Infinity in Descartes
In Descartes's Cogito the mind discovers itself as an infinite power of self-assertion, a subjectivity, positing itself from within. But the mind also knows that it is finite, and receives its being from an "Other"--the infinite substance, or God, of which it finds within itself the idea, as one which cannot be derived from its idea of itself. The Cartesian conception of subjectivity is openness to the infinite.^ Descartes's ontological argument shows the infinite as radically "essence". But more fundamentally than essence, or being, the Cartesian God is that which takes the initiative to create me and to put into my mind its "mark". By causing himself, and making himself known, he posits the order of being.^ A God bound to be the only being would be supreme powerlessness. The Cartesian God, as infinite power, is essentially creator. His power is not one which is immanent in the world and never comes out of itself; it cannot exclude the existence of distinct finite beings. God's infinite creativeness is the source of being in the endless variety of its forms and degrees.^ The infinite freedom of the subject manifests itself as rationality. God's veraciousness, rooted in his infinite creativeness, guarantees the reliability of reason. Thus, the movement of human knowledge proceeds from the infinite implicitly present in the operation of reason (making it possible for the subject to know itself and its creator) to the infinite explicitly recognized and hence opening up the endless possibilities of knowledge metaphysically certain of itself--albeit incapable of becoming actually infinite.^ The physical world, which can become object of knowledge once human reason is assured of its grounding in the infinite, is called by Descartes "indefinite". The world is not finite: the identity of matter and extension makes a limited world inconceivable. The world is not the infinite: it is not God. And if an image of the infinite is to be found in the created, it is not in the extended substance--pure multiplicity, parts next to parts--but in man's infinite freedom. ^
Berman, Sophie, "Infinity in Descartes" (1993). ETD Collection for Fordham University. AAI9403291.