography
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A new solution to the liar paradox is developed using the insight that it is illegitimate to even suppose (let alone assert) that a liar sentence has a truth-status (true or not) on the grounds that supposing this sentence to be true/not-true essentially defeats the telos of supposition in a readily identifiable way. On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus. The lesson of the liar is that not all assumptions are for free. One merit of this proposal is that it is free from the revenge problem.
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| | Other links: st-andrews.ac.uk jstor.org | Scholar | At my library | More options ... The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the self-referential sentence “This sentence is false.”.
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| | Other links: utm.edu | Scholar | At my library | More options ... The solution John Buridan offers for the Paradox of the Liar has not been correctly placed within the framework of his philosophy of language. More precisely, there are two important points of the Buridanian philosophy of language that are crucial to the correct understanding of his solution to the Liar paradox that are either misrepresented or ignored in some important accounts of his theory. The first point is that the Aristotelian formula, ` propositio est vera quia qualitercumque significat in rebus significatis ita est ', once amended, is a correct way to talk about the truth of a sentence. The second one is that he has a double indexing theory of truth: a sentence is true in a time about a time, and such times should be distinguished in the account of the truth-conditions of sentences. These two claims are connected in an important way: the Aristotelian formula indicates the time about which a sentence is true. Some interpreters of the Buridanian solution to the paradox, following the lead of Herzberger, have missed these points and have been led to postulate truth-values gaps, or surrogates of truth-value gaps, when there is nothing of this sort in his theory. I argue against this tradition of interpretation of Buridan and propose an interpretation of his solution to the Liar.
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| | Other links: openurl.ingenta.com dx.doi.org | Scholar | At my library | More options ... Here is the liar paradox. We have a sentence, (L), which somehow says of itself that it is false. Suppose (L) is true. Then things are as (L) says they are. (For it would appear to be a mere platitude that if a sentence is true, then things are as the sentence says they are.) (L) says that (L) is false. So, (L) is false. Since the supposition that (L) is true leads to contradiction, we can assert that (L) is false. But since this is just what (L) says, (L) is then true. (For it would appear to be a mere platitude that if things are as a given sentence says they are, the sentence is true.) So (L) is true. So (L) is both true and false. Contradiction.
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| | Scholar | At my library | More options ... We describe the earliest occurrences of the Liar Paradox in the Arabic tradition. e early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that self-referential sentences, like the Liar, are not truth-apt, and defends this claim by appealing to a correspondence theory of truth. Translations of the texts are provided as an appendix.
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| | Scholar | At my library | More options ... This paper compares two proposed solutions to the liar paradox, both of which involve revisions to classical semantics. The first, that of truth value gaps, denies that all sentences are true or false. The second, that of truth value gluts, asserts that some sentences are true and false. A natural question about these proposals is, ?Do they offer equally good (or bad) solutions, or is one better than the other?? Parsons 1990 suggested an answer to this question, arguing that for every problem for one solution, there is a parallel problem for the other. Since then, several people have given arguments for and against the idea that the two face parallel problems. This paper advances the debate in two ways. First, it answers four attempts by Graham Priest to reject the parallel. In particular, it discusses alleged advantages for the gap solution with regard to the teleological account of truth, an extended liar paradox, Berry's paradox, and inexpressibility. Second, it discusses where, if anywhere, the parallel may be broken.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... “To this day, partiality approaches to the paradox have been dogged by the so-called ‘Strengthened Liar’. .... The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence* neither true nor false (or failing to express a proposition,. or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again.* We are back in paradox.” (Glanzberg 2002, p. 468, bold emphasis added.) Cf.: “We are back in our contradiction,”(Glanzberg 2001, p. 222). *The Liar sentence intended is evidently the sentence ‘the Liar sentence is not true’, and, the Liar sentence = ‘the Liar sentence is not true’. Cf.: “Consider a Liar sentence: ...let us take a sentence l which says l is not true. We can, informally, reason as..
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| | Scholar | More options ... One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth.
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| | Scholar | At my library | More options ... emantic pathologies of self-reference include the Liar (‘this sentence is false’), the Truth-Teller (‘this sentence is true’) and the Open Pair (‘the neighbouring sentence is false’ ‘the neighbouring sentence is false’). Although they seem like perfectly meaningful declarative sentences, truth value assignment to their uses seems either inconsistent (the Liar) or arbitrary (the Truth-Teller and the Open-Pair). These pathologies thus call for a resolution. I propose such a resolution in terms of relative-truth: the truth value of a pathological sentence use varies with the context of its assessment. It always has a determinate truth value, but this truth value is relative to the context of its assessment. I start by considering a fairly esoteric pathology: the Truth-Teller, that is, sentences which assert nothing but their own truth. I make the case that truth value of a given truth-teller use must in general depend on the context of its assessment, and that one can indeed change its truth value at will. I then show how the notion of assessment-sensitive truth can help us provide solutions to other semantic paradoxes such as the Liar and the Open Pair and that those solutions are immune to revenge problems. I conclude by situating my proposal among the main approaches to the semantic paradoxes, and by drawing a very broad moral about pathological self-reference and intentionality.
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| | Scholar | At my library | More options ... The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.
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| | Other links: tandfonline.com dx.doi.org | Scholar | At my library | More options ... Discussion of Patrick Greenough, Truthmaker Gaps and the No-No Paradox
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