Categorical Terms Research Articles

Proof theory in the abstract

Categorical proof theory is an approach to understanding the structure of proofs. We illustrate the idea first by analyzing G0̈del's Dialectica interpretation and the Diller-Nahm variant in categorical terms. Then we consider the problematic question of the structure of classical proofs. We show how double negation translations apply in the case of the Dialectica interpretations. Finally we formulate a proposal as to how to give a more faithful analysis of proofs in the sequent calculus.

A social categorization approach to distributive justice: social identity as the link between relevance of inputs and need for justice.

What are relevant inputs or criteria for judging entitlements in a given situation? As will be argued, an answer to this central problem of distributive justice must consider the perceiver's self-definition and structuring of the social context, in terms of social categorizations. The construal of the primary category of potential recipients is particularly important as its prototypical dimensions are likely criteria for entitlement judgments. Its representation depends on the perceiver's salient identity. Two studies yielded support for this perspective. In Study 1, students regarded their psychology department's distinctive quality as more important for psychologists than an out-group's quality. When highly identified, they perceived a psychologist who outperformed another on the in-group quality to have a higher entitlement to a job. In Study 2, German participants regarded the European Union's (EU) denial of EU membership to Turkey as more just the more prototypically European they thought Germany was, in contrast to Turkey; and, in turn, they did so the more strongly they identified as Germans. The findings suggest that relevance of inputs and, thus, the justice motive are based on identity concerns.

‘For Our Devotion and Pleasure’: The Sexual Objects of Jean, Duc de Berry

Jean, Duc de Berry (1340–1416), often seen as the first great ‘collector’ in Western art, is also described by some historians as a ‘homosexual’. This article examines the relationship between these two terms and the problematic historical evidence for the latter claim, exploring the duke’s desire for things, images and bodies in less categorical terms. The main argument is that we can best understand Jean’s sexual tastes from the artworks he commissioned and in which we know from contemporary accounts he took great personal delight. Reinterpretations are provided of some well‐known images, such as the January page of the unfinished Trés Riches Heures (1416), where the patron is pictured at the centre of a ‘homosocial’ feast for the eyes. This manuscript, along with the marginal decoration of his Grandes Heures, suggests his enjoyment of beautiful youthful bodies in general and of androgyny in particular. However, this has to be viewed within the very different gender system of the late fourteenth century in which women, youths and children were literally objects of male control. Only in this sense can we begin to understand how the duke’s love of things intersected with his political position and power more generally. Rather than see his collecting in all its polymorphous perversity as a symptom of personal trauma, I want to view it as a socially creative and recuperative act that was part of the performance of a ruthless man of power.

Phenomenology and Serial Murder

This article discusses the study of motives of serial murderers using the method of empirical phenomenology. Departing from a traditional clinical approach in terms of diagnostic categorizations of serial killers and from a conventional descriptive study in which generic aspects of serial murder such as modus operandi are described and interpreted, a qualitative approach is presented as essential to a more comprehensive understanding of the perpetrators of serial murder. Specifically, learning about murderers' personal constructions of meaning in their own lives positions us to be able to identify the motivations underlying their repeated acts of killing. Results obtained using this approach raise concerns regarding the validity of conclusions drawn from studies that rely upon more traditional methods of inquiry into motive. Researchers who apply conventional methods are cautioned regarding implied meanings of their data.

Egg Seeks Sperm. End of Story...? Articulating Gay Parenting in Small Ads for Reproductive Partners

Gay men and lesbians place small advertisements in the gay press to find reproductive partners. Analyses of over 200 such `mating ads' reveal that advertisers use a range of discursive methods to manage the potential gay parenting identities. We examine how gay male and lesbian advertisers adapt the formulaic format of the classified ad by exploiting the intertextual resonance of the job ad and the dating ad in order to construe reproductive identities and child-rearing roles. In addition, we discuss how the apparent contradiction of gay parenting is articulated through the use of dual discursive strategies which construe the advertiser and/or target both in identifying terms of lexical categorization (as for example, donor, dad or parent) and by delineation of a child-rearing role by degrees of involvement. Our analyses suggest that gay parenting roles need not correlate one-to-one with the discrete categories chosen to identify reproductive partner. The potential gay parent is personalized across both typological and topological models of meaning-making preventing him/her from becoming a contradiction in terms. We discuss the emergent identity of `co-parent'.

Quadratic division algebras revisited (Remarks on an article by J. M. Osborn)

In his remarkable article “Quadratic division algebras” (Trans. Amer. Math. Soc. 105 (1962), 202–221), J. M. Osborn claims to solve ‘the problem of determining all quadratic division algebras of order 4 over an arbitrary field F F of characteristic not two … \ldots modulo the theory of quadratic forms over F F ’ (cf. p. 206). While we shall explain in which respect he has not achieved this goal, we shall on the other hand complete Osborn’s basic results (by a reasoning which is finer than his) to derive in the real ground field case a classification of all 4-dimensional quadratic division algebras and the construction of a 49-parameter family of pairwise nonisomorphic 8-dimensional quadratic division algebras. To make these points clear, we begin by reformulating Osborn’s fundamental observations on quadratic algebras in categorical terms.

The contribution of the cerebellum to speech processing

Lesions to or diseases of the cerebellum may disrupt the motor components of speech production both at the segmental and suprasegmental level giving rise to “ataxic dysarthria”, a syndrome characterized, among others, by slowed speaking rate, distorted consonant and vowel productions and impaired prosodic modulation of sentence utterances. The concept of ataxic dysarthria has been further refined by measurements at the acoustic speech signal, tracking of articulatory movements and preliminary functional imaging studies. In summary, the available parametric data indicate the cerebellum to support several aspects of speech processing: acceleration of orofacial gestures, timing (coordination) of complex articulatory sequences, presumably, in cooperation with the anterior perisylvian language zone and control of brainstem reflexes monitoring respiratory and laryngeal muscle activity. Lesion studies and functional imaging indicate superior aspects of the cerebellum to mediate the speech motor functions referred to. Laterality and extent of the respective representation area, presumably, depend upon task demands. Besides speech motor deficits, recent investigations found disrupted speech perception in cerebellar subjects in terms of impaired categorization of specific durational minimal pairs.

Pride and Prejudice: Identity Management in English People's Talk about `this Country'

This article discusses the ways in which a sample of English respondents oriented to the task of formulating an account of their country in an interview context. Attention to both the content and the organizational features of talk suggested that respondents were generally reluctant to be heard to speak about `this country' in categorical terms, to adopt an explicitly national footing or to display a sense of patriotic national pride. They treated all of these as potentially hearable as symptomatic of `typical' Anglo-British xenophobia. In contrast to many extant analyses, which suggest that national discourse may provide a legitimate vehicle for the expression of exclusionary or racist sentiments, it appeared that, for these English respondents in this context, talk about `this country' was often treated as a delicate topic, functionally equivalent to, and subject to the same opprobrium as, talk about `race'. At the same time, however, various features of the respondents' discourse pointed to the presence of banal (Billig, 1995) national referents. Possible interpretations of this are discussed.

Sexual Orientation and Sex in Women's Lives: Conceptual and Methodological Issues

Use of such categorical terms as heterosexual, bisexual, and lesbian is widespread, yet research indicates that sexuality is a multidimensional phenomenon. Sexual behavior, identity, and desire are not highly intercorrelated for women, and this has implications for new ways of conceptualizing sexual orientation. Furthermore, the multifaceted nature of sexual orientation has implications for conceptualizing sexual activity and sexual desire for women. Some methodological issues are presented for future research on female sexual orientation, including a better understanding of gender and a more multifaceted approach to sexual orientation.

Fundamental Structures in Physics: A Categorical Approach

As already remarked by Eilenberg and MacLane in their seminal paper on categorytheory, preordered classes can be considered as thin categories, that is, categoriesfor which each Hom-set contains at most one element. In this paper I brieflydescribe how this identification not only allows much of the theory of orderstructures to be reformulated in categorical terms, but also permits the applicationof general categorical techniques to specific order-theoretic problems.

‘An unusual freedom'?; Mbulelo Mzamane's Mzala

Mzamane's comments over the years seem to reflect a doubt or ambivalence over the status of his first collection of stories, Mzala (1980). 1 In his introduction Mzamane describes himself as 'a teacher first, an aspiring literary critic next and only very incidentally a writer' (viii). In an interview in 1983 in the Nigerian journal Okella, he repeats this, and adds, 'I do not consider myself very seriously as a writer'(39).2 However, in the same interview he also defends himself against the criticism that his stories are 'escapist' or 'trivialize life'; people have tended to see him, he says, as 'a writer who is not very serious' (40). In 1979 Mzamane was in fact joint winner of the Mofolo/Piomer Prize for these stories, and Ravan's decision to republish Mzala in 1995 as part of the Ravan Writers Series indicates a continuing interest in the collection. 'This paper looks at Mzamane as a writer, and at Mzala in particular, in an attempt to assess the claims that have been made for this collection. It deserves recognition as an important contribution to the tradition of black South African writing in English. At the same time, it is necessary to look critically at the apparent endorsement of values and attitudes which may seem to contradict the author's stated commitment to a 'culture of liberation'. The stories have received little serious critical attention, and this· is also an attempt to redress the balance.3 If one looks at Mzamane's critical writings dating from the 1970s, something of a paradox emerges: he presents a view of black South African writing as strongly politicized, as a 'committed literature'. In New Classic in I 978 he makes the familiar assertion that 'Art and politics in South Africa have become inseparable for the simple reason that politics pervades all aspects of a black man's existence' (1978:42). Writing in Donga in 1977 he states that 'the only relevant literature in an African context is a committed literature.... We tum to the short story and shout our message loudly and clearly.... We protest in categorical and unambiguous terms' (1977a:8). Yet if one turns to his first collection of stories one finds little evidence of any 'message' being shouted. The stories seem to be characterized by the avoidance of any explicit protest or any obvious attempt to conscientize. These are, at first sight, among the least 'political' of South African black writings of the 70s. It was, in fact, this quality that appealed to some of the early reviewers. For Lionel Abrahams, 'the writing manifests an unusual freedom: to treat of individuals as individuals, to laugh in sheer amusement, to let protest... take a back seat'.4 He also comments on the author's 'distinct gift for starting characters visibly into life', and on his 'flair for dramatic situations' (1981:8). This may owe

Evidence for the independence of speech categories in perception and production

Models of speech processing, which attempt to account for speech input and output in phonological or categorical terms, generally rely on one single underlying representation for both perception and production. Previous research by Hemphill [J. Acoust. Soc. Am. 104, 1757–1758 (1998)] has suggested that two separate representations are necessary to account for asymmetries in acquisition data. Sixteen native speakers of English were trained to categorically perceive a three way voicing contrast in Thai bilabial stop consonants. The results of perception and production tests following training indicate that subjects were unable to accurately produce the contrasts that they had learned from perceptual training, despite the fact that they could identify the perceptual stimuli correctly. Additional perception testing after a two-month interval found that subjects were still able to label the training stimuli accurately, but could not identify their own productions with greater accuracy than they identified the training stimuli or the productions of unfamiliar talkers. These results are explained in terms of separate perception and production representations in the mind and an hypothesis about the reorganization of perceptual categories is explored.

Motivations for Group Membership: The Role of Subjective Importance and Uncertainty Reduction

An experiment was conducted to investigate the idea that an important motive for identifying with social groups is to reduce subjective uncertainty, particularly uncertainty on subjectively important dimensions that have implications for the self-concept (e.g., Hogg, 1996; Hogg & Mullin, 1999). When people are uncertain on a dimension that is subjectively important, they self-categorize in terms of an available social categorization and, thus, exhibit group behaviors. To test this general hypothesis, group membership, task uncertainty, and task importance were manipulated in a 2 × × × 2 between-participants design (N = 128), under relatively minimal group conditions. Ingroup identification and desire for consensual validation of specific attitudes were the key dependent measures, but we also measured social awareness. All three predictions were supported. Participants identified with their group (H1), and desired to obtain consensual validation from ingroup members (H2) when they were uncertain about their judgments on important dimensions, indicating that uncertainty reduction motivated participants towards embracing group membership. In addition, identification mediated the interactive effect of the independent variables on consensual validation (H3), and the experimental results were not associated with an increased sense of social awareness and, therefore, were unlikely to represent only behavioral compliance with generic social norms. Some implications of this research in the study of cults and "totalist" groups and the explication of genocide and group violence are discussed.

Motivations for Group Membership: The Role of Subjective Importance and Uncertainty Reduction

An experiment was conducted to investigate the idea that an important motive for identifying with social groups is to reduce subjective uncertainty, particularly uncertainty on subjectively important dimensions that have implications for the self-concept (e.g., Hogg, 1996; Hogg & Mullin, 1999). When people are uncertain on a dimension that is subjectively important, they self-categorize in terms of an available social categorization and, thus, exhibit group behaviors. To test this general hypothesis, group membership, task uncertainty, and task importance were manipulated in a 2 × × × 2 between-participants design (N = 128), under relatively minimal group conditions. Ingroup identification and desire for consensual validation of specific attitudes were the key dependent measures, but we also measured social awareness. All three predictions were supported. Participants identified with their group (H1), and desired to obtain consensual validation from ingroup members (H2) when they were uncertain about thei...

What's in a title? The strategic use of metaphor and metonymy in "Some like it hot"

The aim of this paper is to call attention upon the strategic and relevant use of the polysemous nature of language as it is instantiated in film titles such as the one in our discussion. The theoretical framework adopted in our analysis of the concept hot in our title is that of Cognitive Linguistics (Lakoff 1987; Langacker 1987), which explains polysemy in terms of conceptual organisation and categorisation. We defend that the cognitive approach to lexis as an array of semantic networks triggered by the words within them proves a useful explanation in solving a number of troublesome issues in the analysis of short texts like titles, namely the use of implicatures, polysemy, and the ambiguity usually resulting from both.

The impact of genetic counselling on risk perception and mental health in women with a family history of breast cancer

The present study investigated: (1) perception of genetic risk and, (2) the psychological effects of genetic counselling in women with a family history of breast cancer. Using a prospective design, with assessment pre- and post-genetic counselling at clinics and by postal follow-up at 1, 6 and 12 months, attenders at four South London genetic clinics were assessed. Participants included 282 women with a family history of breast cancer. Outcome was measured in terms of mental health, cancer-specific distress and risk perception. High levels of cancer-specific distress were found pre-genetic counselling, with 28% of participants reporting that they worried about breast cancer ‘frequently or constantly’ and 18% that worry about breast cancer was ‘a severe or definite problem’. Following genetic counselling, levels of cancer-specific distress were unchanged. General mental health remained unchanged over time (33% psychiatric cases detected pre-genetic counselling, 27% at 12 months after genetic counselling). Prior to their genetics consultation, participants showed poor knowledge of their lifetime risk of breast cancer since there was no association between their perceived lifetime risk (when they were asked to express this as a 1 in x odds ratio) and their actual risk, when the latter was calculated by the geneticist at the clinic using the CASH model. In contrast, women were more accurate about their risk of breast cancer pre-genetic counselling when this was assessed in broad categorical terms (i.e. very much lower/very much higher than the average woman) with a significant association between this rating and the subsequently calculated CASH risk figure (P= 0.001). Genetic counselling produced a modest shift in the accuracy of perceived lifetime risk, expressed as an odds ratio, which was maintained at 12 months' follow-up. A significant minority failed to benefit from genetic counselling; 77 women continued to over-estimate their risk and maintain high levels of cancer-related worry. Most clinic attenders were inaccurate in their estimates of the population risk of breast cancer with only 24% able to give the correct figure prior to genetic counselling and 36% over-estimating this risk. There was some improvement following genetic counselling with 62% able to give the correct figure, but this information was poorly retained and this figure had dropped to 34% by the 1-year follow-up. The study showed that women attending for genetic counselling are worried about breast cancer, with 34% indicating that they had initiated the referral to the genetic clinic themselves. This anxiety is not alleviated by genetic counselling, although women reported that it was less of a problem at follow-up. Women who continue to over-estimate their risk and worry about breast cancer are likely to go on seeking unnecessary screening if they are not reassured. © 1999 Cancer Research Campaign

Early pregnancy assessment; a role for the gynaecology nurse-practitioner

Recent improvements in the investigation of bleeding and pain in early pregnancy has led to simplified clinical guidelines. These in turn have created the opportunity for nurse-led early pregnancy assessment. We arranged for a gynaecology nurse-practitioner with experience to undergo additional training in early pregnancy care. She then took over the daily running of the Early pregnancy assessment centre (EPAC). A review of 200 consecutive cases showed that the nurse followed the guidelines extremely closely in terms of categorisation of patients, referral to the medical team for further investigation and selection of women who required anti-Rh(D) immunoglobulin. In addition, in the first 6 months of the clinic no cases of ectopic pregnancy were overlooked by the nurse-practitioner. Sixty-one per cent of the women attending the clinic did not need to see a doctor.

Termination or Transformation? The "Terminator" Films and Recent Changes in the U. S. Auto Industry

Since the 1970s, the term transparency has been widely used to signify the concealment of the technological means of the cinematic illusion characteristic of classical and realistic film style.1 Such concealment has been assumed necessary for the cinematic apparatus to achieve its ideological subject effect by providing a coherent yet illusory spectator position. Conversely, any self-reflexive inscription of a film's technical means of production, the hallmark of post1968 radical and avant-garde cinema, was assumed to radically subvert this ideological work.2 While these categorical terms may now seem somewhat dated, the relationship between technology, ideology, and subjectivity in the cinema is still worthy of serious investigation. One of the problems with many previous attempts has been their failure to recognize that cinema has always served a dual function with respect to technology, not only as a technology itself, but also as a means of representing technological change and narrativizing its social effects. These two functions interact in very interesting and sometimes contradictory ways, complicating the question

Labeled Families in Modular Software Development

We present a general framework for the modular development of families of programs or specifications through the use of labels. Families, consisting of components or versions, appear naturally in software development. The concept of implementation, as an interpretation into a conservative extension, is generalized to labeled families of specifications and formulated in categorical terms. We also show that the category of such families has pushouts and that this construction preserves conservative extensions, as required for composing implementations.

Introduction: A New Time and Place for Bolivian Popular Politics

The Bolivian national project, provisionally underway with the founding of the in 1825, has been redirected several times in the latter half of the twentieth century. Arguably the most dramatic of these make-overs have been the 1952 Revolution and subsequent Agrarian Reform, and the drive toward neoliberal democratization initiated in 1985. Each has reframed a national cultural politics of identity, successively shifting the meaningful distribution of the native as a cultural category. These shifts have involved rearranging the degree of visibility or invisibility, and mutual relations of emphasis among, at least, Indian, Andean, Highland, Lowland, Quechua, Aymara, and Bolivian-centric definitions of the native. As an ongoing historical process, this is particularly apparent at the juncture of competing definitions of mestizaje (denoting racial or cultural mixing) with successive incarnations of the national project, junctures where categorical slippage is the rule. After Independence and during the early the racial (de sangre) mestizo was ambivalently incorporated into a distinction between the so-called Republic of Indians and the Republic of Spaniards. this scheme the criteria for the stratification of caste (racial-cultural distinctions) and class (economic power) were virtually superimposed, even as class hierarchies began take shape in some regions (Larson 1990). the context of a Creole national movement, native-born Spaniards stood at the apex of their own new nation-state. Rather than as potentially productive mediators between the two republics, mestizos were called traitors, descendants of idolaters, violent, and individualistic. Taken be the product of Spanish men and Andean women, mestizos were sterile, illegitimate, and so potentially disloyal (Rivera 1993:62-69). Conversely, from the Andean point of view, the mestizo colluded with Creoles in colonial extraction, and so were included as part of the oppressive colonial regime. As two analysts concisely put it, in this colonial scheme, In order exist, the mestizo is condemned illegality (Bouysse-Cassagne and Saignes 1992:132). terms of conventional social categorization, at this early juncture racial mixtures were neither betwixt nor between. The late-nineteenth- mid-twentieth-century horizon of liberal and oligarchic politics forged an alliance between Creoles and rural land-owning mestizos. This, then, changed the perception of what today we would call social hybridity. Even as political participation was limited a mostly urban and literate elite, liberal politics reinscribed a more affirmative cultural mestizaje within the category of citizenship. liberal cant the Indian was the primary for the country's backwardness. pursuit of greater economic rationality, the liberals' goal was elevate the Indian the physical and moral level of the mestizo. To be sure, a double standard of exclusionary practices was still easily detectable, but often as the basis for a romanticized reincorporation of indigenous identity (referred as indigenismo), now a part of national democratic window dressing. As Rivera (1993:70) explains the case for Cochabamba, this cultural mestizaje sustained a vigorous popular culture rooted in Quechua tradition but not submitted quite as rigorous a process of segregation. this context, a visible tendency was that of the erasure of specific ethnic differences within the generic category of Indian, usually treated as an aspect of the natural environment. The mestizo became in part a civilizing impulse from within indigenous Bolivia. With its coming power in 1952, the MNR (Movimiento Nacionalista Revolucionario) sought complete the work of citizenship for the nation-state. To do so, it needed erase bothersome traces of the past, reinventing it in order to expunge the anticolonial indigenous cause and to reinterpret an imagined mestizo territory which coincided with the former Inca Empire. …