The Arbitrariness of Symmetry in Mathematical Proofs

Authors

  • Melisa Vivanco The University of Texas Rio Grande Valley

DOI:

https://doi.org/10.22370/rhv2024iss25pp129-148

Keywords:

philosophy of mathematics, mathematical practice, explanation in mathematics, mathematical proof

Abstract

Symmetry is not an inherent characteristic of mathematical proofs; instead, it is a property that arbitrarily manifests in different modes of presentation. This arbitrariness leads to the conclusion that symmetry cannot be part of the defining or essential properties that characterize proofs. Consequently, contrary to some authors’ claims, symmetry does not significantly contribute to the validity, accuracy, or soundness of mathematical proofs. What is more, it does not even play any critical role in heuristic aspects such as explanatory power. The examples developed in this paper constitute compelling evidence supporting these claims.

References

Baker, Alan (2005). Are There Genuine Mathematical Explanations of Physical Phenomena? Mind, 114(454), 223-238. Oxford University Press. https://doi.org/10.1093/mind/fzi223

Bueno, Otávio; Vivanco, Melisa (2019). Resisting Non-causal Explanations. Analysis, 79(3), 550-559.

Edwards, A. W. F. (2002). Pascal’s arithmetical triangle: the story of a mathematical idea. JHU Press, pp. 30-31.

Fehige, Yiftach (2019). Thought Experiments in Philosophy. The Stanford Encyclopedia of Philosophy Stanford University. https://plato.stanford.edu/entries/thought-experiment/

Lange, Marc (2009). Why proofs by mathematical induction are generally not explanatory. Analysis, 69(2), 203-211.

Lange, Marc (2013). What Makes a Scientific Explanation Distinctively Mathematical? The British Journal for the Philosophy of Science, 64(3), 485-511. Oxford University Press. https://doi.org/10.1093/bjps/axs028

Lange, Marc (2014). Depth and Explanation in Mathematics. Philosophia Mathematica, 23(2), 196-214.

Lange, Marc (2017). Because Without Cause. Oxford University Press.

Mancosu, P. (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. Oxford University Press.

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Published

2024-07-25

How to Cite

Vivanco, M. (2024). The Arbitrariness of Symmetry in Mathematical Proofs. Revista De Humanidades De Valparaíso, (25), 129–148. https://doi.org/10.22370/rhv2024iss25pp129-148

Issue

No. 25 (2024)

Section

Articles

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