The Hypercategorematic Infinite

This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss the issue of whether the hypercategorematic infinite is a “whole”, comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things

Evolution of Leibniz's thought in the matter of fictions and infinitesimals

In this paper we offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability and syncategorematicity, and the closely related question of the possibility of infinitesimal quantities, both in physics and in mathematics. Some scholars have argued that syncategorematicity is a mature acquisition, to which Leibniz resorts to solve the question of his infinitesimals namely the idea that infinitesimals are just signs for Archimedean exhaustions, and their unassignability is a nominalist maneuver. On the contrary, we show that sycategorematicity, as a traditional idea of classical scholasticism, is a feature of young Leibniz's thinking, from which he moves away in order to solve the same problem, as he gains mathematical knowledge. We have divided Leibniz's path toward his mature view of infinitesimals into five phases, which are especially significant for reconstructing the entire evolution. In our reconstruction, an important role is played by Leibniz's text De Quadratura Arithmetica. Based on this and other texts we dispute the thesis that fictionality coincides with syncategorematicity, and that unassignability can be bypassed. On the contrary, we maintain that unassignability, as incompatible with the principle of harmony, is the ultimate reason for the fictionality of infinitesimals.Comment: 36 page

On the Relation between Natural Philosophy, Mathematics and Logic in the Investigation on Atomism in the Middle Ages

In the first half of the fourteenth century, a great polemic surrounding atomistic conceptions arose at the University of Oxford and the University of Paris. This paper will focus on the use of two tools of investigation on atomism, to wit, "thought experiments" and the "theory of supposition", which reveal the prominence of the a priori in late medieval debates on atomism. The paper intends to show the heuristic role of those two tools in the investigation of unobservable phenomena. The imaginative scenarios express the relation between natural philosophy, mathematics and logic, illustrating the medieval conception of science.En la primera mitad del siglo xiv, se ha levantado en la Universidad de Oxford y en la Universidad de París una gran polémica en torno a las concepciones atomistas. Este trabajo se centrará en el uso de dos herramientas de investigación en el atomismo, a saber, los "experimentos de pensamiento" y la "teoría de la suposición", que revelan la prominencia de lo a priori en los debates medievales tardíos sobre el atomismo. El artículo pretende mostrar el papel heurístico de estas dos herramientas en la investigación de fenómenos no observables. Los escenarios imaginativos expresan la relación entre la filosofía natural, la matemática y la lógica, ilustrando la concepción medieval de la ciencia

Nominalism Meets Indivisibilism

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