La distinction que Descartes opère entre infini et indéfini est bien connue et a été abondamment commentée. On se trompe souvent, pourtant, sur la véritable nature de cet indéfini. La plupart des interprètes, du XVIIe siècle à nos jours, le réduisent à un infini en son genre, dont le genre serait l’étendue, qualifié notamment d’infini « en extension », « spatial », « négatif », « potentiel », ou « quantitatif ». Allant à l’encontre d’une telle interprétation, cet article montre (...) que l’indéfini cartésien n’est à proprement parler ni infini, pas même en son genre, ni fini, et que sa véritable nature est l’indétermination. (shrink)

This essay explores the vexed issue of individual corporeal substance in Descartes' natural philosophy. Although Descartes' often referred to individual material objects as separate substances, the constraints on his definitions of matter and substance would seem to favor the opposite view; namely, that there exists only one corporeal substance, the plenum. In contrast to this standard interpretation, however, it will be demonstrated that Descartes' hypotheses make a fairly convincing case for the existence of individual material substances; and the key to (...) this new found individuation is a long neglected set of passages in the Principles of Philosophy. (shrink)

Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

Descartes notoriously characterizes substance in two ways: first, as an ultimate subject of properties ; second, as an independent entity. The characterizations have appeared to many to diverge on the definition as well as the scope of the notion of substance. For it is often thought that the ultimate subject of properties need not—and, in some cases, cannot—be independent. Drawing on a suite of historical, textual, and philosophical considerations, this essay argues for an interpretation that reconciles Descartes's two characterizations. It (...) proposes that both characterizations invoke a type of independence that obtains just in case there is no relation to another entity that holds by the nature of the entity in question. Even though the ultimate subject of properties is sometimes not independent in other respects, it satisfies this independence-by-nature condition. (shrink)

the meditations on first philosophy presents us with an alleged proof for the existence of God that proceeds from the existence of an idea of an infinite being in the human mind—an idea of God—to the existence of God himself. Insofar as we have an idea of an infinite being, an idea with “infinite objective reality,” we can legitimately ask whence it came to us. The only possible cause of this idea, claims Descartes, is an infinite being, namely, God. The (...) occurrence of just this idea in the proof is essential. In fact, Descartes maintains that any such causal proof for God’s existence crucially relies on this idea: “it seems to me that all these proofs based on his effects are reducible to a single one; and also .. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

: Given Descartes's conception of extension, space and body, there are deep problems about how there can be any real motion. The argument here is that in fact Descartes takes motion to be only phenomenal. The paper sets out the problems generated by taking motion to be real, the solution to them found in the Cartesian texts, and an explanation of those texts in which Descartes appears on the contrary to regard motion as real.

Seventeenth-century authors frequently infer the attributes of time by analogy from already established features of space. The rationale for this can be traced back to Aristotle's analysis of time as ?the number of movement?, where movement requires a prior understanding of spatial magnitude. Although these authors are anti-Aristotelian, they were concerned, contra Aristotle, to establish the existence of ?empty space?, and a notion of absolute space which fit this idea. Although they had no independent rationale for the existence of absolute (...) time, it seemed to go with absolute space, and they drew on a long tradition of space-time parallelism in securing this. (shrink)

God and time play crucial, intricately related roles in Descartes' project of grounding mathematical physics on metaphysical first principles. This naturally raises the perennial theological question of God's precise relation to time. I argue, against the strong current of recent commentary, that Descartes' God is fully temporal. This means that God's duration is successive, with parts ordered 'before and after', rather than permanent or 'all at once'. My argument will underscore the seamless connection between Descartes' theology and his physics, and (...) the degree to which he was prepared to depart from orthodoxy in the former in order to secure an a priori foundation for the latter. As Newton would later do, Descartes freed time from its traditional dependence on bodily motion and so removed an important barrier to making God temporal. Acting in time, God makes the physical world intelligible in a way He could not were He timeless. (shrink)

Descartes' account of the material world relies heavily on time. Most importantly, time is a component of speed, which figures in his fundamental conservation principle and laws. However, in his most systematic discussion of the concept, time is treated as some-how reducible both to thought and to motion. Such reductionistic views, while common among Descartes' late scholastic contemporaries, are very ill-suited to Cartesian physics. I show that, in spite of the apparent identifications with thought and motion, Cartesian time retains—in the (...) form of what I will call 'successive duration'—precisely the intrinsic structure necessary to serve as an independent parameter of quantitative physics. As is often the case with Descartes, he gives the impression of embracing traditional doctrines while in fact radically transforming the underlying concepts to serve his scientific agenda. His theory of time, though formulated in Aristotelian terms, anticipates Newton in important respects. (shrink)

: Descartes provides an original and puzzling argument for the traditional theological doctrine that the world is continuously created by God. His key premise is that the parts of the duration of anything are "completely independent" of one another. I argue that Descartes derives this temporal independence thesis simply from the principle that causes are necessarily simultaneous with their effects. I argue further that it follows from Descartes's version of the continuous creation doctrine that God is the instantaneous and total (...) cause of everything that happens, and that this is just what his physics demands. But although God is the total cause of everything, he is not the only cause, since Descartes considers it obvious that finite minds have the power to move bodies. In the face of this apparent paradox, several recent commentators have suggested that Descartes accepted the late scholastic view that God and finite causes somehow collaborate or concur in the production of numerically identical effects. But close examination reveals that the case for Cartesian concurrentism is weak. Fortunately, there is a simpler and more fruitful solution to the problem of reconciling divine and human action. I argue that that in Descartes's world certain motions, such as voluntary movements of our bodies, are causally overdetermined This account allows Descartes to avoid occasionalism without embracing an elaborate metaphysics of secondary causality. Finally, I argue that the overdeterminist interpretation sheds new light on two longstanding problems of Cartesian metaphysics. First, it resolves a serious difficulty with a standard reading of Descartes's conception of human freedom. Second, it offers a novel approach to the old problem of reconciling genuine human action with the principle of the conservation of total quantity of motion. (shrink)

Physiologia provides an accessible and comprehensive guide to late Aristotelian natural philosophy; with that context in hand, it offers new interpretations of major themes in Descartes’s natural philosophy.

Drawing on Descartes' account of générosité, a reinterpretation of the Cogito is offered, emphasizing the role of the will. The paper's first part focuses on Cartesian ethics. It is argued that Descartes can be viewed as a Stoical thinker rather than a Baconian one. That is, he holds that theoretical contemplation is itself the primary ground of human happiness and tranquility of mind – experienced as the feeling of générosité. The paper's second part draws on the first in accounting for (...) the relation between radical doubt and certainty. By engaging with doubt, it is argued, the meditator comes to experience générosité, assert freedom. This experience is not, then, as argued by some, merely the Cogito's ethical counterpart. It is rather the Cogito's foundation. The meditator's assertion sum follows from – insofar as freedom is, as the definition of générosité asserts, ‘the only thing truly belonging to us', it consists in – the assertion of freedom. (shrink)

Suárez's discussion of time in the Metaphysical Disputations is one of the earliest long treatises on time (extending over sixty pages), and includes detailed arguments supporting the view that physical actions take place within an absolute temporal reference frame. Whereas some previous thinkers, such as John Duns Scotus and Peter Aureole, had made tantalising suggestions that time exists independently of physical changes, their ideas were primarily negative theses in response to perceived problems with the dominant view that time was caused (...) by the celestial motion. Suárez, in contrast, provides a positive thesis based on his revision of traditional, Scholastic metaphysics. He argues that the ordering of earlier and later events can only be understood by conceiving events as existing within the embrace of a ?flowing and successive space? which he refers to as ?entirely necessary and immutable in its own flux? (omnino necessarium et immutabile in suo fluxu) - something at least very like an absolute temporal reference frame. Yet it would be simplistic to describe Suárez's work on time only in terms of its nascent absolutism, since for him there is a second kind of time, a more properly ?real? time, which is an accident of material being. This kind of time is ontologically tied to the most intimate existence of objects, creating a plurality of individual continua of time - one for each distinct being. He calls this kind of time ?intrinsic time? (tempus intrinsecum). Suárez's dualistic account of time, in which he proposes an ?intrinsic time?, linked to being, which exists within a second order absolute temporal reference frame, or ?imaginary succession?, forms a bridge between scholasticism and early modern philosophy providing a foundation for the work of later absolutists like Gassendi and Newton. (shrink)

These selections from Le système du monde, the classic ten-volume history of the physical sciences written by the great French physicist Pierre Duhem (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology.

This book offers a comprehensive treatment of the philosophical system of the seventeenth-century philosopher Pierre Gassendi. Gassendi's importance is widely recognized and is essential for understanding early modern philosophers and scientists such as Locke, Leibniz and Newton. Offering a systematic overview of his contributions, LoLordo situates Gassendi's views within the context of sixteenth- and early seventeenth-century natural philosophy as represented by a variety of intellectual traditions, including scholastic Aristotelianism, Renaissance Neo-Platonism, and the emerging mechanical philosophy. LoLordo's work will be essential (...) reading for historians of early modern philosophy and science. (shrink)

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

Letter to du Faur de Pibrac, 1621.--Exercises against the Aristotelians, 1624.--Letter to Diodati, 1634.--De motu, 1642.--The rebuttals against Descartes, 1644.--The syntagma, 1658.

We argue that Descartes’s theistic proofs in the ’Meditations’ are much simpler and straightforward than they are traditionally taken to be. In particular, we show how the causal argument of the "Third Meditation" depends on the intuitively innocent principle that nothing comes from nothing, and not on the more controversial principle that the objective reality of an idea must have a cause with at least as much formal reality. We also demonstrate that the so-called ontological "argument" of the "Fifth Meditation" (...) is best understood not as a formal proof but as an axiom, revealed as self-evident by analytic meditation. (shrink)