The Concept of Infinity under German Idealism and Modern Set Theory

Research Article
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The Concept of Infinity under German Idealism and Modern Set Theory

Xin Tong 1* , Siyuan Fu 2 , Kaixuan Huang 3
  • 1 Qingdao No.2 Middle School, Qingdao, Shandong, 266061, China    
  • 2 Shenzhen College of International Education, Shenzhen, Guangdong, 518023, China    
  • 3 Pegasus California School, Qingdao, Shandong, 266114, China    
  • *corresponding author 15020440217@xs.hnit.edu.cn
CHR Vol.4
ISSN (Print): 2753-7072
ISSN (Online): 2753-7064
ISBN (Print): 978-1-915371-31-7
ISBN (Online): 978-1-915371-32-4

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

Tong,X.;Fu,S.;Huang,K. (2023). The Concept of Infinity under German Idealism and Modern Set Theory. Communications in Humanities Research,4,282-290.
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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.


Cite this article

Tong,X.;Fu,S.;Huang,K. (2023). The Concept of Infinity under German Idealism and Modern Set Theory. Communications in Humanities Research,4,282-290.

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About volume

Volume title: Proceedings of the International Conference on Interdisciplinary Humanities and Communication Studies (ICIHCS 2022), Part 2

ISBN:978-1-915371-31-7(Print) / 978-1-915371-32-4(Online)
Editor:Faraz Ali Bughio, David T. Mitchell
Conference website: https://www.icihcs.org/
Conference date: 18 December 2022
Series: Communications in Humanities Research
Volume number: Vol.4
ISSN:2753-7064(Print) / 2753-7072(Online)

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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.