Category theory and the foundations of mathematics: Philosophical excavations

The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory.Various versions of this paper have been read by many people, many of whom have made crucial comments. Needless to say, I am entirely responsible for the claims made in this paper. I would particularly like to thank, in alphabetical order, Mario Bunge, Marta Bunge, Michael Hallett, Andrew Irvine, Saunders Mac Lane, Collin McLarty, Peneloppe Maddy and Mihaly Makkai. Part of the work was done while the author was a visiting fellow at REHSEIS in Paris and at the Center for Philosophy of Science in Pittsburgh. I would like to thank everyone for his or her help and support. I gratefully acknowledge the financial support received from the SSHRC of Canada while this work was done.     

Correlation between Changes in Stress-Induced Corticosterone Secretion and GR mRNA Levels

The current study was conducted to determine the potential relationship between stress-induced corticosterone secretion and corticosteroid receptor mRNA levels after 5 days of intermittent stress. In particular, we were interested in the rate at which animals terminate a stress response, and how this termination may be altered by repeated stress. Adult male Sprague-Dawley rats were subjected to either 5 days of restraint stress or 5 days of an unpredictable stress paradigm. Restraint-stress induced corticosterone secretion was measured on Days 1 and 5 in both groups, and animals were killed on Day 6. Glucocorticoid receptor (GR), and mineralocorticoid (MR) mRNA levels were determined using in-situ hybridization techniques. Five days of restraint stress caused an habituation of the plasma corticosterone response to stress measured 60 and 90 min post-stress initiation; this pattern of corticosterone secretion was not observed in the animals subjected to unpredictable stress. Five days of either stress paradigm did not alter MR mRNA levels measured within the hippocampus or GR mRNA levels within the hippocampus or the medial parvocellular division of the paraventricular nucleus of the hypothalamus (mpPVN). However, an individual's GR mRNA levels measured within the CA1/2 region of the hippocampus and the mpPVN were significantly correlated with the degree of habituation of the corticosterone response to stress measured on Day 5. This suggests that an increase in the rate of termination of the stress response and levels of GR within the hippocampus and mpPVN may be functionally related.     

Action and emotion in everyday life

This study of naturally occurring behaviour employed a "beeper technique" to investigate the actions carried out by 152 subjects in eight different groups, viz. adult students, employed students who were also parents, unemployed, art students, doctoral students, alcoholics, retired people and a control group. Actions were sampled for seven subsequent days, five times per day between 8 a.m. and 10 p.m. at randomly selected occasions. Each action was rated on a number of variables, shortly after it was sampled (median delay approximately 10 min). Some of the findings were: Time allocation corresponded well with national estimates. Being under situational control was highly aversive. Instrumental and consummatory orientations correlated positively. The background variables were, on the whole, only rather weakly related to action ratings, but it was found that women and retired persons tended to report a higher level of well-being.     

Documentary Bioethics: Visual Narratives for Generations X and Y

Narrative bioethics is primarily understood to involve storytelling through the use of literature. This article suggests that other forms of media are necessary to convey stories of an ethical nature to an audience broader than one being trained as medical professionals. "Documentary bioethics" is a manner to present and interpret stories of an ethical nature using forms of popular electronic media in a reality-based documentary style to society at large, specifically Generations X and Y.     

QUAID: A questionnaire evaluation aid for survey methodologists

QUAID (question-understanding aid) is a software tool that assists survey methodologists, social scientists, and designers of questionnaires in improving the wording, syntax, and semantics of questions. The tool identifies potential problems that respondents might have in comprehending the meaning of questions on questionnaires. These problems can be scrutinized by researchers when they revise questions to improve question comprehension and, thereby, enhance the reliability and validity of answers. QUAID was designed to identify nine classes of problems, but only five of these problems are addressed in this article: unfamiliar technical term, vague or imprecise relative term, vague or ambiguous noun phrase, complex syntax, and working memory overload. We compared the output of QUAID with ratings of language experts who evaluated a corpus of questions on the five classes of problems. The corpus consisted of 505 questions on 11 surveys developed by the U.S. Census Bureau. Analyses of hit rates, false alarm rates,d′ scores, recall scores, and precision scores revealed that QUAID was able to identify these five problems with questions, although improvements in QUAID’s performance are anticipated in future research and development.     

An Integral Psychology Response to Helminiak's (2001) “Treating Spiritual Issues in Secular Psychotherapy”

This article is a response to D. A. Helminiak's (2001) “Treating Spiritual Issues in Secular Psychotherapy” from the perspective of K. Wilber's integral psychology. The article consists of 3 sections: (a) a selective summary of integral psychology, including the perennial philosophy, 10 levels of development, lines of development, temporary states, types of orientations, the self, and the 4 quadrants; (b) various conceptual issues; and (c) usefulness to mental health practitioners (MHPs). Although D. A. Helminiak's endeavor to formulate a clear and functional definition of spirituality is commended, his claim of novelty is shown to be unwarranted. It is argued that K. Wilber's integral model is more comprehensive, clear, coherent, and helpful to MHPs.