Quantifying Aristotelian essences: On some fourteenth-century applications of limit decision problems to the perfection of species

Abstract

ABSTRACT This paper explores a specific problem within an important philosophical genre of the fourteenth century: the debates over the perfection of species. It investigates how the problem of defining limits for continuous magnitudes – a problem typical of Aristotelian physics – was integrated into these debates at the levels of genera, species, and individuals as these entities began to be conceptualized in quantitative terms. After explaining the emergence of this problem within fourteenth-century metaphysics, the paper examines the contributions of three philosophers – Hugolinus of Orvieto, John of Ripa, and Paul of Venice – who offered varying solutions to the challenge of defining limits between species. It demonstrates that two primary solutions arose, inspired by continuous and discrete mathematical objects. It is shown that whereas Hugolinus of Orvieto advocates for a continuist model, John of Ripa proposes a discrete one. The last part of the paper examines Paul of Venice's hybrid approach, which combines elements from both models, facilitating a more comprehensive treatment of species particularly difficult to analyse, namely geometric figures. The conclusions of this comparative study underscore how profoundly the metaphysical reflections of the Middle Ages contributed to the analysis of the structure of the continuum and the extension of the notion of quantity to various objects.