This infinite, unanimous dissonance : a study in mathematical existentialism through the work of Jean-Paul Sartre and Alain Badiou

This thesis seeks to elucidate a motif common to the work both of Jean-Paul Sartre and Alain Badiou (with special attention being given to Being and Nothingness and Being and Event respectively): the thesis that the subject 's existence precedes and determines its essence. To this end, the author aims to explicate the structural invariances, common to both philosophies, that allow this thesis to take shape. Their explication requires the construction of an overarching conceptual framework within which it may be possible to embed both the phenomenological ontology elaborated in Being and Event and the mathematical ontology outlined in Being and Event. Within this framework, whose axial concept is that of multiplicity, the precedence of essence by existence becomes intelligible in terms of a priority of extensional over intensional determination. A series of familiar existentialist concepts are reconstructed on this basis, such as lack and value, and these are set to work in the task of fleshing out the more or less skeletal theory of the subject presented in Being and Event.

Beyond g : putting multiple intelligences theory to the test /

The purpose of this study was to investigate Howard Gardner's (1983) Multiple Intelligences theory, which proposes that there are eight independent intelligences: Linguistic, Spatial, Logical/Mathematical, Interpersonal, Intrapersonal, Naturalistic, Bodily-Kinesthetic, and Musical. To explore Gardner's theory, two measures of each ability area were administered to 200 participants. Each participant also completed a measure of general cognitive ability, a personality inventory, an ability self-rating scale, and an ability self-report questionnaire. Nonverbal measures were included for most intelligence domains, and a wide range of content was sampled in Gardner's domains. Results showed that all tests of purely cognitive abilities were significantly correlated with the measure of general cognitive ability, whereas Musical, Bodily-Kinesthetic, and one of the Intrapersonal measures were not. Contrary to what Multiple Intelligences theory would seem to predict, correlations among the tests revealed a positive manifold and factor analysis indicated a large factor of general intelligence, with a mathematical reasoning test and a classification task from the Naturalistic domain having the highest ^- loadings. There were only minor sex differences in performance on the ability tests. Participants' self-estimates of ability were significantly and positively correlated with actual performance in some, but not all, intelligences. With regard to personality, a hypothesized association between Openness to Experience and crystallized intelligence was supported. The implications of the findings in regards to the nature of mental abilities were discussed, and recommendations for further research were made.

Undergraduate Students' Experiences of Their Mathematical Identity

This research study explored how undergraduate mathematics students perceive themselves as capable mathematics learners and whether gender differences exist in the undergraduates students' perceptions. The research was framed by three approaches of understanding identity: self-efficacy, environment, and four faces of learner's identity. A mixed methods approach to the study was used where data were collected from interviews and an online questionnaire. Data analysis revealed that undergraduate mathematics students' perceptions of their mathematical identity as capable mathematics learners are influenced by their perceptions of their experiences such as: (a) perceptions of having previous knowledge of the course, (b) being able teach others and others understand it, (c) being recognized by their professors, (d) contributing and fitting in, (e) having opportunities to interact with their peers, and (f) being able to fit in with their image of a capable mathematics learner.

Subjective Ambivalence and the Expression of Anti-Gay Bias

Univalent attitudes toward gay people have been widely studied, but no research to date has examined ambivalent (i.e., torn, conflicted) attitudes toward gay people. However, the Justification-Suppression Model (JSM; Crandall & Eshleman, 2003) proposes that ambivalence leads to biased expressions through intrapsychic processes which facilitate biased expression, particularly in contexts presenting strong justifications for expressing prejudice and weak pressures to suppress prejudice. I test these implications in the context of bias toward gay people. In Study 1, the measurement of ambivalence is examined in terms of both subjective ambivalence (i.e., the reported experience of “torn” attitudes) and calculated ambivalence (i.e., mathematical conflict between positive and negative attitude components). I find that higher subjective ambivalence is only associated with more negative attitudes toward gay people (and not positive attitudes toward gay people), and that higher subjective ambivalence predicts less gay rights support even after taking negative and positive attitudes toward gay people into account. Further, higher subjective ambivalence is associated with ideological opposition to gay people and more negative intergroup emotions (e.g., intergroup disgust). These findings suggest it is valuable to examine the unique component of subjective ambivalence separate from univalent negativity. Because calculated ambivalence measures are mathematically dependent upon a univalent negative measure, they cannot be examined separately from negativity. Therefore, subjective ambivalence is the focus of Study 2. The main goals of Study 2 were to determine why and when subjective ambivalence is related to bias. I examined the extent to which the negative relation between subjective ambivalence and opposition to anti-gay bullying can be accounted for by lower intergroup empathy and lower collective guilt, which may facilitate the expression of bias in keeping with the JSM. The relation between subjective ambivalence and anti-gay bullying opposition was examined within four social contexts based on a 2 (high vs. low offensiveness) x 2 (normatively unjustified vs. normatively justified) manipulation. I expected that higher subjective ambivalence would be most strongly related to lower intergroup empathy and collective guilt when there are the strongest justifications for bias expression, and that lower intergroup empathy and collective guilt would lead to less opposition to anti-gay bullying. Higher subjective ambivalence predicted less anti-gay bullying opposition. After accounting for positivity and negativity, the direct effect of subjective ambivalence was no longer significant, yet subjective ambivalence uniquely predicted intergroup empathy, which in turn predicted less anti-gay bullying opposition. These findings provide evidence that subjective ambivalence is largely negative in nature, but also presents evidence for a unique component of subjective ambivalence (separate from univalent attitudes) associated with low intergroup empathy and negativity. In contrast to previous research, I found very little evidence for the context-dependency of subjective ambivalence. Further research on subjective ambivalence, including subjective ambivalence toward other social groups, may expand our understanding of the factors leading to biased expressions.