I am a Ph.D. student in philosophy at the University of Western Ontario. I am also a member of the Joseph L. Rotman Institute of Philosophy. My main areas of interest are the philosophy of physics and the philosophy of applied mathematics. My current philosophical interests centre on the relationship between mathematics (abstract structures), scientific theories and natural phenomena. This involves study of both the application and the applicability of mathematics.
Two approaches to the examination of the relationship between mathematics and natural phenomena I have considered are an examination of the tools and techniques of mathematical modelling employed in contemporary applied mathematics, particularly physics, and an historical examination of theory development in physics.
My current focus is on the processes used by applied mathematicians used to gain insight into phenomena of interest through the use of mathematical models and computation. Mathematical modelling in physics usually involves the application of physical theories to particular (classes of) phenomena by the systematic use of idealization to generate models, complemented by computation to obtain solutions. I am interested in the question of how such idealizations enable the extraction of information about the phenomena from theory, and in how to understand the manner in which computation enables the confirmation of the applicability of the model and the resulting implications for theory confirmation.
From the historical point of view I have examined the reasoning used by scientists in the process of the development of physical theories in the 18th and 19th centuries, specifically physical optics and electromagnetic theory. A central concern was the manner in which knowledge of experiential phenomena was developed and converted into a theory in a mathematical form. I considered the relationship between the mathematical theory and the phenomena to which it applies through an examination of how such reasoning led to a successful theory.
I am also interested, more generally, in the ontological implications of contemporary physical theories, the interpretation of quantum theories, the interpretation of divergences and singularities (infinities) in physical theories and in alternative foundations of mathematics, including category theory and topos theory.
- M.Sc. Applied Mathematics - University of Western Ontario (2010)
- M.A. Philosophy - University of Western Ontario (2004)
- B.A. Philosophy and Mathematics (Joint Hons.) - McGill University (2003)
- B.Sc. Physics (Hons.) - McGill University (2001)
- Moir (2010) - Reconsidering Backward Error Analysis for Ordinary Differential Equations (M.Sc. Thesis)
- Moir (2009) - The Conversion of Phenomena to Theory
- Moir (2005) - Smooth Evolution
- Curriculum Vitae