The Spectrum of Thought: Unveiling the Richness of Mathematical Pluralism

Authors

  • Wenjie Ye

DOI:

https://doi.org/10.61173/ybx6az09

Keywords:

Mathematical Pluralism, Mathematics, Philosophy

Abstract

This paper embarks on a thorough journey through mathematical pluralism, examining its philosophical underpinnings, theoretical landscapes, and practical implications. This analysis starkly contrasts the monolithic portrayal of mathematics as an unchanging, universally applicable discipline, instead proposing a vision of mathematics as a mosaic of valid yet diverse frameworks. By dissecting the contributions of innovative scholars such as Michèle Friend, Graham Priest, and Stewart Shapiro and comparing foundational concepts such as set theory with category theory, this paper illuminates the diverse perspectives and approaches that enrich the mathematical landscape. It demonstrates how a pluralistic perspective on mathematics enhances our understanding of the field and compels us to reevaluate our core assumptions about knowledge, truth, and the nature of mathematical inquiry. This paper explores the effects of embracing a pluralistic viewpoint across different areas, calling for a more inclusive, adaptable, and interdisciplinary approach to mathematics education and research. Acknowledging the value of a diversity of mathematical approaches and theories paves the way for a future in which mathematics continues to evolve as a complex and vibrant discipline, mirroring the intricacies of the world it aims to decipher. This investigation serves as a celebration of the human capacity for intellectual pursuit, emphasizing the immense possibilities that arise from fostering a culture of plurality in mathematics and beyond.

References

[1] Benacerraf, Paul., and Hilary. Putnam. Philosophy of Mathematics : Selected Readings / Edited by Paul Benacerraf, Hilary Putnam. 2nd ed. Cambridge [Cambridgeshire] ; Cambridge University Press, 1983. Print.

[2] Bishop, A.J. “Western Mathematics: The Secret Weapon of Cultural Imperialism.” Race & Class. vol. 32, no. 2, 1990, pp. 51-65.

[3] Davies, E.B. “A Defence of Mathematical Pluralism.” Philosophia mathematica 13.3 (2005): 252–276. Web.

[4] Davies, E.B. “Pluralism in Mathematics.” Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences 363.1835 (2005): 2449–2460. Web.

[5] Davis, Philip J., and Reuben Hersh. The Mathematical Experience. Birkhäuser, 1981.

[6] Ernest, Paul. Social Constructivism as a Philosophy of Mathematics. State University of New York Press, 1998.

[7] Friend, Michèle. “Embracing the Crisis in the Foundations of Mathematics.” Les Cahiers D’Ithaque, 2013.

[8] Friend, Michèle. Pluralism in Mathematics: A New Position in Philosophy of Mathematics. 1st ed. 2014. Dordrecht: Springer Netherlands, 2014. Web.

[9] Friend, Michèle. “Pluralism and ‘Bad’ Mathematical Theories: Challenging Our Prejudices.” Paraconsistency: Logic and Applications. Dordrecht: Springer Netherlands, 2013. 277– 307. Web.

[10] Jonas, Silvia. “Mathematical Pluralism and Indispensability.” Erkenntnis (2023): n. pag. Web.

[11] Kitcher, Philip. The Nature of Mathematical Knowledge. Oxford University Press, 1984.

[12] Pedeferri, Andrea, and Friend, Michele. “Are Mathematicians Better Described as Formalists or Pluralists?” Logic and Philosophy of Science, vol. 9, no. 1, 2011, pp. 173- 180.

[13] Penrose, Roger. The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage, 2007.

[14] Priest, Graham. “A Note on Mathematical Pluralism and Logical Pluralism.” Synthese (Dordrecht) 198.Suppl 20 (2021): 4937–4946. Web.

[15] Priest, Graham. “How Do You Apply Mathematics?” Oxford University Press, Axiomathes, 32, 1169-1184.

[16] Priest, Graham. „The Logical Structure of Dialectic.“ History and Philosophy of Logic, vol. 44, 2023, pp. 200-208.

[17] Priest, Graham. „What If? The Exploration of an Idea.“ The Australasian Journal of Logic, vol. 14, 2017.

[18] Rodin, Andrei. “One Mathematic(s) or Many? Foundations of Mathematics in Today’s Mathematical Practice.” arXiv.org (2023): n. pag. Web

[19] Shapiro, Stewart. Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press, 2000.

[20] Tasic, Vladimir. Mathematics and the Roots of Postmodern Thought. Oxford University Press, 2001.

Downloads

Published

2024-06-06

Issue

Vol. 2 No. 3 (2024): Volume 2, Issue 3

Section

Articles

License

Copyright (c) 2024 by the authors.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.