CEU Electronic Theses and Dissertations, 2014
| Author | McCullough-Benner, Colin Matthew |
|---|---|
| Title | Mathematical Truth without Reference |
| Summary | A near-universal assumption in the philosophy of mathematics is that mathematical language, taken at face value, at least purports to refer to mathematical objects. However, this assumption, I argue, is at the heart of some of the most difficult problems in the field—not just for platonist views, but for nominalist views as well. In this thesis, I argue that we should not make this assumption and propose an alternative, non-referential account of mathematical language. According to the view that I favor, mathematical truth is to be identified with provability in a system, and mathematical language is contentful in a way that a mere game is not insofar as the concepts that it employs are used outside of mathematics (or are in some sense parasitic on extra-mathematical concepts). Not only does this account avoid the traditional problems with existing non-referential accounts, but, I argue, it also allows us to deal with more sophisticated arguments concerning phenomena related to Gödel’s incompleteness theorems and the semantics of sentences in which mathematics is applied. |
| Supervisor | Ben-Yami, Hanoch |
| Department | Philosophy MA |
| Full text | https://www.etd.ceu.edu/2014/mccullough_colin.pdf |
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