Philosophy of the Matrix

Philosophia Mathematica 25 (2):246-267 (2017)
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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.

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10.1093/philmat/nkw029

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A. C. Paseau
University of Oxford

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References found in this work

The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press. Edited by Otto Neurath.
The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - Chicago, IL: University of Chicago Press. Edited by Ian Hacking.
The meaning of 'meaning'.Hilary Putnam - 1975 - Minnesota Studies in the Philosophy of Science 7:131-193.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.
Individualism and the mental.Tyler Burge - 1979 - Midwest Studies in Philosophy 4 (1):73-122.

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