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A.C. Paseau, Philosophy of the Matrix, Philosophia Mathematica, Volume 25, Issue 2, June 2017, Pages 246–267, https://doi.org/10.1093/philmat/nkw029
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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.
© The Authors [2016]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
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