Abstraction in Algorithmic Logic

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens.     

A Note on Priest's Finite Inconsistent Arithmetics

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.     

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen     

Projective expected utility

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.     

Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt     

How to eliminate self-reference: a précis

We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h ₀(F), h ₁(F), ..., stated in a quantificational language L ^*. Under certain conditions, we show that none of the translations is self-referential, but that any one of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language.     

The knowledge content of statistical data

An information-theoretic framework is used to analyze the knowledge content in multivariate cross classified data. Several related measures based directly on the information concept are proposed: the knowledge content (S) of a cross classification, its terseness (Zeta), and the separability (Gamma _X ) of one variable, given all others. Exemplary applications are presented which illustrate the solutions obtained where classical analysis is unsatisfactory, such as optimal grouping, the analysis of very skew tables, or the interpretation of well-known paradoxes. Further, the separability suggests a solution for the classic problem of inductive inference which is independent of sample size.     

前瞻记忆年老化研究的自然情境和实验室情境比较

年龄—前瞻记忆矛盾现象在实验室情境和自然情境研究中普遍存在。当任务设置为日常情境时, 前瞻记忆不受年龄影响或随年龄增长而促进, 前瞻记忆成绩可能受人格、生活方式、任务材料、提示等因素的影响; 当任务是实验室情境设置时, 与年轻被试相比, 老年被试前瞻记忆成绩一般都较差, 前瞻记忆成绩可能受回溯记忆负载、线索类型和策略控制加工的需求等因素的影响。年龄-前瞻记忆矛盾现象可能来自于环境与意向的社会性特征、认知资源分配策略等方面的原因。最后, 从被试控制、任务材料的设置、动机因素的探索等方面对今后的研究提出建议和展望。     

艾滋病非刑罪化视阈下我国防控策略的伦理思考

审视我国现有法规对艾滋病防控的影响,剖析其在维护个体权益与促进公共卫生平衡中的挑战,以实证案例和艾滋病悖论为切入点,分析艾滋病刑事定罪涉及的伦理问题,提出科学、伦理和法律方面的应对策略。强调将艾滋病病毒传播作为一个公共卫生问题加以解决是最为有效的手段。在法规制定和司法实践中,应纳入科学事实和医学证据,避免过于宽泛的刑事定罪。在决策过程中,应全面考量生命伦理学原则,最大限度避免可能的交叉歧视、多重污名以及暴力伤害。此外,还应重视公共卫生视角下的补充或替代方案,确保干预措施积极有效。