From a structural point of view

• Main Author: Shipley, Jeremy Robert
• Other Authors: Landini, Gregory
• Format: Others
• Language: English
• Published: University of Iowa 2011
• Subjects: Frege; Hilbert; logicism; philosophy of mathematics; Russell; structuralism; Philosophy
• Online Access: https://ir.uiowa.edu/etd/1178; https://ir.uiowa.edu/cgi/viewcontent.cgi?article=2562&context=etd

In this thesis I argue forin re structuralism in the philosophy of mathematics. In the first chapters of the thesis I argue that there is a genuine epistemic access problem for Platonism, that the semantic challenge to nominalism may be met by paraphrase strategies, and that nominalizations of scientific theories have had adequate success to blunt the force of the indispensability argument for Platonism. In the second part of the thesis I discuss the development of logicism and structuralism as methodologies in the history of mathematics. The goal of this historical investigation is to lay the groundwork for distinguishing between the philosophical analysis of the content of mathematics and the analysis of the breadth and depth of results in mathematics. My central contention is that the notion of logical structure provides a context for the latter not the former. In turn, this contention leads to a rejection of ante rem structuralism in favor of in re structuralism. In the concluding part of the dissertation the philosophy of mathematical structures developed and defended in the preceding chapters is applied to the philosophy of science.