Reverse mathematics & nonstandard analysis: towards a dispensability argument

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)