The present PhD dissertation aims to examine the relation between modality and change in Aristotle’s metaphysics. -/- On the one hand, Aristotle supports his modal realism (i.e., worldly objects have modal properties - potentialities and essences - that ground the ascriptions of possibility and necessity) by arguing that the rejection of modal realism makes change inexplicable, or, worse, banishes it from the realm of reality. On the other hand, the Stagirite analyses processes by means of modal notions (‘change is the (...) actuality of what is virtual insofar as it is virtual’). In other words: to grasp what change is, one has to resort to the modal idiom of potentialities, while the fact that there is change is indicative of the fact that nature is full of modal properties. -/- Aristotle’s modal and kinetic realism finds a negative in the figure of the Megaric Diodorus Kronus. The polemical situation of Greek philosophy has indeed the dialectical advantage of not opposing the Aristotelian position to a sui generis straw man. Both in its reduction of modal judgements to temporal quantifications and in its dissolution of the reality of the state-of-being-in-motion in favour of a cinematographic view of processes, the philosophical figure of reductionist antirealism embodied by Diodorus constitutes an alternative that takes the opposite view of Aristotle’s realism. -/- The present study is structured as a discussion between these two positions. In the face of Diodorus’ antirealist challenges, Aristotle articulates modal and kinetic considerations: the answers he gives to Diodorus’ puzzles thus provide valuable insight into his metaphysics. Moreover, the examination of Aristotle’s and Diodorus’ metaphysics, because of their insight and originality, will not fail to interest the philosopher concerned with the metaphysical foundations of modern physics, insofar as the entanglement between modalities and processes is nowadays at the core of mechanics (phase spaces, path integrals, etc.). (shrink)

This anthology is about the signal change in Leibniz’s metaphysics with his explicit adoption of substantial forms in 1678-79. This change can either be seen as a moment of discontinuity with his metaphysics of maturity or as a moment of continuity, such as a passage to the metaphysics from his last years. Between the end of his sejour at Paris and the first part of the Hanover period, Leibniz reformed his dynamics and began to use the theory of corporeal substance. (...) This book explores a very important part of the philosophical work of the young Leibniz. Expertise from around the globe is collated here, including Daniel Garber’s work based on the recent publication of Leibniz's correspondence from the late 1690s, examining how the theory of monads developed during these crucial years. Richard Arthur argues that the introduction of substantial forms, reinterpreted as enduring primitive forces of action in each corporeal substance, allows Leibniz to found the reality of the phenomena of motion in force and thus avoid reducing motion to a mere appearance. Amongst other themes covered in this book, Pauline Phemister’s paper investigates Leibniz’s views on animals and plants, highlighting changes, modifications and elaborations over time of Leibniz’s views and supporting arguments and paying particular attention to his claim that the future is already contained in the seeds of living things. The editor, Adrian Nita, contributes a paper on the continuity or discontinuity of Leibniz’s work on the question of the unity and identity of substance from the perspective of the relation with soul and mind. (shrink)

In this paper we study the impact of Leibniz’s critique of infinite numbers in his metaphysics of bodies. After presenting the relation that the German philosopher establishes in his youth between the notions of body, extension and infinite quantities, we analyze his thoughts on the paradoxes of the infinite numbers and we claim that his defense of the inconsistency of such numbers is an inflexion point in his conception of body and mark the beginning of his offensive against the res (...) extensa. (shrink)

This paper is intended to examine the distinction made by Leibniz in Generales Inquisitiones de Analysi Notionum et Veritatum between essential and existential propositions, in order to shed some light on the nature of the analogies that Leibniz proposes between the logical problem of contingency and the geometrical problem of the continuum.

Resumen: En este trabajo examinaremos la evolución del tratamiento de la noción de “espacio” en los escritos de juventud de Leibniz. Distinguiremos tres momentos del desarrollo de esta noción. En un primer momento, consideraremos la concepción del espacio como un “lugar universal” que el filósofo de Leipzig presentó entre 1669 y 1671. En segundo lugar, abordaremos algunos escritos físicos de 1672 en los que introdujo el movimiento en la definición de cuerpo. Esto lo llevó a rechazar su concepción anterior del (...) espacio como “lugar universal”. En tercer lugar, consideraremos algunos textos redactados entre 1675 y 1676 en los que elaboró un examen de la noción de “espacio universal” que difiere de la concepción desarrollada en el periodo preparisino y que se vincula con el surgimiento de la noción de extensión como atributo de Dios.: In this paper we will examine the evolution of the treatment of the notion of “space” in the young Leibniz’s writings. We will distinguish three moments of the development of this notion. First, we will consider the conception of space as a “universal place” which the philosopher of Leipzig presented between 1669 and 1671. Then, we will examine some physical writings of 1672 in which he introduced motion in the definition of body. This led him to reject his previous conception of space as “universal place”. Third, we will consider some texts written between 1675 and 1676 in which he developed an exam of the notion of “universal space” which differs from the conception he held in the pre-Parisian period and which is related with the emergence of the notion of extension as an attribute of God. (shrink)

Resumen En este trabajo evaluamos el impacto que la adopción de la relatividad del movimiento tiene en la metafísica de Leibniz. En particular argumentamos que el abandono de la comprensión absolutista del mismo anula su noción juvenil de sustancia corpórea. En primer lugar analizamos cómo entiende Leibniz las nociones de cuerpo y movimiento en el periodo juvenil y defendemos que la comprensión absolutista de este último constituye una piedra angular en su primera concepción de la sustancia corpórea. En segundo lugar (...) exponemos los argumentos leibnizianos a favor de la relatividad del movimiento durante el período parisino y mostramos su repercusión en el concepto juvenil de sustancia corpórea.In this paper we evaluate the impact of Leibniz's defense of relativity of motion on his metaphysics. We argue that the abandonment of the absolutist position makes void his first notion of corporeal substance. First, we analyze Leibniz's conception of body and movement in his youth and explain how the assumption of absolute motion during these years plays a role in his notion of corporeal substance. Second, we examine his arguments in favor of relativity of motion during the Parisian period and show the repercussion on his first conception of the corporeal substance. (shrink)

En el presente trabajo analizamos la reforma que Leibniz propone entre 1677 y 1695 en la noción de cuerpo y, a partir de ello, esclarecemos el concepto de sustancia corpórea que presenta en esos años. En primer lugar, desarrollamos las críticas que esgrime contra la concepción geométrica del cuerpo propia de los filósofos modernos; en segundo lugar, examinamos los cambios que propone en dicha noción y su caracterización en clave de fuerza primitiva pasiva; en tercer lugar, estudiamos la definición hilemórfica (...) de la sustancia corpórea que ofrece y evaluamos el lugar que ella ocupa en su esquema metafísico. (shrink)

Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means of both (...) manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics. (shrink)