Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

Leibniz propôs mais de um conceito para descrever filosoficamente a substância. Ironia instrutiva, esta pluralidade que tem por fim uma explicação unificada da realidade culminou em uma definição dos componentes fundamentais do mundo – as mônadas – como unidades que abrigam a multiplicidade. Estas substâncias, bem como a sua função essencial de se exprimirem mutuamente, apenas se tornam plenamente inteligíveis quando observamos os conceitos anteriores, de que a filosofia madura de Leibniz herdou algumas intuições. Guiando-nos pelas obras-chave do filósofo e (...) físico alemão, procuraremos retraçar esse percurso intelectual, a fim não de esboçar um hipotético sistema seu, mas de _unificar_ o tratamento que ele dispensou à _unidade_. Tal hipótese de leitura concorda fundamentalmente com aquela sustentada por Michel Fichant, mas traz pontuais acréscimos ou desacordos, que serão indicados neste artigo. (shrink)

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)

Leibniz frequently argued that reasons are to be weighed against each other as in a pair of scales, as Professor Marcelo Dascal has shown in his article "The Balance of Reason." In this kind of weighing it is not necessary to reach demonstrative certainty – one need only judge whether the reasons weigh more on behalf of one or the other option However, a different kind of account about rational decision-making can be found in some of Leibniz's writings. In his (...) article "Was Leibniz's Deity an Akrates?" Professor Jaakko Hintikka has argued that Leibniz developed a new vectorial model for rational decisions which is better suited to complicated decisions, where values are complementary to each other. This model, related closely to his work in metaphysics and the philosophy of mind, is a heuristic device which helps in finding rational combinations - and in an ideal case an optimum - between plural inclinations to the good. I shall argue that Leibniz applies more or less implicitly both of these models in his practical rationality. In simple situations he applied the pair of scales model and in more complicated situations he applied the vectorial model. (shrink)