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Foundational Theories of Classical and Constructive Mathematics pp 265–310Cite as

Foundations for Computable Topology

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Part of the book series: The Western Ontario Series in Philosophy of Science ((WONS,volume 76))

Abstract

Foundations should be designed for the needs of mathematics and not vice versa. We propose a technique for doing this using the correspondence between category theory and logic and is potentially applicable to several mathematical disciplines.

“In these days the angel of topology and the devil of abstract algebra fight for the soul of every individual discipline of mathematics.” (Hermann Weyl.)

“Point-set topology is a disease from which the human race will soon recover.” (Henri Poincaré)

“Logic is the hygiene that the mathematician practises to keep his ideas healthy and strong.” (Hermann Weyl)

“Mathematics is the queen of the sciences and number theory is the queen of mathematics.” (Carl Friedrich Gauss)

“Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.” (Pierre-Simon Laplace)

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Acknowledgements

I would like to thank Andrej Bauer, David Corfield, Anders Kock, Fred Linton, Gabor Lukasz, Andy Pitts, Sridhar Ramesh, Guiseppe Rosolini, Giovanni Sommaruga, Hayo Thielecke and Graham White for their very helpful comments on earlier drafts of this paper.

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    Paul Taylor

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  1. Dépt. d'Informatique, Université de Fribourg, bd. de Pérolles 90, Fribourg, 1700, Switzerland

    Giovanni Sommaruga

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Taylor, P. (2011). Foundations for Computable Topology. In: Sommaruga, G. (eds) Foundational Theories of Classical and Constructive Mathematics. The Western Ontario Series in Philosophy of Science, vol 76. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0431-2_14

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