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The Infinite in Descartes’ Conversation with Burman
Abstract
L'A analyse la distinction entre infini et indefini dans l'" Entretien avec Burman ". Examinant les diverses interpretations de cette oeuvre, et en particulier le probleme de son authencite, il montre que le Descartes de Burman ne respecte pas cette distinction, fondamentale dans sa philosophie parce qu'elle correspond a la distinction entre l'etre et le connaitre
In this article, I consider Descartes’ enigmatic claim that we must assert that the material world is indefinite rather than infinite. The focus here is on the discussion of this claim in Descartes’ late correspondence with More. One puzzle that emerges from this correspondence is that Descartes insists to More that we are not in a position to deny the indefinite universe has limits, while at the same time indicating that we conceive a contradiction in the notion that the universe has a limit. I reject one attempt to resolve this apparent conflict which appeals to Descartes’ admission to More that divine omnipotence requires that God can create a vacuum in nature, and focus instead on his response to More’s claim that this omnipotence requires the possibility of a completion of the division of matter that results in atoms. Finally, I distinguish Descartes’ indefinite from two other kinds of infinity with which it might well be confused. The first is an essentially incomplete ‘potential infinity’ that Descartes discusses in the Third Meditation, and the second is the sort of quantitative infinity that Leibniz – contrary to Descartes – denies can constitute a completed whole.
I address two questions prompted by the discussion in Roger Ariew's Descartes and the First Cartesians. The first is whether the sort of scholasticization of Cartesianism to which First Cartesians draws attention is merely a matter of packaging, or whether it indicates rather a substantive connection between Cartesianism and Aristotelian scholasticism. The second question is whether the French Cartesians Ariew emphasizes played a central role in the transition from the widespread condemnation of Cartesian doctrines in France in the decades following Descartes's death to the widespread acceptance of Cartesianism within the French universities by the beginning of the eighteenth century. In response to the first question, I focus on the deviation in later Cartesianism from Descartes's own rejection of scholastic syllogistic logic. In response to the second, I offer some reasons to question the significance of the influence of the figures that Ariew highlights, and I argue that Cartesians such as Pourchot and Malebranche had a relatively greater impact on the teaching of Cartesianism in French universities in the late-seventeenth and early-eighteenth centuries.
Descartes’s metaphysics posits a sharp distinction between two types of non-finitude, or unlimitedness: whereas God alone is infinite, numbers, space, and time are indefinite. The distinction has proven difficult to interpret in a way that abides by the textual evidence and conserves the theoretical roles that the distinction plays in Descartes’s philosophy—in particular, the important role it plays in the causal proof for God’s existence in the Meditations. After formulating the interpretive task, I criticize extant interpretations of the distinction. I then propose an alternative at whose core is the idea that whereas the indefinite is a structural, iterative notion, designating the absence of an upper bound, the infinite is an ontic notion, signifying being in general, or what is, without qualification.
In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite (or indefinite) extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we always imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real (as opposed to imaginary or abstract) time. In contrast, extension does not depend on any enduring substance besides itself.
Descartes believed the extended world did not terminate in a boundary: but why? After elucidating Descartes’s position in §1, suggesting his conception of the indefinite extension of the universe should be understood as actual but syncategorematic, we turn in §2 to his argument: any postulation of an outermost surface for the world will be self-defeating, because merely contemplating such a boundary will lead us to recognise the existence of further extension beyond it. In §3, we identify the fundamental assumption underlying this argument by comparing Descartes’s and Malebranche’s respective conceptions of the ontological status of modes of extension.
La primera prueba cartesiana de la existencia de Dios tiene como condición la certeza de la finitud del ego. Esta certeza se obtiene, a su vez, mediante actos por los cuales el ego conoce su propia finitud al compararse con una idea implícita de l’infini (Dios). Estos actos son la duda y el deseo. Sin embargo, estos importantes problemas exigen previamente el análisis de la ideas de l’infini y l’indéfini. Sostengo en este artículo que l’indéfini es el término que ocasionalmente designa en propiedad lo que el término l’infini designa por analogía de atribución cuando Descartes lo predica de entes ontológicamente finitos tales como la idea del número o extensión interminable.
The concept of the infinite has often been regarded as inherently problematic in mathematics and in philosophy. The idea that the universe itself might be infinite has been the subject of intense debate not only on mathematical and philosophical grounds, but for theological and political reasons as well. When Copernicus
and his followers challenged the old Aristotelian and Ptolemaic conceptions of the world’s finiteness, if not its boundedness, the idea of an infinite, if not merely unbounded, world seemed more attractive. Indeed, the infinity of space has been called the “fundamental principle of the new ontology” (Koyré
in From the Closed World to the Infinite Universe. Johns Hopkins University Press, Baltimore, 1957, p. 126). Influential scholarship in the first half of the twentieth century helped to solidify the idea that it was specifically in the seventeenth century that astronomers and natural philosophers fully embraced the infinity of the universe. As Kuhn
writes in his Copernican Revolution (1957, p. 289): “From Bruno
’s death in 1600 to the publication of Descartes
’s Principles of Philosophy in 1644, no Copernican of any prominence appears to have espoused the infinite universe, at least in public. After Descartes
, however, no Copernican seems to have opposed the conception.” That same year saw the publication of Alexandre Koyré
’s sweeping volume about the scientific revolution, From the Closed World to the Infinite Universe. The decision to describe and conceive of the world as infinite might be seen as a crucial, if not decisive, aspect of the overthrow of Scholasticism. As Kuhn
and Koyré
knew, one finds a particularly invigorating expression of this historical-philosophical interpretation in an earlier article by Marjorie Nicholson
(Studies in Philology 25:356–374, 1929, p. 370).
Through a close analysis of texts from the Second Objections and Replies to the "Meditations", this article addresses the tension between the pursuit of certainty and the preservation of divine transcendence in Descartes's philosophy. Via a hypothetical "atheist geometer", the Objectors charge Descartes with pantheism. While the Objectors' motivations are not clear, the objection raises provocative questions about the relation of the divine and the human mind and about the being of created or dependent entities in Descartes's metaphysics. Descartes contends that there are real, eternal essences present in the human intellect as innate ideas. I argue that this claim implicates him in pantheism, not merely univocity. In the course of the analysis, I consider recent interpretations by Wells, Marion, and Hatfield.
The distinction made by Descartes between the infinite and the indefinite is well-known and has spurred a great deal of commentary. We often err, however, concerning the true nature of the indefinite. The majority of interpreters, from the 17th Century until now, reduce the indefinite to the infinite in its kind, of which the kind would be extension, notably qualified as the infinite "in extension", as well as the "spatial", "negative", "potential", or "quantitative" infinite. Going against the grain of such an interpretation, this article shows that the Cartesian indefinite is not properly speaking either the infinite, or even the infinite in its kind, or the finite, and that its true nature is indetermination.
Are there only metaphysical reasons for the Cartesian distinction between infinite and indefinite? This article explores the political and languagerelated reasons that led Descartes to reserve the infinite (that which is positively whitout limits) to God alone and the indefinite (that which cannot be proved to have limits) to the physical world and to mathematics. It shows that this famous distinction is partly - but not exclusively - policital, in reaction to the pressure exercised by the School and the Church that had got the better of Galileo a few years earlier. It also reveals the language-related reasons: the distinction is methodological and inspired by the use of words. With Levinas it draws conclusions in regard to the importance of discourse in presenting the transcendent - which is found by extension in Cartesian philosophy (transl. by J. Dudley).
Through a close analysis of texts from the Second Objections and Replies to the Meditations, this article addresses the tension between the pursuit of certainty and the preservation of divine transcendence in Descartes's philosophy. Via a hypothetical "atheist geometer," the Objectors charge Descartes with pantheism. While the Objectors' motivations are not clear, the objection raises provocative questions about the relation of the divine and the human mind and about the being of created or dependent entities in Descartes's metaphysics. Descartes contends that there are real, eternal essences present in the human intellect as innate ideas. I argue that this claim implicates him in pantheism, not merely univocity. In the course of the analysis, I consider recent interpretations by Wells, Marion, and Hatfield.
Etude de la notion d'infini qui fonde la preuve de l'existence de Dieu dans la troisieme des «Meditations metaphysiques» de Descartes. Soulevant le probleme des conceptions contradictoires de l'infini dans la reponse a Caterus et dans la reponse a Gassendi, la premiere utilisant des metaphores insatisfaisantes, la seconde s'appuyant sur la doctrine cartesienne de la creation des verites eternelles, l'A. montre que la notion d'infini sape le fondement metaphysique de la verite chez Descartes, malgre les criteres epistemologiques et ontologiques pour distinguer l'infini de l'indefini
Descartes’ Third Meditation presents an alleged proof for the existence of God that proceeds from the existence of an idea of an infinite being, God—an idea with infinite objective reality—to the existence of God himself. There is a tendency to understand the meditator as simply assuming the premise that he has an idea with infinite objective reality, or alternatively, as drawing it from the reach of introspection and the transparency of thought. Either way, readers of the Meditations often find the premise unmotivated, and do not take Descartes to provide any argument for it. This paper aims to show that Descartes does provide an argument for the premise. My interpretation focuses on the meditator’s evolving conception of his idea of an infinite being in the Third Meditation. In so doing, the interpretation highlights a way in which epistemic progress is achieved in the Meditations, namely, through a process of correcting misconceptions.
In the course of a lengthy interview, Descartes is reported to have claimed that ‘the axiom is common and true: the effect is similar to the cause’ (AT 5:156). There has been much discussion in the recent secondary literature about whether Descartes’ various causal principles require a sort of resemblance between cause and effect that rules out the interaction of substances as distinct in nature as mind and body. However, it is clear from the record of the Descartes interview that the axiomatic principle that effects are similar to their causes- call this the ‘Similarity Principle'- applies primarily to the case of God's production of created substances, and of created minds in particular. This record thus provides one reason for the focus here on that particular case. Another is that a consideration of this case broaches difficulties for the Similarity Principle that have an interesting though somewhat neglected role in the history of Cartesianism.
Readers of Spinoza's philosophy have often been discouraged, as well as fascinated, by the geometrical method which he employs in his masterpiece Ethics. Aaron Garrett examines this method and suggests that Spinoza intended not only to make claims and propositions but also to transform readers by enabling them to view themselves and the world in a different way. This original and controversial book will be of interest to historians of philosophy.
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