Towards a Mapping Account of Applicability: An Exposition, Explanation, and Justification of the Representational Conception of Applied Mathematics

This thesis defends the view that the role of applied mathematics is a representational one, and develops a mapping account of the applicability of mathematics that does justice to this representational conception. The first chapter outlines some philosophical problems of applicability and some of its history. In the second chapter I explain in detail what the mapping account is, examining mappings, and representation theorems, and give any account how mathematics can represent derived attributes and laws. In chapter three I argue against the possibility of genuine platonistic explanations of physical phenomena. This is necessary as if there were such explanations they would entail that platonistic mathematics is not extrinsic to what actually goes on in the physical world, and that a purely representational conception of the applicability of mathematics is either straightforwardly false or radically incomplete. In chapter four a positive proposal, based largely upon the work of Hartry Field, is given for showing how it is that we can state scientific theories in such a way that platonistic mathematics does not appear as part of scientific theories. This is essential, since although the previous chapter argued that such genuine explanations are impossible, it did not show positively how we could dispense with platonistic mathematics in scientific explanations. Chapter five concerns a philosophical problem of applicability, the ’descriptive problem of applicability’ which, it has been argued, goes beyond mere ’representational’ issues and poses a problem for the mapping account of applicability. I identify three species of descriptive problems and reject the possibility of anthropocentrism as a solution to the descriptive problem.

Name dc:type.qualificationname

Doctor of Philosophy

Level dc:type.qualificationlevel

Doctoral Thesis

Grantor dc:publisher.institution

King's College London

Year dc:date.issued

2012

Author dc:creator

• Pointon, Daniel

Advisor dc:contributor.advisor

• Papineau, David Calder

Language dc:language

eng

Identifier

oai:kclpure.kcl.ac.uk:studenttheses/c6a0dd2d-8cd0-4825-b108-4912491bb2a2

OAI identifier oai:identifier

oai:kclpure.kcl.ac.uk:studenttheses/c6a0dd2d-8cd0-4825-b108-4912491bb2a2