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  • Descartes, la métaphysique et l'infini by Dan Arbib
  • Igor Agostini
Dan Arbib. Descartes, la métaphysique et l'infini. Paris: Presses Universitaires de France, 2017. Pp. 368. Paper, €32.00.

Dan Arbib's book follows the numerous studies devoted, in the last twenty years, to the topic of the infinite in Descartes. For the first time, however, with Arbib's work, this question is addressed thematically.

Its fundamental purpose is the demonstration of what Arbib calls an "induction a priori" (78): the Cartesian infinite belongs, and at the same time does not belong, to metaphysics as ontotheology. The verification of this hypothesis depends on a "non-negotiable condition" (79): the infinite belongs to metaphysics insofar as it is subordinated to the ego, and for this reason is supremely representable. The infinite, indeed, arises along the metaphysical path of Duns Scotus (and Bonaventure) that, in the thirteenth century, against apophatism, transforms the infinite to a metaphysical name of God (chapter 2). The epistemological positivity of the infinite determines, in turn, its ontological positivity and, consequently, on the one hand, the coherence between the infinite and the perfect and, on the other hand, the abandonment of Aristotle's conception of the infinite, which, however, is not rejected, but transferred to the notion of the indefinite (chapter 3). However, as Arbib shows, an integrally "substantialist" interpretation of the infinite engenders a series of aporias, which culminate in the causa sui. The causa sui belongs to metaphysics insofar as it answers the question of the cause, but, at the same time, as ratio of the non-cause, it is not subjected to causality. And the ambivalence of the causa sui is mirrored in the situation of the infinite in Cartesian metaphysics; in 1630, the infinite establishes the eternal truths, but, in 1641, is also subjected to them (chapter 1). For Arbib, such aporias "must" (274) be solved by a "non-metaphysical" interpretation; the famous doctrine of the priority of the infinite over the finite must be read in the phenomenological-transcendental sense outlined by Emmanuel Lévinas: the idea of the infinite is maxime clear and distinct insofar as it is a transcendental condition of the experience (of finitude), given in this very experience. The idea of the infinite expresses an anteriority impervious to any temporality and any interpretation in terms of present-at-hand (Vorhandenheit): it is an ecstasy. Accordingly, the passage from the second to the third meditation marks not only the primacy of the infinite over the ego, but also a "deplacement" of the ego.

This wonderful book keeps its promises. It offers not only the first thematic study of the Cartesian notion of the infinite, but also a deep analysis of the relations between the infinite and other main notions of Cartesian metaphysics. In this way, Arbib argues convincingly for the centrality of the infinite in Descartes's philosophy. Furthermore, he identifies with accuracy, and against the interpretation of his teacher, Jean-Luc Marion, the true origin of the main aporia generated by the infinite: its representability.

An ambivalent relation with Marion, however, is silently involved in Arbib's book. Marion's position constitutes Arbib's main polemical target: the opposition between representability and non-representability, which Marion had mapped onto the couple perfect/infinite, is here located within the infinite. Nevertheless, for Arbib, as for Marion (and Lévinas), the alleged finitude of the idea of the infinite depends on its representability: the objective reality of the representation "contracts" (302) the infinite. But this is a questionable claim: in the Meditations, a quite different sense of "contraction" from the phenomenological one is at work. Given the inclusion of incomprehensibility in intelligibility (which Arbib himself stresses), the limitations of the clarity and distinctness of the idea of God are [End Page 562] traced back to the fact that God's infinity cannot be entirely intelligible for the ego (ATVII.46). Consequently, it is the human incapacity of representing the whole infinite (and not its representability as such) that explains why Descartes hesitates to call God's objective reality infinite. In sum, it is not insofar as the infinite is representable, but insofar as it is not...


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