| 书目名称 | Logic Without Gaps or Gluts | | 副标题 | How to Solve the Par | | 编辑 | Benjamin Alan Burgis | | 视频video | http://file.papertrans.cn/588/587945/587945.mp4 | | 概述 | Argues that the paradoxes give no reason to reject classical logic.The first full-length book to deal with this topic indepthly.Touches on the work of Graham Priest, Hartry Field and JC Beal. | | 丛书名称 | Synthese Library | | 图书封面 |  | | 描述 | .This book offers a defense against non-classical approaches to the paradoxes. The author argues that, despite appearances, the paradoxes give no reason at all to reject classical logic. In fact, he believes classical solutions fare better than non-classical ones with respect to key tests like Curry’s Paradox, a Liar-like paradox that dialetheists are forced to solve in a way totally disjoint from their solution to the Liar. ..Graham Priest’s .In Contradiction .was the first major work that advocated the use of non-classical approaches. Since then, these views have moved into the philosophical mainstream. Much of this movement is fueled by a widespread sense that these logically heterodox solutions get to the real nub of the issue. They lack the ad hoc feel of many other solutions to the paradoxes. The author believes that it‘s long past time for a response to these attacks against classical orthodoxy. He presents a non-logically-revisionary solution to the paradoxes...This title offers a literal way of cashing out the disquotation metaphor. While the details of the view are novel, the idea has a pre-history in the relevant literature. The author examines objections in detail. He r | | 出版日期 | Book 2022 | | 关键词 | Paraconsistent logic; Dialetheism Excluded Middle; Disquotationalism; Graham Priest; Hartry Field; JC Bea | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-94624-1 | | isbn_softcover | 978-3-030-94626-5 | | isbn_ebook | 978-3-030-94624-1Series ISSN 0166-6991 Series E-ISSN 2542-8292 | | issn_series | 0166-6991 | | copyright | Springer Nature Switzerland AG 2022 |
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Front Matter |
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Abstract
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,Logic and the Liar Paradox, |
Benjamin Alan Burgis |
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Abstract
The Liar and related paradoxes create a prima facie conflict between two equally important principles of classical logic—the Law of the Excluded Middle (LEM) and the Law of Non-Contradiction (LNC). Dialetheists such as Graham Priest and JC Beall solve the paradoxes by accepting the negations of some instances of the LNC and rejecting classical logic in favor of a “paraconsistent” logical framework in which contradictions do not entail every conclusion. Hartry Field advocates the mirror image of this solution, rejecting certain instances of the LEM and thus rejecting classical logic in favor of a “paracomplete” framework in which not every LEM instance is entailed by every premise. Some paradox-solvers, eager to avoid either of these amputations of classical logic, reject paradoxical instances of the T-Schema. This is an easy way out, but the search for an adequate solution is best conducted elsewhere. The rest of the book will be spent on the project of resisting the paraconsistent and paracomplete solutions to the paradoxes and finally proposing a positive solution that retains classical logic without sacrificing the T-Schema.
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,Graham Priest and Dialetheism, |
Benjamin Alan Burgis |
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Abstract
Most dialetheists and most non-dialetheists agree that the argument from the semantic paradoxes to the existence of true contradictions is the strongest argument for dialetheism. Indeed, apart from Graham Priest, most dialetheists regard contradicts about the alethetic status of paradoxical sentences as the . true contradictions. Priest, however, has made independent arguments for true contradictions in several other domains. He postulates true mathematical contradictions based on Russell’s Paradox and other antinomies of naïve set theory, some of which seem to be closely related to the semantic paradoxes, as well as true contradictions arising from inconsistent laws and norms, true contradictions at the limits of conceivability, and even true contradictions in the physical world derived from what Priest calls “the paradoxes of motion and change.” In principle, Field could offer paracomplete versions of all of these arguments, but he has declined to do so. The “priestly” arguments for dialetheism are explored as well as reactions to them by Priest and Beall.
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,How to Solve Priest’s Paradoxes Without Sacrificing Classical Logic, |
Benjamin Alan Burgis |
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Abstract
Objections are made to (almost) all of the “priestly” arguments for dialetheism discussed in Chap. .. For example, we can accept normative . either in the law or in other domains without having any particularly compelling reason to postulate the existence of true normative contradictions. An argument is made against realism about naïve set theory, and hence against belief in the truth of contradictions that arise from naïve set theory. It is granted that we might have a good reason to be realists about naïve set theory if we had sufficiently compelling non-set-theoretic reasons to accept dialetheism, but it is argued that in the absence of such reasons the antinomies of naïve set theory give us no independent reason to accept the existence of true contradictions. The “paradoxes of motion and change” are undermined by means of a defense of Bertrand Russell’s theory of change against Priest’s critique. Bishop Berkeley’s argument is shown to rest on a fundamental equivocation—one that also arises in a classic argument by Max Black. Finally, it is granted that the version of Russell’s Paradox that concerns not sets but predicates or properties has not been solves, and that any adequate
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,Dialetheism and the Laws of Logic, |
Benjamin Alan Burgis |
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Abstract
Graham Priest accepts the traditional definition of validity as truth-preservation, but conceptual headaches arise when we try to dialetheically make sense of truth-preservation. Does truth-preservation mean that true premises always lead to true conclusions, or that they never lead to false ones? Problems appear either way. Alan Weir points out that we normally expect valid inferences to preserve falsity in the direction going from conclusions to premises as well as preserving truth in the direction going from premises to conclusions, but it is deeply unclear that dialetheism can satisfy this requirement. Contraposition and . might be invalid if dialetheism is true. When we put this together with more obvious losses such as . and ., it begins to appear that the dialetheist cannot make sense of massive chunks of ordinary reasoning. Thus, “classical recapture,” whereby it is shown that it would still be rational to use the full resources of classical logic to reason about every domain if dialetheism was true, is crucial to making dialetheism plausible. Unfortunately, such recapture is far more difficult than it might appear. An initially promising attempt embodied in Priest’s “Princ
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,Dialetheism, Rejection, and Curry’s Paradox, |
Benjamin Alan Burgis |
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Abstract
The dialetheist proposes to block the inference from paradox to triviality not by blocking the inference from paradox to contradiction but by blocking the inference from contradiction to triviality. This strategy is undermined by Curry’s Paradox, in which the inference goes from paradox to triviality without stopping at the waystation of contradiction. Priest’s attempted solution is critiqued for several reasons, including its failure to honor Priest’s own “Principle of Uniform Solution,” according to which paradoxes of the same type should be solved in the same way. Beall’s solution to Curry fares better on that score, but it turns out that it relies on Principle R, and it has already been shown that this principle cannot be made sense of on dialetheic assumptions. A much larger problem lurks in all of this for dialetheist (and paracomplete) attempts to use rejection-talk to do work that cannot be done by negation once classical orthodoxy is abandoned. This strategy is undermined by the failure of Principle R as well as further problems pointed out from within the dialetheic camp by Francesco Berto.
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,Dialetheism, Rejection, and Probability Theory, |
Benjamin Alan Burgis |
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Abstract
If Principle R and related attempts to substitute rejection-talk for negation-talk fail, what remaining options does the dialetheist have at her disposal? Priest has suggested that, since the statistical frequency of true contradictions is quite low, classical laws that are not deductively valid if dialetheism is true nevertheless have probabilistic force. In Priest’s terminology, such rules may, while being invalid in the strict sense, still be “quasi-valid” and thus appropriate for use in most contexts. When this strategy is held up to the light, significant problems emerge. First, if true contradictions exist in all the domains in which Priest says they exist, there is no particularly good reason to think their overall statistical frequency is very low. Priest has argued that the “observable world” would still be contradiction-free, but his arguments are weak. The probabilistic strategy appears to be as dubious as the strategy premised on emphasizing rejection. Other strategies, some proposed by Priest and others proposed by other dialetheists, which rely on non-monotonicity, logical pluralism, local validity, or a kind of super-negation postulated by Francesco Berto, are simila
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,Hartry Field and Paracompleteness, |
Benjamin Alan Burgis |
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Abstract
The paracomplete solution to the semantic paradoxes championed by Hartry Field might seem to be more promising than its paraconsistent competitor. Embracing some logical contradictions is more initially implausible than rejecting both disjuncts of some instances of the LEM. On closer investigation, however, this intuitive disadvantage disappears. The LEM turns out to be as important to our reasoning practices as the LNC. The importance is simply less obvious because implicit appeals to the LEM tend to have in the background of arguments rather than at flashy and obvious points such as the discovery of a contradiction in an opponent’s views. Moreover, while incompleteness is normally far less of a strike against a theory than inconsistency, . is a very different beast than mere incompleteness. In fact, to even make sense of what it means to reject propositions without accepting their negations we have to abandon the probability calculus that is essential to our understanding of subjects ranging from weather prediction to the mysteries of quantum mechanics.
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,How to Solve the Liar Paradox Without Sacrificing Classical Logic, |
Benjamin Alan Burgis |
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Abstract
After seven chapters of seeing how important proposed solutions to the paradoxes can go wrong, several important things learned along the way are pulled together to propose a positive alternative (rooted in a non-standard way of parsing disquotationalism about truth called Content Inheritance Disquotationalism) that retains the full resources of both classical logic and a fully transparent truth predicate. A wide range of possible objections are considered and resolved. The CID-based solution is compared to its paracomplete and paraconsistent rivals on a crucial standard emphasized by Graham Priest—the Principle of Uniform Solution. Finally, several loose ends are tied up through a survey of objections to classical logic rooted in quantum weirdness, borderline applications of vague terms, and Edwin Mares’s claim that predicates can be not only “underdefined” (leading to truth-value gaps) but “overdefined” (leading to truth-value gluts). Some of these, particularly concerns about vagueness, are difficult philosophical problems not resolved by anything said here, but none add up to a good reason to abandon classical logic.
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Back Matter |
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Abstract
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