The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology
DOI:
https://doi.org/10.54097/ehss.v8i.4282Keywords:
Set Theory; Infinity; Metaphysics.Abstract
Infinity is possibly one of the most complicated conceptions confronting mathematics and philosophy. People could always conceive it via intuition, but find it hard to describe in the logical realm. In the 19th century, German mathematician Cantor proposed the set theory, for the first time, people could use mathematical tools to explain the nature of infinity. However, such an explanation still lies on the axiomatic foundation, which does not directly fit our intuition about infinity. Therefore, this study will attempt to establish a 'bridge' between the infinity that fits intuition and the infinity that is described by set theory, hence arguing why the set theory could describe infinity universally in the senses of metaphysics and ontology.
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References
Schechtman, A. Three Infinities in Early Modern Philosophy. Mind, 2019, 128(512): 1117–1147. DOI: https://doi.org/10.1093/mind/fzy034
Soteropoulos, People. Metaphysics of infinity: The problem of motion and the infinite brain. UPA, 2013.
Aristotle, A., & Aristotle. Metaphysics (Vol. 1, p. 9). Cambridge, MA: Harvard University Press, 1993.
Usó-Doménech, J.-L., Selva, J. A. N., & Requena, M. B. Mathematical, Philosophical and Semantic Considerations on Infinity (People): General Concepts. Foundations of Science, 2015, 21(4): 615–630. DOI: https://doi.org/10.1007/s10699-015-9428-9
Linnebo, Øystein, & Shapiro, S. Actual and Potential Infinity. Noûs (Bloomington, Indiana), 2019, 53(1): 160–191. DOI: https://doi.org/10.1111/nous.12208
Bussotti, P., & Tapp, C. The influence of Spinoza’s concept of infinity on Cantor’s set theory. Studies in History and Philosophy of Science. Part A, 2009, 40(1): 25–35. DOI: https://doi.org/10.1016/j.shpsa.2008.12.010
Pantsar, M. In search of ℵ₀: how infinity can be created. Synthese (Dordrecht), 2015, 192(8): 2489–2511. DOI: https://doi.org/10.1007/s11229-015-0775-4
Kuhn, G. J. Metaphysics and mathematics: perspectives on reality. Hervormde Teologiese Studies, 2017, 73(3): 1–8. DOI: https://doi.org/10.4102/hts.v73i3.4663
Krátká, M., Eisenmann, P., & Cihlář, J. Four conceptions of infinity. International Journal of Mathematical Education in Science and Technology, ahead-of-print(ahead-of-print), 2021, 1–25. DOI: https://doi.org/10.1080/0020739X.2021.1897894
Usó-Doménech, J. L., Nescolarde-Selva, J., Belmonte-Requena, M., & Gash, H. Walking Through Cantor's Paradise and Escher's Garden: Epistemological Reflections on the Mathematical Infinite (People). Cybernetics and Systems, 2015, 46(6-7): 423–437. DOI: https://doi.org/10.1080/01969722.2015.1038473
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