The Platonic Theory of the One, the Many, and the Cosmos within Contemporary Philosophy of Mathematic

In this article, the authors analyze unity as a fundamental principle of Platonic philosophy from in relation to the foundations of modern mathematics, identifying its inherent limitations. They explore the ancient natural philosophical sources and the historical context of the Platonic understanding of number, which shaped the Platonic concept of the One and the Many, revealing its problematic aspects. These issues were subsequently preserved in Christianized Platonism (notably in the Areopagitica and its dependent traditions), which provided an orthodox theology with its classical theoretical framework. The authors believe that this analysis complements (1) Heidegger's critique of Platonic ontology; (2) post-metaphysical discourse in theology; and (3) the tradition of employing mathematical analysis to address theological and philosophical problems, particularly with Anglo-American analytical philosophy. The purpose of this work is to characterize the fundamental problem of cosmogony based on the Platonic concept presented in the dialogue Parmenides through mathematical analysis. The specific objectives are: 1) to prove the relevance and significance of the mathematical approach to analyzing classical European philosophical systems, including their theological implications; 2) to provide a brief overview of the Platonic concept of the Absolute; 3) to identify problematic aspects of this concept within the context of mathematical foundations; 4) and to examine the Platonic notion of the Absolute concerning the principles of continuity in unity.

Keywords: Plato; platonism; One; Many; number; continuity; Parmenides; philosophy of mathematics