Field's Paradox and Its Medieval Solution

Hartry Field's revised logic for the theory of truth in his new book, Saving Truth from Paradox, seeking to preserve Tarski's T-scheme, does not admit a full theory of negation. In response, Crispin Wright proposed that the negation of a proposition is the proposition saying that some proposition inconsistent with the first is true. For this to work, we have to show that this proposition is entailed by any proposition incompatible with the first, that is, that it is the weakest proposition incompatible with the proposition whose negation it should be. To show that his proposal gave a full intuitionist theory of negation, Wright appealed to two principles, about incompatibility and entailment, and using them Field formulated a paradox of validity (or more precisely, of inconsistency).

The medieval mathematician, theologian and logician, Thomas Bradwardine, writing in the fourteenth century, proposed a solution to the paradoxes of truth which does not require any revision of logic. The key principle behind Bradwardine's solution is a pluralist doctrine of meaning, or signification, that propositions can mean more than they explicitly say. In particular, he proposed that signification is closed under entailment. In light of this, Bradwardine revised the truth-rules, in particular, refining the T-scheme, so that a proposition is true only if everything that it signifies obtains. Thereby, he was able to show that any proposition which signifies that it itself is false, also signifies that it is true, and consequently is false and not true. I show that Bradwardine's solution is also able to deal with Field's paradox and others of a similar nature. Hence Field's logical revisions are unnecessary to save truth from paradox.     

The Mere Addition Paradox,Parity and Vagueness*

Derek Parfit’s mere addition paradox has generated a large literature. This paper articulates one response to this paradox—which Parfit himself suggested—in terms of a formal account of the relation of parity. I term this response the ‘parity view’. It is consistent with transitivity of ‘at least as good as’, but implies incompleteness of this relation. The parity view is compatible with critical‐band utilitarianism if this is adjusted to allow for vagueness. John Broome argues against accounts which involve incompleteness. He thinks they are based on an intuition of ‘neutrality’, which is most naturally understood in terms of equality. There is no rationale, on Broome’s view, for seeing it as ‘incommensurateness’ which leads to incompleteness. Parity provides one. Broome’s worries that ‘incommensurateness’ makes neutrality implausibly ‘greedy’, and that ‘incommensurateness’ and vagueness are incompatible do not constitute a knock‐down case against the parity view. Similar worries arise for his preferred vagueness view.     

A New Solution to Moore's Paradox

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) buys us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all.     

A Solution to the Paradox of Analysis

This essay attempts to solve the so-called paradox of analysis: if one is to have any questions about x , one must know x ; but if one knows x , one has no questions about x . The obvious solution is this: one can inquire into x if one knows some, but not all, of x 's parts. But this solution is erroneous. Let x ' be those parts of x with which one is acquainted, and let S be the percipient in question. As with x , either S knows x ', in which case he has no questions about it; or S does not know x ', in which case he has no questions about it.
My solution is this. Perception and cognition give us, not the thing-in-itself, but a certain analogue of the thing-in-itself. To inquire into x , it is necessary to know not x , but only some analogue of x ; and to learn more about x is to become acquainted with increasingly precise analogues of x .     

A Solution to the Cable Guy Paradox

The Cable Guy will definitely come between 8 a.m. and 4 p.m., and I can bet on one of two possibilities: that he will arrive between 8 and 12, or between 12 and 4. Since I have no more information, it seems (eminently) plausible to suppose the two bets are equally attractive. Yet Hajek has presented a tantalising argument that purports to show that the later interval is, initial appearances to the contrary, more choice worthy. In this paper, I rebut the argument.     

说谎者悖论及其相关悖论的一种解决

依本文之见,说谎者悖论以及某些与之相关的悖论之被导出源于对某些不合理的前提的接受;而这些前提之被接受又源于对＂是真的＂与＂是假的＂这两个词的关键语义特性缺乏认识。本文为决定这些语义特性的基础提供了说明;这一基础包含两个论点,第一,每一语句均有其含义;第二,每一语句陈说的字面内容是一个命题态度的内容,因而具有某种一般形式。借助于这一基础,本文为这两个词构造了一个不同于传统意义上的塔尔斯基式真理理论的意义理论以说明这些特性,并借助于该理论论证说谎者悖论及其某些相关悖论的导出没有根据。     

Buridan's Solution to the Liar Paradox

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 (2), 189–218] or else (2) it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 (Chapter 5); Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 (242), 58–78]. Against (1), I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity.     

The Solution to the Surprise Exam Paradox

The Surprise Exam Paradox continues to perplex and torment despite the many solutions that have been offered. This paper proposes to end the intrigue once and for all by refuting one of the central pillars of the Surprise Exam Paradox, the “No Friday Argument,” which concludes that an exam given on the last day of the testing period cannot be a surprise. This refutation consists of three arguments, all of which are borrowed from the literature: the “Unprojectible Announcement Argument,” the “Wright & Sudbury Argument,” and the “Epistemic Blindspot Argument.” The reason that the Surprise Exam Paradox has persisted this long is not because any of these arguments is problematic. On the contrary, each of them is correct. The reason that it has persisted so long is because each argument is only part of the solution. The correct solution requires all three of them to be combined together. Once they are, we may see exactly why the No Friday Argument fails and therefore why we have a solution to the Surprise Exam Paradox that should stick.     

说谎者悖论的一种解决

本文意在论证,说谎者悖论的导出源于两个关键契机:第一,塔尔斯基关于T-约定的表述并不确切,该不确切性的根源在于,塔尔斯基未能注意到经验陈述语句陈说的一个根本属性,根据这一属性,仅当一个经验陈述语句的陈说满足一个适当条件时,适用于该陈说的T-约定例证才能成立.第二,说谎者悖论的导出者未能认识到,涉及自我指称的经验陈述语句陈说不满足第一点中提到的条件,因而适用于该陈说的T-约定例证不能成立.     

道德悖论界说及其意义

中国改革开放过程中出现的“道德失范”及由此引起的一些社会不和谐现象,多与道德悖论有关,需要运用道德悖论的方法加以分析和认识。近几年,一些研究者陆续涉足道德悖论问题,但其研究的视阈多限于社会思想史和道德教育,很少论及现实社会普遍存在的道德悖论,加上研究者对道德悖论含义的界说又见仁见智,所以不仅没有从认识上把道德悖论从现实存在的诸多道德矛盾中剥离出来,揭示其真实性状,帮助人们探索走出“奇异的循环”的路径,反而造成一些新的思想混乱。因此,从学理上说明道德悖论与道德现象世界中其他矛盾的边界,具有重要的理论和现实意义…     

A Deflationist Approach to Indeterminacy and Vagueness

Deflationists cannot make sense ofthe notion of referential indeterminacybecause they deny the existence of substantivereference. One way for them to make sense ofthe objective existence of linguisticindeterminacy is by embracing theworldly (or objectual) view ofindeterminacy, the view that indeterminacyexists not in reference relations but in the(non-linguistic) world itself. On this view,the entire world is divided into precisified worlds, just as it is dividedinto temporal slices and (arguably) alethicpossible worlds. Supervaluationism proves tobe neutral with respect to the debate betweenthe worldly view and the referential view ofindeterminacy.     

视觉的伦理关涉和悖论

视觉的悖论是由"看"与"被看"、权力和权利、形式设计与意义关怀等相反相成的关涉组成的混合体."看"与"被看"既反映出一种主客体之间的张力关系,也逐渐表现出其权力变化的趋向.通过权力和权利作为视觉伦理关系的两极,可以清晰地看到隐藏在视觉背后的意识形态性.视觉的形式设计与意义关怀的失衡必然带来视觉互动过程中的伦理偏差,过度强调视觉的形式设计必然会影响到视觉本身的传达效果,消解视觉的意义关怀所在,也会误导人们的价值观念.在视觉的伦理关涉和悖论后面,我们更需要寻找到实质为人与自然、人与自身、人与人、人与社会之间关系的平衡.     

论Priest对Sorites悖论的模糊解悖方案

G.Priest在1998-2003年之间有一个对sorites悖论的模糊解悖方案,根据该解悖方案,对含混语言的最佳语意论应该是某种的模糊语意论。在这样的模糊语意论中,边界语句是既真且假的语句,而sorites悖论中所涉及的离断律和等同传递律则不是有效的推论步骤。Priest并试图利用这样的语意论去说明：为什么sorites悖论看起来像是有效的论证,以及为什么切割点的存在尽管必然却违反直觉。我在本文中论证：Priest的模糊解悖方案是一个完全失败的方案,因此最好被放弃。我论证,Priest的模糊解悖方案至少有以下几个主要的问题：它与Priest的真理理论以及双面真理论不兼容、它对于sorites悖论的诊断有特设的嫌疑、它对于sorites悖论为何看起来有效的说明不具有可信度、它对于切割点存在何以违反直觉的说明也不具有可信度、它有将高阶含混性崩塌为一阶含混性之虞。