Describing mathematics without revision: Wittgenstein's radical constructivism
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Date
2020
Authors
Ladeira, Thiago
University of Lethbridge. Faculty of Arts and Science
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Publisher
Lethbridge, Alta. : University of Lethbridge, Dept. of Philosophy
Abstract
In this thesis, I present a critical exposition of Wittgenstein’s philosophy of mathematics, and attempt to show that Wittgenstein’s philosophy of mathematics constitutes a viable alternative to the Standard View of mathematics. To this end, I show that there are two important interpretations that support the Standard View: a) Platonism; and b) Modalism. I argue that neither Platonism nor Modalism can provide a satisfactory account of mathematics. In explicating Wittgenstein’s Finitistic Constructivist interpretation of mathematics, I endeavour to emphasize the main reasons why Wittgenstein's descriptive account of mathematics is better that either variant of the Standard View. Wittgenstein’s formalistic view better captures what mathematicians do, and it better evaluates and rejects some verbal interpretations that mathematicians attach to their work.
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Keywords
Constructive realism , Constructivism (Philosophy) , Dissertations, Academic , Logic , Logic, Symbolic and mathematical , Mathematics , Mathematics -- Philosophy