### Project Description

# ROBERT MOIR

**M.Sc. Student;**

Department of Applied Mathematics, Department of Philosophy

Robert Moir is a graduate student in the philosophy department at Western University and a resident member of the Rotman Institute of Philosophy. His academic interests centre on the ways in which mathematics allows us to gain insight into the workings of natural phenomena. This involves examining both how mathematical theories of nature are developed, and how a theory, once developed, is applied to model different phenomena. His current research focuses on the mathematical methods used in applications, including techniques of formal manipulation and scientific computation. The main goal of this research is to deepen our understanding of how, in actual scientific practice, mathematics connects our theories of nature to nature itself. This clarifies both the nature and the limitations of scientific knowledge.

My current philosophical interests centre on the relationship between mathematics (abstract structures), scientific theories, and natural phenomena. 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 modeling 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 modeling 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.

**MSc Thesis:**

Moir, R. (2010). Reconsidering Backward Error Analysis for Ordinary Differential Equations. UWO.

**Proceedings:**

Moir, R. (2009). The Conversion of Phenomena to Theory: Lessons on Applicability from the Early Development of Electromagnetism. In: A. Cupillari (Ed.), Proceedings of the Canadian Society for History and Philosophy of Mathematics, St John’s NL, June 2009, pp. 68-91.

**Conference Presentations:**

With Nicolas Fillion, “Explanation and Abstraction: The Case of Backward Error Analysis” Philosophy of Science Association Biennial Meeting, Montreal, Quebec, 4-6 November 2010.

With Nicolas Fillion, “Modeling and Explanation: Lessons from Modern Error Theory.” Canadian Society for the History and Philosophy of Science (CSHPS) Conference, Concordia University, Montreal, Quebec, 28-30 May 2010.

With Nicolas Fillion, “A Step Forward with Backward Error,” PGSA Colloquium Series, Department of Philosophy, The University of Western Ontario, 12 March 2010.

“The Conversion of Phenomena to Theory: Lessons on Applicability from the Development of Electromagnetism.” Canadian Mathematical Society/Canadian Society for the History and Philosophy of Mathematics (CMS/CSHPM) Conference, Memorial University, St. John’s, Newfoundland, 6-8 June 2009.

“From the World to Mathematics and Back Again: What We Can Understand About Applicability from the Development of Electromagnetism.” PGSA Collo- quium Series, Department of Philosophy, The University of Western Ontario, 25 March 2009.

“Theories, Models and Representation: Lessons from Solid State Physics.” Canadian Society for the History and Philosophy of Science (CSHPS) Conference, University of British Columbia, Vancouver, British Columbia, 3-5 June 2008.

“Theories, Models and Representation: Lessons from Solid State Physics.” PGSA Colloquium Series, Department of Philosophy, University of Western Ontario, 12 March 2008.

“Interpretations of Probability in Quantum Mechanics.” PGSA Conference, Department of Philosophy, University of Waterloo, June 2005.

Introduction to Logic, 2011, Summer Evening Term, The University of Western Ontario (Instructor)

Critical Thinking, 2010-11, Fall/Winter Terms, The University of Western Ontario (Instructor)

Linear Algebra For Engineers, 2010, Winter Term, The University of Western Ontario (Tutorial Leader)

Calculus, 2009, Fall Term, The University of Western Ontario (Grader)

Introduction to Modern Mathematics (Algebra and Analysis), 2008-09, Fall/Winter Terms, Rotman Institute (Workshop Leader)

Introduction to Philosophy, 2005-06, 2007-08, Fall/Winter Terms, The University of Western Ontario (Tutorial Leader)

Critical Thinking and Reasoning, 2003-2005, Fall/Winter Terms, The University of Western Ontario (Tutorial Leader)