Philosophy at St Andrews

Indirect Mathematical Naturalism

Wed 15th February 2017 16:15

Room 104, Edgecliffe

Dr Marianna Antonutti Marfori, Munich


Scientific naturalism (roughly intended as the idea that science is the ultimate arbiter of truth) entails some degree of revisionism about mathematical practice. If only those parts of mathematics which are (or are liable to be) applied in science are confirmed or legitimised, those parts which are not (or are not liable to be) applied are not candidates for truth (e.g. the higher reaches of set theory). Revisionism about mathematical practice is incompatible with the methodological autonomy of mathematics, roughly intended as the idea that mathematics should be judged by its own standards, rather than by scientific ones. This view has been most notably defended by Maddy 1997 and 2005 as a type of mathematical naturalism. However, defending the methodological autonomy of mathematics leaves the mathematical naturalist without a demarcation criterion: she cannot appeal to the special role that mathematics plays in science in distinguishing science from pseudoscience (see Antonutti Marfori 2012). This paper proposes a two-tier epistemological framework that allows the mathematical naturalist to maintain that mathematics is ultimately justified on scientific grounds, but that mathematics as a whole (including unapplied and unapplicable mathematics) is a legitimate part of our best theory of the world. The notion of interpretability in logic will play a key role in providing the naturalist with a demarcation criterion.

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