The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish (...) between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved. (shrink)

En el presente trabajo analizamos la reforma que Leibniz propone entre 1677 y 1695 en la noción de cuerpo y, a partir de ello, esclarecemos el concepto de sustancia corpórea que presenta en esos años. En primer lugar, desarrollamos las críticas que esgrime contra la concepción geométrica del cuerpo propia de los filósofos modernos; en segundo lugar, examinamos los cambios que propone en dicha noción y su caracterización en clave de fuerza primitiva pasiva; en tercer lugar, estudiamos la definición hilemórfica (...) de la sustancia corpórea que ofrece y evaluamos el lugar que ella ocupa en su esquema metafísico. (shrink)

In this paper we study the impact of Leibniz’s critique of infinite numbers in his metaphysics of bodies. After presenting the relation that the German philosopher establishes in his youth between the notions of body, extension and infinite quantities, we analyze his thoughts on the paradoxes of the infinite numbers and we claim that his defense of the inconsistency of such numbers is an inflexion point in his conception of body and mark the beginning of his offensive against the res (...) extensa. (shrink)