Steiner on the Applicability of Mathematics and Naturalism

Philosophia Mathematica 14 (1):26-43 (2006)
Steiner defines naturalism in opposition to anthropocentrism, the doctrine that the human mind holds a privileged place in the universe. He assumes the anthropocentric nature of mathematics and argues that physicists' employment of mathematically guided strategies in the discovery of quantum mechanics challenges scientists' naturalism. In this paper I show that Steiner's assumption about the anthropocentric character of mathematics is questionable. I draw attention to mathematicians' rejection of what Maddy calls ‘definabilism’, a methodological maxim governing the development of mathematics. I contend that because definabilism is anthropocentric, its rejection casts doubts on Steiner's assumption.
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DOI 10.1093/philmat/nkj002
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Sorin Bangu (2008). Reifying Mathematics? Prediction and Symmetry Classification. Studies in History and Philosophy of Science Part B 39 (2):239-258.
Sorin Bangu (2009). Wigner's Puzzle for Mathematical Naturalism. International Studies in the Philosophy of Science 23 (3):245-263.

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