Mathematics and Geometry: Two Key Concepts in Plato’s Theory of Ideas

Year 2025, Volume: 13 Issue: 2, 170 - 174, 31.10.2025

Aysun Aydın

Abstract

The mathematical reasoning, mathematical objects and the mathematical knowledge are important aspects of Greek philosopher Plato’s philosophy. In his Theory of Ideas, mathematical reasoning provides the truth and the method for achieving the true knowledge of reality. In his theory, Plato argues the distinction between two worlds. The first is world of Ideas, which refers the timeless, abstract and unchanged world of Being, and the second is world of appearances, which refers visible, sensible and changeable world of Becoming. According to this dualist theory, mathematical objects belongs to the world of Being and mathematical reasoning is an only method that provides to conceive the idea of good and the truths in this real world. Plato frequently presents and expresses the priority of mathematics in his dialogues and he refers mathematical objects as the main subjects of philosophy. Accordingly, he puts the mathematics as a propaedeutic to philosophy. In this respect, the evaluation and analyzing the place of mathematics in Plato’s view and showing the importance of mathematical reasoning in philosophy are main purposes of this study. This evaluation is valuable for both understanding Plato’s Theory of Ideas and showing the inseparable relationship between mathematics and philosophy.

Keywords

Plato , mathematics , mathematical ontology , geometry.

References

• [1] Burgin, M., “Ideas of Plato in the Context of Contemporary Science and Mathematics”, Athens Journal of Humanities and Arts, 4. 3 (2017), 161-182.
• [2] Burnyeat, M.F., “Plato on Why Mathematics Good for the Soul”, Proceedings of the British Academy, 103 (2000), 1-81.
• [3] Brumbaugh, R. S., “Plato’s Divided Line”, The Review of Metaphysics, 5. 4 (1952), 529-534.
• [4] Cherniss, H., Plato as Mathematician, The Review of Metaphysics, 4. 3 (1951), 395-425.
• [5] Dembinski, B., “The Theory of Ideas and Plato’s Philosophy of Mathematics”, Philosophical Problems in Science, 66 (2019), 95-108.
• [6] Fogelin, R. J., “Three Platonic Analogies”, The Philosophical Review, 80. 3 (1971), 371-382.
• [7] Miller, J. G., “Plato and Pythagoreanism by Horky”, HOPOS: The Journal of the International Society for the History of Philosophy of Science, 4. 2 (2014), 391-393.
• [8] Mueller, I., “Mathematics and the Divine in Plato”, Mathematics and the Divine: A Historical Study, (ed. T. Koetsier & L. Bergmans), Elsevier B. V. (2005)
• [9] Plato, Meno, (trans.G. M. A. Grube), https://commons.princeton.edu/eng574-s23/wp-content/uploads/sites/348/2023/02/Plato-Meno.pdf
• [10] Plato, The Republic, Cambridge University Press, Cambridge, 2018.
• [11] Ebert, T. “Plato’s Theory of Recollection reconsidered an interpretation of Meno 80a–86c”, Continental Philosophy Review, 6 (1973), 163-181.
• [12] Rose L. E., “Plato’s Divided Line”, The Review of Metaphysics, 17. 3 (1964), 425-435.
• [13] Stumpf, S. E., Philosophy History and Problems, McGraw Hill, New York, 1994.