The Role of Mathematics in Deleuze’s Critical Engagement with Hegel

Abstract

The role of mathematics in the development of Gilles Deleuze’s (1925–95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze’s interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770–1831) presents in the Science of Logic. Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal calculus in his treatment of the problem of the infinitesimal. Against the role that Hegel assigns to integration as the inverse transformation of differentiation in the development of his dialectical logic, Deleuze strategically redeploys Leibniz’s account of integration as a method of summation in the form of a series in the development of his philosophy of difference. By demonstrating the relation between the differential point of view of the Leibnizian infinitesimal calculus and the differential calculus of contemporary mathematics, I argue that Deleuze effectively bypasses the methods of the differential calculus which Hegel uses to support the development of the dialectical logic, and by doing so, sets up the critical perspective from which to construct an alternative logic of relations characteristic of a philosophy of difference. The mode of operation of this logic is then demonstrated by drawing upon the mathematical philosophy of Albert Lautman (1908–44), which plays a significant role in Deleuze’s project of constructing a philosophy of difference. Indeed, the logic of relations that Deleuze constructs is dialectical in the Lautmanian sense.     

EDITORIAL COMMENT: GUEST COMMENTARY TEACHERS'THEORETICAL ORIENTATIONS AND THE REAL CLASSROOM

A four year‐study of teacher beliefs and conceptions about reading is reported. Teacher beliefs were determined outside the classroom context and while conducting instruction. It was determined that classroom teachers can articulate theories of reading outside the classroom but that their actual instructional practice is governed by a complex set of contextual factors. It is concluded that reading educators must not only teach reading theory but must also help teachers apply theory to the complex instructional context of classrooms.     

Predicting the job and life satisfaction of Italian teachers: Test of a social cognitive model

This study tested a social cognitive model of work and life satisfaction (Lent & Brown, 2006, 2008) in a sample of 235 Italian school teachers. The model offered good overall fit to the data, though not all individual path coefficients were significant. Three of five predictors (favorable work conditions, efficacy-relevant supports, and positive affectivity) produced significant, direct paths to job satisfaction. Job satisfaction, progress at personal work goals, and positive affectivity were predictive of teachers' life satisfaction. Task self-efficacy was related indirectly both to job satisfaction (via work conditions) and life satisfaction (via goal progress). Implications of the findings for future research and efforts to promote teachers' job satisfaction are discussed.     

The presence of a calling and academic satisfaction: Examining potential mediators

The present study examined the relation of calling and academic satisfaction with a diverse sample of 312 undergraduate students. The presence of a calling was moderately correlated with academic satisfaction, and a multiple mediation model was utilized to test three potential mediators to this relation: career decision self-efficacy, work hope, and meaning in life. Using bootstrapping techniques, significant indirect effects were found for two of the three mediators, career decision self-efficacy, and work hope. After including the mediators in the model, the relation of calling and academic satisfaction was non-significant. These results indicate that calling relates to greater satisfaction in the academic domain in part because of increased career decision self-efficacy and work hope. Directions for future research are discussed.     

Physician job satisfaction across six major specialties

A random sample of 763 physicians was surveyed to examine the relation of 18 critical work-related factors to job satisfaction. On the whole, physicians reported that they were satisfied with their careers and believed that caring for patients, sense of accomplishment, continuity of care, autonomy, and personal time were the five most important factors for their personal job satisfaction. Regression analyses were run to determine the role of each of the 18 critical factors in predicting job satisfaction. Dissimilar to the self-report, the five most significant predictors were sense of accomplishment, creativity, income satisfaction, security, and autonomy. Additional regression analyses were run using the 18 critical factors to predict job satisfaction across the six major medical specialties. Significant factors varied greatly depending on specialty area, suggesting that physician job satisfaction may be better understood in terms of specialty rather than as a whole.     

Response to Gordon Baker

Studies in Philosophy and Education -     

Down but not out: Newcomers can compensate for low vertical access with strong horizontal ties and favorable core self‐evaluations

We draw upon and extend socialization resources theory to explain how organizational newcomers leverage their social capital resources (i.e., vertical access and horizontal tie strength within their communication networks) and personal resources (i.e., core self‐evaluations) to learn about and assimilate into their work and organizations. The findings of a multiwave study of organizational entrants in China reveal the synergistic effects of relational and personal resources for newcomer adjustment. Newcomers learn and assimilate effectively not only when they have vertical connections to high‐status organization members but also when they can compensate for their lack of high‐status connections by leveraging their strong horizontal ties with peers and favorable core self‐evaluations. These findings provide a practical perspective on how to tailor newcomer onboarding practices to facilitate effective newcomer adjustment.     

The representation of ontological category concepts as affected by healthy aging: normative data and theoretical implications

Attributes associated with concept representations, such as familiarity, typicality, and age of acquisition, have been shown to be important influences on lexical-semantic processing. In most previous studies of healthy and pathological aging, these attributes are not equated for younger and older adults separately on the stimuli used. In this study, normative data were collected to test whether there exist any age differences in these attributes. The results demonstrate that the ratings given by younger and older adults on natural and manmade category items correlated positively. However, age differences were also apparent, whereby older adults provided higher ratings overall than younger adults. Suggestions and hypotheses are presented to explain this pattern of age differences, which relate to how category concepts may be represented by healthy younger and older adults. Also, the possible implications for these differential age ratings on lexical-semantic processing are discussed. The age differences apparent in this study demonstrate the need to consider age-appropriate normative ratings in the selection of stimuli for use in lexical-semantic processing studies of aging, and the normative data presented provide a means of equating category stimuli. The complete list of all the means is available at www.psychonomic.org/archive.     

The moderating roles of self-esteem and neuroticism in the relationship between group and individual undermining behavior

The authors developed and tested a multilevel interactive model of the relationship between group undermining and individual undermining behavior in 2 multiwave studies of group members. Integrating the literature on group influences on individual behavior with the individual difference literature, the authors predicted a 3-way Group Undermining x Self-Esteem x Neuroticism interaction, such that the relationship between group and individual undermining would be strongest among those simultaneously high in self-esteem and neuroticism. The 3-way interaction was supported in Study 1 (457 participants in 103 groups) and replicated in Study 2 (415 participants in 93 groups) with additional controls and alternative measures of key constructs. The authors discuss the implications of the research and identify future research directions.