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.     

Symmetric Propositions and Logical Quantifiers

Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.     

临床方法依然是神经内科医师最重要的诊断法宝

通过7例疑难、危重患者的诊治过程说明临床方法的重要性,在神经科疾病研究中尤为突出。忽视细致的病史采集和体查,常导致了诊疗的失误;面对种目繁多的检查,更需要以临床方法选择之;临床逻辑思维能力非常重要,正确的临床思维出新知。在实验室检查方法越来越多的今天,临床方法是神经内科医师最重要、方便、快捷、有效的诊断法宝,具有不可替代性。     

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.     

Why Freud and Jung Can’t Speak: A Neurological Proposal

This article provides a modern neurological explanation for the theoretical differences in psychoanalytic concepts and techniques between Freud and Jung. Specifically, the article contrasts their analytic skills as arising in the left and right brain, respectively. Modern neurological techniques reveal unique brain functions that explain many of the visionary and so-called mystic phenomena discussed by Jung. Many of his psychoanalytic concepts can be traced to right brain function. Modern research and philosophic analyses also provide light on Freud’s research method and its limitations.Barbara Stevens Barnum, RN, PhD, FAAN, former editor of Nursing Leadership Forum and Nursing & Health Care, is presently a writer/consultant. Before retiring, her positions at Columbia University included holding the directorship, Division of Health Services, Sciences and Education at Teachers College, where she also held the Stewart Chair in the Department of Nursing Education. Dr. Barnum has written in areas of nursing management, theory, education, and aspects of spirtuality/holistic nursing. Her books include: Nursing theory: Analysis, application, evaluation, Spirituality in nursing: From traditional to New Age, and The New Healers: Minds and Hands in Complementary Medicine.     

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     

四卡问题解决中的内容与逻辑分析效应

选取条件概率(P(Q|P))由低到高的四个命题作为四卡问题中的检验规则,探讨了大学生被试对四张卡片的逻辑证明作用的推断能力及其对解决四卡问题的影响。结果发现:(1)不同条件概率的命题之间正确选择P-Q的人数百分比不存在显著差异,命题的条件概率因素对四卡问题的正确解决没有影响。(2)逻辑分析过程对四卡问题的正确解决产生了一定的抑制作用,这可能是因为被试不能从整体上思考四张卡片在命题检验中的逻辑作用的缘故。(3)一些被试即使在逻辑分析过程中表现出知道-Q卡片的证伪作用,仍然倾向于选择卡片Q而非-Q,这一现象再次证实了人类思维的非形式逻辑的一面。     

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.