McBride, Ennis Christopher John
(2004)
Is Maddy's naturalism a defensible view of mathematics?
MPhil thesis, London School of Economics and Political Science.
Abstract
The thesis is an examination of Penelope Maddy's book Naturalism in Mathematics and of the defensibility of the arguments she presents in support of her version of naturalism, with emphasis on the philosophical significance of her work. In Part A I first give an overview of the aim of the book and the methods used to achieve this aim. I then set out and appraise the arguments Maddy advances showing how she supports these arguments with her appeals to historical and current scientific and mathematical practice, I discuss and appraise her comments on the work of the authors she cites and give examples of the way in which she presents her case. I examine the extent to which the work of these authors can be seen to give support to Maddy's arguments. I also examine the validity of her appeals to the analogy between naturalism in science and naturalism in mathematics with reference to her descriptions of scientific practice. In Part B I discuss the objections advanced against Maddy's version of naturalism by contemporary critics of her book, with reference to seven authors in particular, considering the similarities and differences of the approach taken by each to Maddy. I show how their objections fall under two specific heads and appraise the persuasiveness of their criticisms. Finaly, I assess the effect of the objections which can be raised against Maddy's naturalism and examine the question of how compelling they are and whether Maddy's naturalism is still a convincing approach to mathematics in the light of these criticisms.
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