Corfield, David
(2017)
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Homotopy type theory and the vertical unity of concepts in mathematics.
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In: de Freitas, Elizabeth and Sinclair, Nathalie and Coles, Alf, eds.
What is a Mathematical Concept?
Cambridge University Press, Cambridge, UK, pp. 125-142.
ISBN 978-1-316-47112-8.
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Official URL https://doi.org/10.1017/9781316471128 |

## Abstract

The mathematician Alexander Borovik speaks of the importance of the `vertical unity' of mathematics. By this he means to draw our attention to the fact that many sophisticated mathematical concepts, even those introduced at the cutting-edge of research, have their roots in our most basic conceptualisations of the world. If this is so, we might expect any truly fundamental mathematical language to detect such structural commonalities. It is reasonable to suppose then that the lack of philosophical interest in such vertical unity is related to the prominence given by philosophers to languages which do not express well such relations. In this chapter, I suggest that we look beyond set theory to the newly emerging homotopy type theory, which makes plain what there is in common between very simple aspects of logic, arithmetic and geometry and much more sophisticated concepts. With this language in mind, new light is thrown on thenature of mathematical concepts with clear benefits for educationalists.

Item Type: | Book section |
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Uncontrolled keywords: | concept; homotopy type theory; vertical unity; arithmetic;space; duality |

Subjects: | B Philosophy. Psychology. Religion > B Philosophy (General) |

Divisions: | Faculties > Humanities > School of European Culture and Languages > Philosophy |

Depositing User: | David Corfield |

Date Deposited: | 18 Oct 2017 09:43 UTC |

Last Modified: | 29 May 2019 19:43 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/64072 (The current URI for this page, for reference purposes) |

Corfield, David: | https://orcid.org/0000-0003-0432-3221 |

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