The categorical vision of logic
DOI:
https://doi.org/10.35494/topsem.2020.1.43.664Keywords:
Logic, Theory of categories, Topos, Grothendieck, FormAbstract
In this paper the development of logic since its inclusion to the
mathematical knowledge is briefly outlined with the purpose
of describe the way in which category theory is related with
logic. We discuss the emergence of categorical concepts within
mathematics in order to summarize how logical notions acquire
greater clarity and are completely unified as a branch of mathematics
through the language of categories. Finally, we conclude
explaining how a concept of shape is developed by category
theory to get this unification.
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References
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Manuscrito inédito disponible en: http://matematicas.unex.es/~navarro/res/res.pdf
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euclid.bams/1183407629
LAWVERE, W. & SCHNAUEL, H. (2009). Conceptual Mathematics. A First Introduction to Categories. Cambridge:
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http://www.acsu.buffalo.edu/~wlawvere/concep-3.pdf]
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TILES, M. (1989). The Philosophy of Set Theory. Nueva York: Dover Publications.
TORRETI, R. (1978). Philosophy of Geometry from Riemann to Poincaré. Dodrecht: Reidel Publishing Company.
Manuscrito inédito disponible en: http://matematicas.unex.es/~navarro/res/res.pdf
KLEIN, F. (1893). "A Comparative Review of Recent Researches in Geometry". Bulletin of the New York
Mathematical Society, vol. 2, núm. 10, pp. 215-249. Disponible en: https://projecteuclid.org/
euclid.bams/1183407629
LAWVERE, W. & SCHNAUEL, H. (2009). Conceptual Mathematics. A First Introduction to Categories. Cambridge:
Cambridge University Press [Traducción al español por Francisco Marmolejo. Disponible en:
http://www.acsu.buffalo.edu/~wlawvere/concep-3.pdf]
MAC LANE, S. & MOERDIJK, I. (1992). Sheaves in Geometry and Logic. Springer: Nueva York.
NAGEL, E. y NEWMAN, J. (2007). El teorema de Gödel. Madrid: Tecnos.
PRIEST, G. (2008). An Introduction to Non-Classical Logics. From if to Is. Cambridge: Cambridge University
Press.
SMULLYAN, R. (2002). Bosques curiosos y pájaros aristocráticos. Barcelona: Gedisa.
TILES, M. (1989). The Philosophy of Set Theory. Nueva York: Dover Publications.
TORRETI, R. (1978). Philosophy of Geometry from Riemann to Poincaré. Dodrecht: Reidel Publishing Company.
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Published
2020-05-06
How to Cite
Herrera Hernández, J. A. (2020). The categorical vision of logic. Tópicos Del Seminario, 1(43), 65–92. https://doi.org/10.35494/topsem.2020.1.43.664
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