This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to (...) three concepts of mathematical fictions. Moreover, such a distinction is the base for the claim that infinitesimal quantities, as mathematical fictions, do not imply an absolute impossibility, resulting from self-contradiction, but a relative impossibility, founded on irrepresentability and on the fact that it does not conform to architectural principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status. (shrink)

Commentators have long been fascinated by the problem of freedom in Leibniz's system. Many of the recent studies begin with Leibniz's views on modality, truth, and so-called superessentialism, and then investigate whether these doctrines are compatible with freedom and contingency. There is, however, another dimension to Leibniz's thinking about freedom that has been largely overlooked in the recent literature. ;Leibniz inherited a medieval debate about God's foreknowledge of and providence over human free actions, and unlike the other great philosophers of (...) the early modern period, set out to solve it. This means the problem of human freedom for Leibniz was nested in the larger problem of God's creation, preservation, and governance of the entire created order. ;In this dissertation I set out the late medieval debate and Leibniz's adjudication of it. I argue that Leibniz offers a strong notion of providence that is a via media between the two competing paradigms of the late seventeenth century, Molinism and Banezianism. In light of these theological commitments, I offer a new assessment of Leibniz's views of divine and human freedom. (shrink)