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Full-Text Articles in Philosophy of Science
Structures In Real Theory Application: A Study In Feasible Epistemology, Robert H. C. Moir
Structures In Real Theory Application: A Study In Feasible Epistemology, Robert H. C. Moir
Electronic Thesis and Dissertation Repository
This thesis considers the following problem: What methods should the epistemology 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 …
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …