Communications in Humanities Research ISSN: 2753-7072
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Research Article

The Concept of Infinity under German Idealism and Modern Set Theory

Xin TongQingdao No.2 Middle School, Qingdao, Shandong, 266061, China* Siyuan FuShenzhen College of International Education, Shenzhen, Guangdong, 518023, China Kaixuan HuangPegasus California School, Qingdao, Shandong, 266114, China

* Corresponding author: [email protected]

Abstract

The purpose of this paper is to compare and analyse the concepts of infinity in German idealism and Modern set theory. The fisrt part of this paper analyses Kant and Hegel’s views on mathematical infinity, where Kant suggests a notion of potential infinity constructed by means of intuition, while Hegel that of actual infinity. The second part illustrates the characteristics of Cantorian transfinite sets and both the progress it has made and the limitations. Following the two main parts, not only a clear contrast between the notions of infinity under German idealism and Cantorian set theory can be made but their close link can also be shown. By analysing perspectives of Frege’s logicism, Hilbert’s formalism, Brouwer’s intuitionism, and Badiou’s comments, it is clear German idealism has lost its mainstream position in understanding the mathematical concept of infinity. However, the concept of infinity in German idealism can be supplied as a powerful facilitator for philosophers and mathematicians to understand this concept in the realm of mathematics.

Keywords: German idealism; set theory; infinity
Published: May 17, 2023
DOI: 10.54254/2753-7064/4/20220494
Volume: CHR Vol.4
pp. 282-290
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References

  1. Kant, I., Critique of Pure Reason, Penguin Classics, London, 2007.
  2. Liu, F.J., Kant’s Conception of Real Infinity, Philosophical Research, 2020.
  3. Shabel, L., Kant’s Philosophy of Mathematics, Stanford Encyclopedia of Philosophy, First published Fri Jul 19, 2013, substantive revision Wed Aug 11, 2021. Received from https://plato.stanford.edu/entries/kant-mathematics/.
  4. Shapiro, S., Thinking about Mathematics: The Philosophy of Mathematics, Oxford University Press, Oxford, 2000.
  5. Shapiro, S., Linnedo, Ø., Actual and Potential Infinity, NOUS, 2019.
  6. Hegel, G. W. F., Die Wissenschaft der Logik, China Remin University Press, Beijing,2019.
  7. Zambrana, R., Hegel’s Theory of Intelligibility, The University of Chicago Press, Chicago, 2015.
  8. Zizek, S., Tarrying with the Negative: Kant, Hegel, and the Critique of Ideology, Nanjing University Press, Nanjing, 2015.
  9. Hausman, A., Kahane, H., Tidman, P., Logic and Philosophy: A Modern Introduction, Wadswords Cengage Learning, Boston, 2010.
  10. Why Psychology is “Not a Science”: Base on A Hegelian Perspective
  11. Papineau, D., Philosophical Devices, Oxford University Press, Oxford, 2012.
  12. Hao, Z. K., Yang, Y., Set Theory: Exploration to the Concept of Infinity
  13. Eawaran, K., Hájek, A., Mancosu, P., Oppym, G., Infinity, Stanford Encyclopedia of Philosophy, 2021. Received from https://plato.stanford.edu/entries/infinity/.
  14. Wang, H., Beyond Analytic Philosophy, Zhejiang University Press, Hangzhou, 2010.
  15. Badiou, A., Being and Event, Nanjing University Press, Nanjing, 2018.
  16. On Kant’s Time Graphics and its Phenomenological Interpretation, Yang, Y. F., Wuhan University, Wuhan, 2004.
  17. Caygill, H., A Kant Dictionary, Wiley-Blackwell, Malden, 1995.
  18. Yan, Z. S., Badiou on Being and Event, Journal of Tsinghua University, 2013.