Philosophy of the Matrix
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 genera...
| Main Author: | |
|---|---|
| Format: | Journal article |
| Published: |
Oxford University Press
2016
|
| _version_ | 1797077675147264000 |
|---|---|
| author | Paseau, A |
| author_facet | Paseau, A |
| author_sort | Paseau, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T00:21:22Z |
| format | Journal article |
| id | oxford-uuid:7ca7ebf0-65ba-4526-8407-eda25e3a2d82 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:21:22Z |
| publishDate | 2016 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:7ca7ebf0-65ba-4526-8407-eda25e3a2d822022-03-26T20:58:32ZPhilosophy of the MatrixJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7ca7ebf0-65ba-4526-8407-eda25e3a2d82Symplectic Elements at OxfordOxford University Press2016Paseau, AA 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. |
| spellingShingle | Paseau, A Philosophy of the Matrix |
| title | Philosophy of the Matrix |
| title_full | Philosophy of the Matrix |
| title_fullStr | Philosophy of the Matrix |
| title_full_unstemmed | Philosophy of the Matrix |
| title_short | Philosophy of the Matrix |
| title_sort | philosophy of the matrix |
| work_keys_str_mv | AT paseaua philosophyofthematrix |