R??SUM???? travers l?????tude de la correspondance philosophique entre Descartes et Henry More, je souhaiterais montrer que les th??mes centraux en sont la consid??ration de la nature de l???espace et le statut de l???infini, bien que la pol??mique aborde??galement le probl??me ontologique de la distinction entre l?????tendue et la pens??e, et les questions physiques de la n??gation du vide et de l???atomisme. More rejette l???hypoth??se cart??sienne d???un univers ind??fini, qu???il consid??re??tre une mani??re d??tourn??e de postuler le caract??re infini de l???univers, ce (...) qui revient?? attribuer tout autant l???infinit???? la mati??re qu????? Dieu, d???o?? le fait que Descartes soit un mat??rialiste selon Henry More. ABSTRACT The correspondence between Descartes and More covers a diversity of each author???s fundamental philosophical views. Their polemics range over not only general aspects of physics, but also extend to cosmology and theology. On the one hand, we have God as infinite and His creation as indefinite for Descartes; on the other hand, God as extant, ubiquitous and omnipresent, and His creation as limited for Henry More. It is this last problem that constitutes the focus of my essay, strictly speaking??? the problem of the universe as infinite. (shrink)

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. (shrink)

"This book considers conditions of applicability of mathematics to the study of natural phenomena. The possibility of such an application is one of the fundamental assumptions underlying the enormous theoretical and practical success of modern science. Addressing problems of matter, substance, infinity, number, structure of cognitive faculties, imagination, and of construction of mathematical object, Dmitri Nikulin examines mathematical (geometrical) objects in their relation to geometrical or intelligible matter and to imagination. The author explores questions in the history of philosophy and (...) science, particularly in late antiquity and early modernity. The focus is on key thinkers Plotinus and Descartes (with the occasional appearance of Plato, Aristotle, Euclid, Proclus, Newton and others), in whom the fundamental presuppositions of ripe antiquity and of early modernity find their definite expression."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved. (shrink)

83 The SHIP-MASTER'S ASSISTANT, and OWNER'S MA- NUAL ; containing general Information necessary for Merchants, Owners, and Masters of Ships, Officers, ...

This chapter proposes to take the first few steps toward understanding the problematics of imagination in Descartes. It aims to show that in writings preceding the Regulae, Descartes conceived imagination as the chief faculty in the work of cognition, indeed the chief faculty for unifying knowledge. In this light the Regulae appears not simply as an early formulation of the principles of method, but as the tension-filled outcome of an attempt to think through the heuristic and cognitive competencies of imagination (...) on the basis of a human psychology strongly correlated with human physiology. Although the inadequacies of this attempt ultimately led to the cognitive demotion of imagination, there are nevertheless reasons for thinking that the early framework, shaped by the primacy of imagination, was not so much rejected as transformed in Descartes' mature work. The chapter further explains that imagination is the foundation of physics and mathematics and that it is both corporeal and spiritual. In addition imagination also serves as agent of all intelligent perception and the chief faculty for rising to higher level of spiritual truths. It further explains phantasia, a crucial organ of the brain where images occur, either derived from the senses, memory or from the intellect. (shrink)

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite number, and, as such, (...) Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz’s rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’– collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts. (shrink)

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)

The primary objective of this study is to provide a description of the major ideas about void space within and beyond the world that were formulated between the fourteenth and early eighteenth centuries. The second part of the book - on infinite, extracosmic void space - is of special significance. The significance of Professor Grant's account is twofold: it provides the first comprehensive and detailed description of the scholastic Aristotelian arguments for and against the existence of void space; and it (...) presents (again for the first time) an analysis of the possible influence of scholastic ideas and arguments on the interpretations of space proposed by the nonscholastic authors who made the Scientific Revolution possible. The concluding chapter of the book is unique in not only describing the conceptualizations of space proposed by the makers of the Scientific Revolution, but in assessing the role of readily available scholastic ideas on the conception of space adopted for the Newtonian world. (shrink)

Alexandre Koyré. of the fixed stars is infinite commit a contradiction in adjecto. In truth, an infinite body cannot be comprehended by thought. For the concepts of the mind concerning the infinite are either about the meaning oftheterm "infinite,"  ...

Descartes’ philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes’ mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes’ physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity.In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. (shrink)

Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s Paradox. It (...) concerns the set of all numbers, N: since to every number there is a corresponding square, there are as many squares as numbers. But since there are non-squares between the squares, “all numbers, comprising the squares and the non-squares, are greater than the squares alone”, i.e. there must be fewer numbers in the set of all squares S than in N. Thus N is both equal to and greater than S. This is a contradiction, so one of the premises must be given up: the question is, which one? (shrink)

The volume touches upon many topics and themes shared by Cartesian and late scholastic philosophy: matter and form; infinity, place, time, void, and motion; the ...

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)

L’indéfini cartésien, qui désigne ce dont on ne peut prouver les bornes, s’applique à deux domaines : les mathématiques et la physique. Cet article examine son application au monde physique, en deux moments. D’abord, par l’examen de l’indéfinité de l’univers, où l’on montre que l’univers cartésien n’est ni fini ni infini, mais in-défini, à la fois selon l’espace et selon le temps . Ensuite, par l’examen de l’indéfinité dans l’univers, qui pose le problème de la continuité, à la fois dans (...) l’espace et dans le temps, où nous défendons une interprétation continuiste et aprioriste selon laquelle le temps cartésien est continu, et cette continuité n’est jamais qu’un pour soi. (shrink)