Heylen, Jan and Tump, Lars Arthur
(2019)
The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy.
[Preprint]
Abstract
Within the context of the QuinePutnam indispensability argument, one discussion about the status of mathematics is concerned with the `Enhanced Indispensability Argument', which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (2005, 2009). Furthermore, the result is then also used to strengthen the platonist position (e.g. Baker 2017a). We pick up the circularity problem brought up by Leng (2005) and Bangu (2008). We will argue that Baker's attempt to solve this problem fails, if Hume's Principle is analytic. We will also provide the opponent of the Enhanced Indispensability Argument with the socalled 'interpretability strategy', which can be used to come up with alternative explanations in case Hume's Principle is nonanalytic.
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