A revision of the definition of lying as an untruth told with intent to deceive

The traditional and prevailing definition of lying is that lying is some variation or combination of: an untruth told with intent to deceive. I establish that this is the case, and that, as a result, contradictions and injustices arise. An alternative definition is proposed which is shown to avoid these difficulties. It is also shown that and how on the new definition the alleged Liar paradox is easily dissolved.     

受欺负与青少年外化问题关系的“健康环境悖论”：敌意性归因的中介作用

“健康环境悖论”是指在总体受欺负水平较低的环境中, 受欺负的个体会表现出更多适应问题。本研究以来自47个班级的1764名5年级到8年级学生为被试(男生956人, 平均年龄14.46岁), 考察了班级平均受欺负水平在个体受欺负经历与外化问题间的调节作用及敌意性归因的中介作用。结果发现：(1)受欺负与外化问题的关系存在“健康环境悖论”现象, 即班级平均受欺负水平能调节个体受欺负经历与外化问题的关系, 在班级平均受欺负水平较低的班级中受欺负经历与外化问题的关联更强; (2)班级平均受欺负水平对受欺负与外化问题的调节作用通过敌意性归因的中介作用实现。本研究证实了受欺负与外化问题的健康环境悖论现象, 并首次揭示了敌意性归因的中介作用机制。     

班级环境如何影响受欺负者的适应？健康环境悖论及其发生机制

“健康环境悖论”是指在受欺负水平相对较低的环境中,受欺负个体有更多的适应问题。通过梳理相关实证研究,本文从人际与认知两大方面分析健康环境悖论的发生机制。人际机制强调健康环境会影响同伴群体对于受欺负者的态度和受欺负者的友谊,这些不良的人际关系进一步加剧受欺负者的适应困难。认知机制认为健康环境会通过向上的社会比较和消极归因方式,影响受欺负者的适应问题。最后,我们讨论了中国文化背景下“健康环境悖论”的适用性问题、未来研究的发展方向和对于干预实践的建议。     

How representations of number and numeracy predict decision paradoxes: A fuzzy-trace theory approach

Higher numeracy has been associated with decision biases in some numerical judgment-and-decision problems. According to fuzzy-trace theory, understanding such paradoxes involves broadening the concept of numeracy to include processing the gist of numbers—their categorical and ordinal relations—in addition to objective (verbatim) knowledge about numbers. We assess multiple representations of gist, as well as numeracy, and use them to better understand and predict systematic paradoxes in judgment and decision-making. In two samples (Ns = 978 and 957), we assessed categorical (some vs. none) and ordinal gist representations of numbers (higher vs. lower, as in relative magnitude judgment, estimation, approximation, and simple ratio comparison), objective numeracy, and a nonverbal, nonnumeric measure of fluid intelligence in predicting: (a) decision preferences exhibiting the Allais paradox and (b) attractiveness ratings of bets with and without a small loss in which the loss bet is rated higher than the objectively superior no-loss bet. Categorical and ordinal gist tasks predicted unique variance in paradoxical decisions and judgments, beyond objective numeracy and intelligence. Whereas objective numeracy predicted choosing or rating according to literal numerical superiority, appreciating the categorical and ordinal gist of numbers was pivotal in predicting paradoxes. These results bring important paradoxes under the same explanatory umbrella, which assumes three types of representations of numbers—categorical gist, ordinal gist, and objective (verbatim)—that vary in their strength across individuals.     

On the Consistency of the Δ1 1-CA Fragment of Frege's Grundgesetze

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing ¹ ₁-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.     

蒯因和伽登佛斯对绿蓝悖论"解决"思路评析

关于绿蓝问题的讨论一直在持续着。逻辑操作路线更为“本质”的方法,即“自然类’他们的思路。蒯因和伽登佛斯寻求的是比纯粹的语言和和“概念空间”的解决方法,本文试评析     

Equivalents of Mingle and Positive Paradox

Relevant logic is a proper subset of classical logic. It does not include among its theorems any ofpositive paradox A (B A)mingle A (A A)linear order (A B) (B A)unrelated extremes (A ) (B B¯)This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.