A note on russell's paradox in locally cartesian closed categories

Working in the fragment of Martin-Löfs extensional type theory [12] which has products (but not sums) of dependent types, we consider two additional assumptions: firstly, that there are (strong) equality types; and secondly, that there is a type which is universal in the sense that terms of that type name all types, up to isomorphism. For such a type theory, we give a version of Russell's paradox showing that each type possesses a closed term and (hence) that all terms of each type are provably equal. We consider the kind of category theoretic structure which corresponds to this kind of type theory and obtain a categorical version of the paradox. A special case of this result is the degeneracy of a locally cartesian closed category with a morphism which is generic in the sense that every other morphism in the category can be obtained from it via pullback.The financial support of the Royal Society in London is gratefully acknowledged.     

λ-Normal forms in an intensional logic for English

Montague [7] translates English into a tensed intensional logic, an extension of the typed -calculus. We prove that each translation reduces to a formula without -applications, unique to within change of bound variable. The proof has two main steps. We first prove that translations of English phrases have the special property that arguments to functions are modally closed. We then show that formulas in which arguments are modally closed have a unique fully reduced -normal form. As a corollary, translations of English phrases are contained in a simply defined proper subclass of the formulas of the intensional logic.This research is supported in part by National Science Foundation Grant BNS 76-23840.     

Alternate methods and software for calculating interobserver agreement for continuous observation data

Portable electronic data collection devices permit investigators to collect large amounts of observational data in a form ready for computer analysis. These devices are particularly efficient for gathering continuous data on multiple behavior categories. We expect that the increasing availability of these devices will lead to greater use of continuous data collection methods in observational research. This paper addresses the difficulties encountered when calculating traditional interobserver agreement statistics for continuous, multiple-code scoring. Two alternative strategies are described that yield interobserver agreement values based on the exact time of behavior code entries by the primary and secondary observers.Work on this paper was supported in part by NICHD Grants P01HD15051 and R01HD17650 and Office of Special Education and Rehabilitation Services Grant G008302980.     

Manufacturing a cartesian closed category with exactly two objects out of a C-monoid

A construction is described of a cartesian closed category A with exactly two elements out of a C-monoid such that can be recovered from A without reference to the construction.The first author was partially supported by the Dutch government through the SPIN project PRISMA; the second author was partially supported by the EEC through Esprit project 415.     

Orthographic neighborhood size effect in Chinese character naming: orthographic and phonological activations

The present study examined the effects of orthographic neighborhood (N) size on the cognitive processes underlying Chinese character reading. Previous research has shown increasing N size facilitates word naming and recognition performance in alphabetic languages. Experiment 1 revealed that a large N size was associated with a general inhibition of processes underlying character reading, in contrast to previous findings with alphabetic languages. This inhibitory effect was influenced by regularity and consistency. Experiment 2 sought to assess the effects of higher-frequency neighbors on character naming performance. The results revealed that higher-frequency neighbors with different pronunciation to the target interfered with the phonological retrieval of targets. We propose that this type of interference may have caused the N size effect observed in Experiment 1. The results of Experiment 3 revealed that a large N size facilitated target naming in the absence of higher-frequency neighbors. The current results shed light on the processes underlying character naming, and we propose possible cognitive mechanisms of the N size effect on Chinese character naming.     

Monoidal categories with natural numbers object

The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness of the concept.This work was partially carried out while both authors were guests of McGill University and while the second author was a guest of Dalhousie University. Both authors acknowledge support from the Natural Sciences and Engineering Research Council of Canada and the Québec Department of Education.     

Frege on Syntax,Ontology, and Truth's Pride of Place

Frege's strict alignment between his syntactic and ontological categories is not, as is commonly assumed, some kind of a philosophical thesis. There is no thesis that proper names refer only to objects, say, or that what refers to an object is a proper name. Rather, the alignment of categories is internal to Frege's conception of what syntax and ontology are. To understand this, we need to recognise the pride of place Frege assigns within his theorising to the notion of truth. For both language and the world, the Fregean categories are logical categories, categories, that is, of truth. The elaboration of this point makes clear the incoherence of supposing that they might not align.     

Hegel's notion of Aufheben

The paper is an attempt to make sense of Hegel's notion of aufheben. The double meaning of aufheben and its alleged ‘rise above the mere “either‐or”; of understanding’ have been taken, by some, to constitute a criticism of the logic of either‐or. It is argued, on the contrary, that Hegel's notion of aufheben, explicated in its primary and philosophical context, turns out to be a substantiation of that logic. The intelligibility of the formula of either‐or depends, for example, on the categories of Being and Not‐Being. But if these categories are regarded as particular finite determinations themselves subject to the formula of either‐or, then the formula, far from being intelligible, ‘falls apart’. Hegel is arguing, in other words, that if we are to substantiate the logic of either‐or, we must, at the same time, ‘rise above’ that logic. The role of aufheben is then considered in the special sciences. Here it is argued that we must distinguish between empirical transitions, governed by the finite determinations of things, and logical or dialectical transitions, governed by considerations of the intelligibility of the notions involved. Applying the notion of aufheben to the former transitions suggests wrongly that empirical transitions have an objective or philosophic necessity. Finally, the place of ‘immanent transformation’ in the context of aufheben is examined. It is concluded that if there is to be a transformation, then a distinction must be drawn between thought and its content, but then the transformation cannot be regarded as immanent.     

Wajsberg algebras and post algebras

We give a presentation of Post algebras of ordern+1 (n1) asn+1 bounded Wajsberg algebras with an additional constant, and we show that a Wajsberg algebra admits a P-algebra reduct if and only if it isn+1 bounded.This autor is partially supported by Grant PB90-0465-C02-01 of D.G.I.C.Y.T. of SpainPresented byJan Zygmunt     

Modal logics of domains on the real plane

This paper concerns modal logics appearing from the temporal ordering of domains in two-dimensional Minkowski spacetime. As R. Goldblatt has proved recently, the logic of the whole plane isS4.2. We consider closed or open convex polygons and closed or open domains bounded by simple differentiable curves; this leads to the logics:S4,S4.1,S4.2 orS4.1.2.     

Perception and the Categories: A Conceptualist Reading of Kant's Critique of Pure Reason

Abstract: Philosophers interested in Kant's relevance to contemporary debates over the nature of mental content—notably Robert Hanna and Lucy Allais—have argued that Kant ought to be credited with being the original proponent of the existence of ‘nonconceptual content’. However, I think the ‘nonconceptualist’ interpretations that Hanna and Allais give do not show that Kant allowed for nonconceptual content as they construe it. I argue, on the basis of an analysis of certain sections of the A and B editions of the Transcendental Deduction, for a ‘conceptualist’ reading of Kant's Critique of Pure Reason. My contention is that since Kant's notion of empirical intuition makes essential reference to the categories, it must be true for him that no empirical intuition can be given in sensibility independently of the understanding and its categories.     

The Logic of Knowledge Based Obligation

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. Earlier versions of this paper were presented at the conferences SEP-2004, and DALT-2004.     

The Pre-reflective Situational Self

It is often held that to have a conscious experience presupposes having some form of implicit self-awareness. The most dominant phenomenological view usually claims that we essentially perceive experiences as our own. This is the so called “mineness” character, or dimension of experience. According to  this view, mineness is not only essential to conscious experience, it also grounds the idea that pre-reflective self-awareness constitutes a minimal self. In this paper, we show that there are reasons to doubt this constituting role of mineness. We argue that there are alternative possibilities and that the necessity for an adequate theory of the self within psychopathology gives us good reasons to believe that we need a thicker notion of the pre-reflective self. To this end, we develop such a notion: the Pre-Reflective Situational Self. To do so, we will first show how alternative conceptions of pre-reflective self-awareness point to philosophical problems with the standard phenomenological view. We claim that this is mainly due to fact that within the phenomenological account the mineness aspect is implicitly playing several roles. Consequently, we argue that a thin interpretation of pre-reflective self-awareness—based on a thin notion of mineness—cannot do its needed job within, at least within psychopathology. This leads us to believe that a thicker conception of pre-reflective self is needed. We, therefore, develop the notion of the pre-reflective situational self by analyzing the dynamical nature of the relation between self-awareness and the world, specifically through our interactive inhabitation of the social world.

     

Kuhnianism and Neo-Kantianism: On Friedman’s Account of Scientific Change

Friedman’s perspective on scientific change is a sophisticated attempt to combine Kantian transcendental philosophy and the Kuhnian historiographical model. In this article, I will argue that Friedman’s account, despite its virtues, fails to achieve the philosophical goals that it self-consciously sets, namely to unproblematically combine the revolutionary perspective of scientific development and the neo-Kantian philosophical framework. As I attempt to show, the impossibility of putting together these two aspects stems from the incompatibility between (a) Friedman’s neo-Kantian conception of the role of philosophy and the role of the notion of incommensurability, and (b) the framework of transcendental idealism and the radical character of scientific revolutions. Hence, I suggest that pace Friedman and pace Kuhn’s own self-understanding, the Kuhnian theory of scientific revolutions cannot be seen as ‘Kantianism with moveable categories’ and consequently we should either abandon the notion of radical scientific revolution or place the Kuhnian account into another, non-Kantian philosophical framework.     

Differences between Chinese morphosyllabic and German alphabetic readers in the Stroop interference effect

The goal of our study was to localize the source of the stronger Stroop interference effect found in morphosyllabic readers as compared with alphabetic readers. Twenty-three Chinese and 24 German undergraduate students were tested in a Stroop paradigm with the following stimuli: color patches, colorneutral words (e.g.,friend printed in yellow), incongruent color-associated words (e.g.,blood printed in blue), and incongruent color words (e.g.,yellow printed in blue). Results revealed no differences in German and Chinese students’ response times to color patches. Chinese participants, however, showed longer color naming latencies for neutral words as well as for color words and color-related words. No differences between German and Chinese participants were found when print color latencies for neutral words were subtracted from print color latencies for color words and color-related words. This result does not support theories which suggest that for morphosyllabic readers there is a direct route from orthography to the semantics of a word. We rather argue, with reference to dual route models of reading, that access from print to phonology is faster for morphosyllabic than for alphabetic readers, and therefore interference caused by conflicting phonologies of color name and written word will be stronger in Chinese readers than in German readers.     

Is Sāṁkhya a Form of Idealism? An Exploration into Classical Sāṁkhya

Introduction

I have aims to shed light on two points in this paper. The first is to illumine that Sāṁkhya realist conception is based on false assumptions, and second is to shed light on the idealistic leanings of the system.

Text and Methods

I argue that in the light of textual evidences as well as phenomenological interpretation, Sāṁkhya metaphysics can be viewed as a form of idealism. I begin by proposing that the established realistic interpretation is based on an assumption that prakṛti and its evolutes are material and cosmic. In fact, prakṛti and its evolutes are mental categories, and the ontological dualism of puruṣa and prakṛti enunciated in the Sāṁkhya system is nothing but a form of idealism. The prakṛti and its evolutes are the principles/categories of cognition or experience. The conception that evolution is a process in prakṛti that takes place in the presence of puruṣa can also be conceived after the manner of form idealism. In fact, even the conception of puruṣa being simple and pure consciousness, together with its notion of liberation as aloneness of puruṣa and its separation from prakṛti and its activities (kaivalya), tends to advocate a form of idealism.

Conclusion

Thus, notion of evolution and liberation becomes the apparatus to interpret the Sāṁkhya as idealism.

     

Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.     

On the Idea of Freedom and Its Rejection in Chinese Thought and Institutions

In this paper I undertake a historical investigation to show that one of the most important cognitive reasons of being afraid of the notion of freedom in the mainstream of Chinese society and Chinese people since the Qin and Han dynasties is: people mistakenly relate freedom with indulgence. The essential feature of the culture of courtesy and humanization is to attach importance to the function and value of social order. The need for order crushes the appeal to open-minded and diverse lives. This ‘closed view’ of ideology still deeply constrains Chinese thinking today for politicians in particular.     

Further lesion evidence for the neural basis of conceptual knowledge for persons and other concrete entities

The neural underpinnings of conceptual knowledge have been studied intensively, but many unanswered questions remain. In a previous study examining recognition of persons, animals, and tools in 116 participants with unilateral brain lesions, we found no instance of a patient who manifested defective recognition in all three categories. We reasoned that the spatial distribution of the lesion loci critical for the appearance of recognition defects for these different categories explained why this ‘three‐way’ defect could not be found in patients with unilateral lesions, and we proposed that only a suitable bilateral lesion would be likely to produce such a combined defect. In the study reported here, we tested this hypothesis by investigating recognition performances in 55 participants with bilateral cortical lesions. In support of the hypothesis, nine patients, all of whose lesions included bilateral occipitotemporal and/or temporal cortices, had a three‐way recognition impairment (persons, M=18.3%; animals, M=35.7%; tools, M=71.3%; all scores >2 SDs below normal). As expected, bilateral lesions to other neural sectors, for example prefrontal cortices, did not lead to recognition impairments. These findings provide further support for the notion that retrieval of knowledge for concrete entities from different conceptual categories depends on partially segregated neural systems, located in different sectors of occipitotemporal and temporal regions in right and left hemisphere.