Naturalism in Mathematics and the Authority of Philosophy
Author: Paseau, Alexander
Source: British Journal for the Philosophy of Science, Volume 56, Number 2, June 2005 , pp. 377-396(20)
Publisher: Oxford University Press
Abstract:Naturalism in the philosophy of mathematics is the view that philosophy cannot legitimately gainsay mathematics. I distinguish between reinterpretation and reconstruction naturalism: the former states that philosophy cannot legitimately sanction a reinterpretation of mathematics (i.e. an interpretation different from the standard one); the latter that philosophy cannot legitimately change standard mathematics (as opposed to its interpretation). I begin by showing that neither form of naturalism is self-refuting. I then focus on reinterpretation naturalism, which comes in two forms, and examine the only available argument for it. I argue that this argument, the so-called Failure Argument, itself fails. My overall conclusion is that although there is no self-refutation argument against reinterpretation naturalism, there are as yet no good reasons to accept it. <LIST><ITEM> Naturalism in mathematics</ITEM><ITEM> The consistency of mathematical naturalism</ITEM><ITEM> The failure argument</ITEM><ITEM> Objections to the failure argument</ITEM><ITEM> Philosophy as the default</ITEM></LIST>
Document Type: Research article
Publication date: 2005-06-01
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