On Philosophical Problems in the Foundations of Chaos Theory

This dissertation examines several philosophical issues in the foundations of chaos theory and fractal geometry. In Chapter 1, I argue that our epistemological and ontological investigations would be better served by looking at the particular successes and failures of individual chaotic models, rather than focussing on broad questions of approximate truth. The rest of the dissertation can then be seen as a set of attempts to put this program into practice. In Chapter 2 I consider the prospects for instrumental fractal models of non-fractal physical objects. Although philosophers have contended that such models must always be inferior to non-fractal models, I argue that in some cases fractal models can be vastly epistemologically superior to their non-fractal rivals. In Chapter 3 I take up questions of ontology, and consider the prospects for the existence of fractals in physical space. Although philosophers have argued that physical fractals are an impossibility, I argue that classical mechanics and chaotic models could entail the existence of interesting fractal regions of space. In Chapter 4 I consider two definitions of observational equivalence for chaotic models, and ague that they fail to meet acceptability criteria.Ph.D