Chapter

Mathematics and Physical Reality

Geoffrey Hellman

in Mathematics without Numbers

Published in print November 1993 | ISBN: 9780198240341
Published online November 2003 | e-ISBN: 9780191597664 | DOI: http://dx.doi.org/10.1093/0198240341.003.0004

Series: Clarendon Paperbacks

 Mathematics and Physical Reality

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Strategies for extending the modal‐structural approach to applications of mathematics are explored. The basic idea is to entertain what relationships would hold between a non‐mathematical system of interest and ‘non‐interfering’ additional hypothetical objects that may be needed to carry relevant mathematical structure. Usually, structures for real analysis suffice, although still more ‘abstract’ structures may arise in modern physics. Certain interesting connections between the modal‐structural approach and a minimal scientific realism are exposed (the latter aiding the former), and comparisons are drawn with Hartry Field's nominalization program.

Keywords: analytic; applied mathematics; modern physics; scientific realism; synthetic

Chapter.  21856 words. 

Subjects: Philosophy of Mathematics and Logic

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