This paper argues for two related theses. The first is that mathematical abstraction can play an important role in shaping the way we think about and hence understand certain phenomena, an enterprise that extends well beyond simply representing those phenomena for the purpose of calculating/predicting their behaviour. The second is that much of our contemporary understanding and interpretation of natural selection has resulted from the way it has been described in the context of statistics and mathematics. I argue for these (...) claims by tracing attempts to understand the basis of natural selection from its early formulation as a statistical theory to its later development by R.A. Fisher, one of the founders of modern population genetics. Not only did these developments put natural selection of a firm theoretical foundation but its mathematization changed the way it was understood as a biological process. Instead of simply clarifying its status, mathematical techniques were responsible for redefining or reconceptualising selection. As a corollary I show how a highly idealised mathematical law that seemingly fails to describe any concrete system can nevertheless contain a great deal of accurate information that can enhance our understanding far beyond simply predictive capabilities. (shrink)

Recent arguments for scientific realism have emphasized the importance of both methodological factors, such as theoretical unification , and experiments , as evidence for a realistic view of certain aspects of theoretical structure . Throughout this dissertation I argue that neither strategy is sufficient as a defense of realism. ;Chapter one consists of a discussion of Friedman's argument for realism as outlined in his Foundations of Space-Time Theories . I argue that his reliance on theoretical unification and conjunction as grounds (...) for a selective brand of realism is unsatisfactory for a variety of reasons. Not only does his structure-substructure reductivist model of theories and the emphasis on conjunction fail to fit actual cases of theory evolution, but the historical relativity built into the approach is undesirable even from a realist perspective. The relationship between conjunctive inference and unification is discussed and it is suggested that although theoretical unification is desirable at some stages of theory development it contributes nothing to the justification or evidential warrant of theories. ;In chapter two my claims regarding unification are applied to the development of Maxwell's electromagnetic theory. I discuss the difficulties in specifying a workable model of the aether as the unifying theoretical structure as well as the importance of models and analogies in Maxwell's work. It is argued that this obvious unification of electromagnetism and optics played virtually no evidential role in the final acceptance of the theory. It was not until the completion of Hertz's experiments that Maxwell's theory was actually vindicated. ;Chapter three focuses on the experimental difficulties associated with Maxwell's theory and the relationship between Hertz's experiments and his theoretical interpretation of electromagnetism. ;In chapter four I summarize some of the general difficulties associated with the notion of independent evidence as it pertains to experimental results. I conclude by arguing that although experiment provides a more persuasive case for realism than methodological factors, in many instances it fails to provide the kind of epistemological justification required for the realist assumptions about the ontology of scientific theories. (shrink)