Leibniz in Paris

The first section of this chapter presents Leibniz’s rejection of infinite number in response to Galileo’s paradox. The next section presents a problem that arises from his resolution of the paradox. The problem is this: if Leibniz regards the notion of infinite number as inconsistent, how is it that he regards the notion of infinite being as consistent? In the third section, the author considers a semantic solution to this problem and concludes that it is appealing but ultimately inadequate. In the fourth section, the author considers a more promising solution—namely that Leibniz distinguishes between different senses of infinity. The chapter concludes with a discussion of Leibniz’s attitude toward infinity vis-à-vis his critique of Descartes’s distinction between the infinite and the indefinite.