Philosophy of the Matrix

Author: 

Paseau, A

Publication Date: 

26 December 2016

Journal: 

Philosophia Mathematica

Last Updated: 

2020-01-31T22:42:32.64+00:00

Issue: 

2

Volume: 

25

DOI: 

10.1093/philmat/nkw029

page: 

246-267

abstract: 

A mathematical matrix is usually defined as a two-dimensional array of scalars. And yet, as I explain, matrices are not in fact two-dimensional arrays. So are we to conclude that matrices do not exist? I show how to resolve the puzzle, for both contemporary and older mathematics. The solution generalises to the interpretation of all mathematical discourse. The paper as a whole attempts to reinforce mathematical structuralism by reflecting on how best to interpret mathematics.

Symplectic id: 

644317

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article