Naturalism in the Philosophy of Mathematics: On Mathematical Explanations of Empirical Phenomena

This research is concerned with a current debate on naturalism in the philosophy of mathematics. Discussing key notions like truth, (logical) necessity, and justification to approach the topic, an investigation into the different positions within this debate will be carried out. These will subsequently be contrasted with other schools of thought, such as nominalism and platonism. The dialectics of the debate between these different schools of thought is used to shed light on those issues which need to be addressed in order for one to be able to uphold a naturalistic approach towards logic and mathematics. Take for instance the specific debate about the status of mathematics in general, and pure and applied mathematics in particular. In contrast with other naturalistic philosophers, most notably Quine, Maddy holds that mathematics is autonomous, that is, it is not subject to scientific standards. This would on the one hand be in line with actual mathematical practice (mathematicians are not always interested in truth and applicability), but on the other hand raises the acute issue of reconciling this autonomy of mathematics with a naturalistic framework. The possibility of such a reconciliation is one of the main research topics. Another research topic, in some respects related to the previous point about interests, is to gain insight into the role of mathematics in scientific theories harbouring true propositions: propositions of which we want to say that they contribute to our knowledge of the world. It appears that scientists are also not necessarily interested in the truth of the mathematics they use. In fact, in some cases scientists knowingly invoke false (mathematical) assumptions, in order to get a (possibly true) result.

Publication year:2021

Accessibility:Closed