Understanding the Infinite I: Niceness, Robustness, and Realism

Philosophia Mathematica 18 (3):253-275 (2010)
Abstract
This paper treats the situation where a single mathematical construction satisfies a multitude of interesting mathematical properties. The examples treated are all infinitely large entities. The clustering of properties is termed ‘niceness’ by the mathematician Michiel Hazewinkel, a concept we compare to the ‘robustness’ described by the philosopher of science William Wimsatt. In the final part of the paper, we bring our findings to bear on the question of realism which concerns not whether mathematical entities exist as abstract objects, but rather whether the choice of our concepts is forced upon us
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DOI 10.1093/philmat/nkq014
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References found in this work BETA
A Confutation of Convergent Realism.Larry Laudan - 1981 - Philosophy of Science 48 (1):19-49.

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Understanding the Infinite II: Coalgebra.David Corfield - 2011 - Studies in History and Philosophy of Science Part A 42 (4):571-579.

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