ScholarWorks@숙명여자대학교

초록

The aims of this article are, first, to infer the mathematical principles that Plato applied in designing the politeia (Plato’s state constitution) in the Laws, and second, to illuminate the mathematical principles he employed in structuring the institutions corresponding to a legislature and an executive. By doing so, the article aims to clarify the implications of these principles for determining the optimal size of legislative and executive bodies in representative democracies. To this end, the article examines the mathematical achievements of Plato’s era and their influence on his political philosophy, and then investigates the mathematical principles used in the design of the cosmos in the Timaeus - in particular, the number-theoretic and numerological properties of the numbers; the tetractys and the golden ratio; and the properties of the Platonic solids - in order to infer how these principles were applied to politeia and the number of citizens, 5,040 in the Laws. Next, it focuses on the Nocturnal Council (nykterinos syllogos) as a legislature and on the Law-Wardens (nomophylakas) and the Council ( boulé) as an executive, and interprets the characteristics of wisdom (phronēsis), friendship (philia), equality, and geometric-harmonic relations by applying mathematical principles to their purposes, composition, and relationship. Finally, it seeks to elucidate the implications of these applications and interpretations for the legislative and executive institutions of contemporary representative democracy.

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