Mathematics – Logic
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011gregr..43.3657h&link_type=abstract
General Relativity and Gravitation, Volume 43, Issue 12, pp.3657-3664
Mathematics
Logic
Philosophy Of Science, History Of Science
Scientific paper
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
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