TY - GEN UR - http://lib.ugent.be/catalog/pug01:1942944 ID - pug01:1942944 LA - eng TI - Reverse mathematics & nonstandard analysis: towards a dispensability argument PY - 2011 PB - Tokyo AU - Sanders, Sam 002000184759 801001831539 AU - Okada, Mitsuhiro editor AB - Reverse Mathematics is a program in the foundations of mathematics initiated by Harvey Friedman and developed extensively by Stephen Simpson. Its aim is to determine which minimal axioms prove theorems of ordinary mathematics. Nonstandard Analysis plays an important role in this program. We consider Reverse Mathematics where equality is replaced by the predicate 'approx', i.e. equality up to infinitesimals from Nonstandard Analysis. This context allows us to model mathematical practice in Physics particularly well. In this way, our mathematical results have implications for Ontology and the Philosophy of Science. In particular, we prove the dispensability argument, which states that the very nature of Mathematics in Physics implies that real numbers are not essential (i.e. dispensable) for Physics (cf. the Quine-Putnam indispensability argument). ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1942944 | ||
005 | 20170102095250.0 | ||
008 | 111116s2011------------------------eng-- | ||
024 | a 1854/LU-1942944 2 handle | ||
040 | a UGent | ||
245 | a Reverse mathematics & nonstandard analysis: towards a dispensability argument | ||
260 | a Tokyo, Japan b Keio University Press c 2011 | ||
520 | a Reverse Mathematics is a program in the foundations of mathematics initiated by Harvey Friedman and developed extensively by Stephen Simpson. Its aim is to determine which minimal axioms prove theorems of ordinary mathematics. Nonstandard Analysis plays an important role in this program. We consider Reverse Mathematics where equality is replaced by the predicate 'approx', i.e. equality up to infinitesimals from Nonstandard Analysis. This context allows us to model mathematical practice in Physics particularly well. In this way, our mathematical results have implications for Ontology and the Philosophy of Science. In particular, we prove the dispensability argument, which states that the very nature of Mathematics in Physics implies that real numbers are not essential (i.e. dispensable) for Physics (cf. the Quine-Putnam indispensability argument). | ||
598 | a C1 | ||
100 | a Sanders, Sam 0 002000184759 0 801001831539 0 974184985982 | ||
700 | a Okada, Mitsuhiro e editor | ||
650 | a Philosophy and Religion | ||
653 | a Quine-Putnam indispensability argument | ||
653 | a Nonstandard Analysis | ||
653 | a Reverse Mathematics | ||
773 | t Ontology and Analytic Metaphysics Meeting g Keio University Publications. 2011. Keio University Press. q :< | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1942944/file/1942946 z [open] y Proceedings_Sam_Sanders_ontology_and_RM.pdf | ||
920 | a confcontrib | ||
852 | x WE b WE01 | ||
922 | a UGENT-WE |
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