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Structures in Real Theory Application: a Study in Feasible Epistemology

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Structures in Real Theory Application: a Study in Feasible Epistemology Western University Scholarship@Western Electronic Thesis and Dissertation Repository 8-13-2013 12:00 AM Structures in Real Theory Application: A Study in Feasible Epistemology Robert H. C. Moir The University of Western Ontario Supervisor Robert W. Batterman The University of Western Ontario Joint Supervisor John L. Bell The University of Western Ontario Graduate Program in Philosophy A thesis submitted in partial fulfillment of the equirr ements for the degree in Doctor of Philosophy © Robert H. C. Moir 2013 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Epistemology Commons, Logic and Foundations of Mathematics Commons, and the Philosophy of Science Commons Recommended Citation Moir, Robert H. C., "Structures in Real Theory Application: A Study in Feasible Epistemology" (2013). Electronic Thesis and Dissertation Repository. 1578. https://ir.lib.uwo.ca/etd/1578 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. Structures in Real Theory Application: A Study in Feasible Epistemology (Thesis Format: Monograph) by Robert H. C. Moir Graduate Program in Philosophy A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada ©Robert H. C. Moir 2013 Abstract This thesis considers the following problem: What methods should the episte- mology of science use to gain insight into the structure and behaviour of scientific knowledge and method in actual scientific practice? After arguing that the elucidation of epistemological and methodological phenomena in science requires a method that is rooted in formal methods, I consider two alternative methods for epistemology of science. One approach is the classical approaches of the syntactic and semantic views of theories. I show that typical approaches of this sort are inadequate and inaccurate in their representation of scientific knowledge by showing how they fail to account for and misrepresent important epistemological structure and behaviour in science. The other method for epistemology of science I consider is modeled on the methods used to construct valid models of natural phenomena in applied mathematics. This new epistemological method is itself a modeling method that is developed through the detailed consideration of two main examples of theory application in science: double pendulum systems and the modeling of near-Earth objects to compute probability of future Earth impact. I show that not only does this new method accurately rep- resent actual methods used to apply theories in applied mathematics, it also reveals interesting structural and behavioural patterns in the application process and gives insight into what underlies the stability of methods of application. I therefore con- clude that for epistemology of science to develop fully as a scientific discipline it must use methods from applied mathematics, not only methods from pure mathematics and metamathematics as traditional formal epistemology of science has done. Keywords: mathematical modeling, computation, scientific data, epistemology, method- ology, semantic view, syntactic view, feasible epistemology i Acknowledgements The local origin of this project was work done during my eight month stay in Pitts- burgh as a Visiting Scholar at the University of Pittsbirgh. The first four months I shared with Nic Fillion provided the inspiration, with many stimulating conversa- tions along with our attending the fine foundations of mathematics lectures given by Wilfried Sieg at Carnegie Mellon University. During the entire period Bob Batter- man played an important role in the shaping of the project and helping to develop clearer expression of my ideas. Conversations with Mark Wilson and Julia Bursten were also helpful for conceptualizing the project in this period. After my return to London, many conversations with Lori Kantymir and Emerson Doyle were essential for the clarification and development of ideas both before and during my writing the dissertation. Paul Wiegert was also a great help in getting oriented in contemporary computational approaches to modeling near-Earth objects. The global origin of this project extends back to my time in Montreal, since which time my parents have been a constant source of support for my intellectual pursuits, no matter how wandering they have been. I simply would not have reached the point of completion of this project without their enormously generous care and support. During the same period a small group of people have been a constant source of support for the underlying ideas: Sona Ghosh, Emerson Doyle, Nic Fillion and Lori Kantymir. Nic's influence permeates this work. Our intellectual exchanges began shortly after we met when we quickly found that we shared a very similar perspective on the relationship between mathematics and phenomena, but deepened significantly following our encounter with backward error analysis in the graduate Introduction to Numerical Methods course taught by Rob Corless. Rob's influence on this work is similar in extent, from the idea of a \feasible epistemology" coming out of a conversation at the Grad Club one evening, to all I have learned from him about the epistemology of applied mathematics. The influence on my thinking coming from Bob Batterman has been great, as has his support and openness to allow me to find my own way. I am indebted to him for his scientific style of thinking about phenomena and his challenging my inclinations toward more formal representations. Possibly the deepest influence on my thought, however, has come from my long professional and personal relationship with John Bell. It is through his influence that I even came to ii realize my case of the Platonistic measles, but more significant has been his constantly challenging me to walk that fine line between the ideal and the actual. Although it may not appear such on the surface, the ideas expressed and developed in this work are influenced by his work, thinking and conversations more than any other. At a more practical level, a number of people have contributed to making the completion of the dissertation possible. Comments from and conversations with Bob Batterman, Chris Smeenk and Emerson Doyle over the last few months have been in- valuable. As have comments on drafts of the dissertation itself from Bob Batterman, Bill Harper, Chris Smeenk, and Rob Corless. The editing work that Abby Egerter has skillfully and seemingly effortlessly contributed, even under very strict time con- straints, has also been invaluable. Finally, Lori Kantymir has provided incredible support and encouragement through the arduous process of writing this summer. Al- though it is my parents, Anne and Frank Moir, that have made this work possible in the overall sense, in the most immediate and direct sense it is my dear Lori that has made it feasible. Robert Moir August 30, 2013 London iii To Anne and Frank Moir for their invariant love and support and for making this work feasible iv Contents Abstracti Acknowledgements ii Dedication iv List of Tables vii List of Figures viii List of Abbreviations, Symbols and Terminologyx I Classical and Feasible Epistemology1 1 Applying Theories in the Real World: Feasible Epistemological Access to Natural Phenomena2 1.1 Studying Scientific Method..........................2 1.1.1 The Phenomenon of Scientific Method...............2 1.2 Epistemological Approaches to Scientific Knowledge...........5 1.3 Understanding the Methods of Applied Mathematics.......... 12 1.3.1 Using Applied Mathematics to Answer Real-World Questions.................... 12 1.3.2 Modeling Simple Pendulums Using Newtonian Mechanics..................... 14 1.3.3 Modeling Double Pendulums Using Hamiltonian Mechanics.................... 24 1.4 New Perspectives on the Relation of Theory to Data and Phenomena....................... 33 2 Applying Theories in an Ideal World: Classical Accounts of Epistemological Access to the World 38 2.0.1 Abstraction and Formal Reconstructions of Science....... 40 2.1 Syntactic Approaches to Theories...................... 44 2.1.1 The Received View of Theories................... 45 v 2.1.2 Limitations of the Syntactic View................. 49 2.1.3 Modeling Application on the Syntactic Approach........ 51 2.2 Semantic Approaches to Theories...................... 56 2.2.1 Suppes's Sets of Models Approach................. 57 2.2.2 Van Fraassen's Semi-Interpreted Languages Approach..... 60 2.2.3 Limitations of the Semantic View................. 65 2.3 Feasible Approaches to Theories....................... 71 2.3.1 Logico-Structural Approaches to Theories............ 73 II Modeling Feasible Theory Application 77 3 Modeling in the Real World: Feasibly Constructing Models 78 3.1 A Feasible Approach to Theories and Models............... 78 3.1.1 Algebro-Geometric Approaches to Modeling Theories...... 81 3.1.2 Algebro-Geometric Constraints................... 87 3.1.3 Local Constraint Logic........................ 94 3.2 Structural Features of Feasible Model Construction........... 103 3.2.1 Handling Complex Structure.................... 106 3.2.2 Handling Complex Dynamics.................... 117 3.2.3 Handling Complex Computations................. 122 3.3 Sources of Model Error and Their Structural
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