# The theory of ideas and Plato’s philosophy of mathematics

## Main Article Content

## Abstract

In this article I analyze the issue of many levels of reality that are studied by natural sciences. Particularly interesting is the level of mathematics and the question of the relationship between mathematics and the structure of the real world. The mathematical nature of the world has been considered since ancient times and is the subject of ongoing research for philosophers of science to this day. One of the viewpoints in this field is mathematical Platonism.

In contemporary philosophy it is widely accepted that according to Plato mathematics is the domain of ideal beings (ideas) that are eternal and unalterable and exist independently from the subject’s beliefs and decisions. Two issues seem to be important here. The first issue concerns the question: was Plato really a proponent of present-day mathematical Platonism? The second one is of greater importance: how mathematics influences our understanding of the nature of the world on its many ontological levels?

In the article I consider three issues: the Platonic theory of “two worlds”, the method of building a mathematical structure, and the ontology of mathematics.

## Article Details

*Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce)*, (66), 95–108. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/468

## References

Aristotle, 1924. Aristotle’s Metaphysics: A Revised Text with Introduction and Commentary. Ed. by W.D. Ross. Vol. 2. Oxford: Clarendon Press.

Brown, J.R., 2008. Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures. 2nd ed, Routledge contemporary introductions to philosophy. New York - London: Routledge.

Dembiński, B., 2003. Późna nauka Platona: związki ontologii i matematyki, Prace Naukowe Uniwersytetu Śląskiego w Katowicach nr 2143. Katowice: Wydaw. Uniwersytetu Śląskiego.

Dembiński, B., 2007. Streit um die "Zweiweltentheorie" in der Philosophie von Plato. Proceedings of the Twenty-First World Congress of Philosophy. Ankara: Philosophical Society of Turkey, pp.67–72. Available at: https://doi.org/10.5840/wcp21200710115.

Dembiński, B., 2010. Późny Platon i Stara Akademia [Late Plato and the Old Academy], Fundamenta: studia z historii filozofii t. 63. Kęty: Wydawnictwo Marek Derewiecki.

Dillon, J.M., 2003. The Heirs of Plato: A Study of the Old Academy (347-274 B.c.) Oxford: Clarendon Press.

Heller, M., 2006. Filozofia i wszechświat: wybór pism. Kraków: TAiWPN UNIVERSITAS.

Plato, 1955. Platonis Opera. Recognovit Brevique Adnotatione Critica Instruxit Joannes Burnet. Vol 1-5. Ed. by J. Burnet, Scriptorum Classicorum Bibliotheca Oxoniensis. Oxonium: Typographeo Clarendoniano.