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Volume 32, Number 1, pages 005-023 (2021)
https://doi.org/10.26830/symmetry_2021_1_005
A STORY OF MATHEMATICAL SYMMETRIES
Mihir Kumar Chakraborty*
* School of Cognitive Science, Jadavpur University, 188 Raja S. C. Mullik Road, Kolkata, 700032, India.
E-mail: mihirc4@gmail.com
Abstract: Various kinds of symmetries in mathematics are considered. Consistency is argued to be a grand-symmetry. A parallel between symmetries in mathematics and art is discussed. In a comparison with art the possibility of going beyond consistency in mathematical endeavours is explored.
Keywords: symmetric group, Boolean algebra, duality, consistency.
References:
Beziau, J.E., Chakraborty, M., Dutta, S. (2015) New Directions in Paraconsistent Logic, New Delhi, India: Springer. https://doi.org/10.1007/978-81-322-2719-9
Chakraborty, M.K. (2012) Mathematical Rupas and Their Artists, In: Sengupta, P.K., ed. History of Science, Philosophy and Culture in Indian Civilization, Vol. 13, Part 7, 527–533, Delhi, India: Pearson.
Chakraborty, M., Dutta, S. (2019) Theory of Graded Consequence, Singapore: Springer. https://doi.org/10.1007/978-981-13-8896-5
Dekkers, M. (2008) Stone Duality, [Master Thesis], Nijmegen, The Netherlands: Radbound University.
Farmer, D.W. (1996) Group and Symmetry: A Guide to Discovering Mathematics, Delhi, India: Universities Press. https://doi.org/10.1090/mawrld/005
Friend, M. (2014) Pluralism in Mathematics: A New Position in Philosophy of Mathematics, Dordrecht, The Netherlands: Springer. https://doi.org/10.1007/978-94-007-7058-4
Gehrke, M. (2009) Duality, Nijmegen, The Netherlands: Radbound University.
Kline, M. (1990) Mathematics in Western Culture, London, UK: Penguin Books.
Kosso, P. (2000) The empirical status of symmetries in physics, British Journal of Philosophy of Science, 51, 1, 81–98. https://doi.org/10.1093/bjps/51.1.81
Lucas, J.R. (1984) Space, Time and Causality, Oxford, UK: Clarendon Press.
Rescher, N., Brandom, R. (1980) The Logic of Inconsistency. A Study in Non-Standard Possible-World Semantics and Ontology, Oxford, UK: Basil Blackwell, x + 174 pp.
Rosen, J. (1995) Symmetry in Science, New York, NY: Springer. https://doi.org/10.1007/978-1-4612-2506-5
Sarukkai, S. (2004) Philosophy of Symmetry, Shimla, India: Indian Institute of Advanced Study.
Van Fraassen, B.C. (1989) Law and Symmetry, Oxford, UK: Oxford University Press.
Zadeh, L.A. (1965) Fuzzy sets, Information and Control, 8, 3, 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
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