Logical, Semantic and Cultural Paradoxes

The property common to three kinds of paradoxes (logical, semantic, and cultural) is the underlying presence of an exclusive disjunction: even when it is put to a check by the paradox, it is still invoked at the level of implicit discourse. Hence the argumentative strength of paradoxical propositions is derived. Logical paradoxes (insolubilia) always involve two contradictory, mutually exclusive, truths. One truth is always perceived to the detriment of the other, in accordance with a succession which is endlessly repetitive. A check is put on the principle of the excluded middle by the logical paradoxes, because self-reference leads to an endlessly repeating circle, out of which no resolution is conceivable. Logical paradoxes are to be compared with the `objective ambiguity' prevalent in oracles (Gallet, 1990). Semantic paradoxes are contextually-determined occurrences, whose resolution at the metalinguistic level is made possible by the discovery of a middle term. They express a wilful ambiguity, in which the interlocutor is invited to take an active part in the construction of sense, since what must be found is the unexpected sense thanks to which A and not-A can be asserted simultaneously. Cultural paradoxes play about doxa (`common sense') and openly challenge common opinion because of their character as inopinata (`unexpected'). My aim is to show that even cultural paradoxes hide sometimes a flaw of argumentation similar to logical or semantic paradox; they too imply an exclusive disjunction leading to the disappearance of the middle terms. Finally, basing myself on the theory of topoi (Anscombre and Ducrot, 1983), a tentative resolution of the cultural paradoxes will be suggested.     

Informative Aboutness

Pretheoretically, (B) ‘all believers are immortal’ is about all believers, but (1) B is not about any unbeliever. Similarly, (M) ‘all mortals are unbelievers’ is not about any immortal, but (2) M is about all mortals. But B and M are logically equivalent universal generalizations, so arguably they are about exactly the same objects; by (2), they are about those mortals who are unbelievers, contradicting (1). If one responds by giving up (1), is there still a sense in which B treats unbelievers differently from believers? I argue that there is. B is uninformative about unbelievers but informative about believers, in the following sense: for any object o, the information that B provides only about o—namely, ‘o is a believer only if o is immortal’—is entailed (and thus rendered redundant) by ‘o is an unbeliever’ but not by ‘o is a believer’.     

Dummett and Frege on sense and Selbständigkeit

As part of his attack on Frege’s ‘myth’ that senses reside in the third realm, Dummett alleges that Frege’s view that all objects are selbständig (‘self-subsistent’, ‘independent’) is an underlying mistake, since some objects depend upon others. Whatever the merits of Dummett’s other arguments against Frege’s conception of sense, this objection fails. First, Frege’s view that senses are third-realm entities is not traceable to his view that all objects are selbständig. Second, while Frege recognizes that there are objects that are dependent upon other objects, he does not take this to compromise the Selbständigkeit of any objects. Thus, Frege’s doctrine that objects are selbständig does not make the claim of absolute independence that Dummett appears to have taken it to make. Nevertheless, in order to make a good case against Frege based on the dependency of senses, Dummett need only establish his claim that senses depend upon expressions: appeal to an absolute conception of independence is unnecessary. However, Dummett’s arguments for the dependency of senses upon expressions are unsuccessful and they show that Dummett’s conception of what it is to be an expression also differs significantly from Frege’s.     

四卡问题解决中的匹配偏向再探

选取经典的四卡问题作为实验材料,深入探讨了“综合考虑证真证伪作用”的提示以及逻辑分析过程对被试解决四卡问题不能产生促进效应的原因。结果发现:(1)多数被试能对卡片P和-Q进行正确的逻辑推断,但是最后却仍然倾向于选择卡片Q而非-Q,这种错误并非是由于附加的认知任务使得被试的短时记忆容量超载所致。(2)元音偶数组与元音非偶数组的被试对四张卡片作出正确逻辑推断的人数百分比基本一致,但是后者选择P-Q的人数百分比却显著高于前者,这表明多数被试似乎并不依据逻辑分析的结果及其命题检验的规则来作出选择,而是采用匹配策略,错误地选择了Q卡片。     

Review Essay on the Roots of Evil

I consider two essays by Joel Feinberg: his treatment of the moral obligation to obey the law, and his exploration of the evils of the Holocaust.     

Developmental grey matter changes in superior parietal cortex accompany improved transitive reasoning

The neural basis of developmental changes in transitive reasoning in parietal regions was examined, using voxel-based morphometry. Young adolescents and adults performed a transitive reasoning task, subsequent to undergoing anatomical magnetic resonance imaging (MRI) brain scans. Behaviorally, adults reasoned more accurately than did the young adolescents. Neural results showed (i) less grey matter density in superior parietal cortex in the adults than in the young adolescents, possibly due to a developmental period of synaptic pruning; (ii) improved performance in the reasoning task was negatively correlated with grey matter density in superior parietal cortex in the adolescents, but not in the adult group; and (iii) the latter results were driven by the more difficult trials, requiring greater spatial manipulation. Taken together, the results support the idea that during development, regions in superior parietal cortex are fine-tuned, to support more robust spatial manipulation, resulting in greater accuracy and efficiency in transitive reasoning.     

Generalized Logical Consequence: Making Room for Induction in the Logic of Science

We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logical consequence are also presented.     

西方消费者研究概述

消费者研究是近年来西方心理学应用研究中一个非常活跃的领域。在近 40年的发展中 ,消费者研究的范围不断扩大 ,数量不断增多 ,质量也不断提高。本文考察了西方消费者研究的发展趋势 ,对比了主要的消费者研究阵营 ,并通过对消费者研究中三个亚领域———社会认知、BDT和后现代消费者研究之间的差异和共同之处的探讨 ,强调了各领域之间有很大的合作空间。     

Quine and Slater on Paraconsistency and Deviance

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant ^*c^* in a given logic: its operational meaning, given by the operational rules for ^*c^* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing ^*c^* which can be proved in the same calculus. Subsequently, we use the same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics ^*L^* and ^*L^* is possible whenever each constant in ^*L^* has the same operational meaning as its counterpart in ^*L^* although differences in global meaning arise in at least one case.     

Projective Geometry in Logical Space: Rethinking Tractarian Thoughts

Customary interpretations state that Tractarian thoughts are pictures, and, a fortiori, facts. I argue that important difficulties are unavoidable if we assume this standard view, and I propose a reading of the concept taking advantage of an analogy that Wittgenstein introduces, namely, the analogy between thoughts and projective geometry. I claim that thoughts should be understood neither as pictures nor as facts, but as acts of geometric projection in logical space. The interpretation I propose thus removes the root of the identified difficulties. Moreover, it allows important clarification concerning some central aspects of the Tractarian theory of representation, and it yields a unifying elucidation regarding Wittgenstein’s remarks on the solipsistic thesis.