It can be shown by means of a paradox that, given the Principle of Sufficient Reason, there is no conjunction of all contingent truths. The question is, or ought to be, how to interpret that result: _Quid sibi velit?_ A celebrated argument against PSR due to Peter van Inwagen and Jonathan Bennett in effect interprets the result to mean that PSR entails that there are no contingent truths. But reflection on parallels in philosophy of mathematics shows it can equally be (...) interpreted either as a proof that there are "too many" contingent truths to combine in a single conjunction or as a proof that the concept _contingent truth_ is indefinitely extensible and there is no such thing as "all contingent truths." Either interpretation would reconcile PSR with contingent truth, but the natural rationales of those interpretations are at odds. This essay argues that the second interpretation is a more satisfactory explanation of why, if PSR is true, there should be no conjunction of all contingent truths. This sheds new light on the nature of the explanatory demand embedded in PSR and uncovers a number of surprising implications for the commitments of rationalism. (shrink)

Mathematician and philosopher Hermann Weyl had our subject dead to rights.

In this paper I argue that what has been called Leibniz’s “aggregate argument” for unities in things in fact comprises three quite distinct lines of argument, with different concepts being advanced under the name ‘unity’ and meriting quite different conceptual treatment. Two of those arguments, what I call the Borrowed Reality Argument and the Multitude Argument, also appear in later writings to be further elaborated into arguments not just for unities but for simples. I consider the arguments in detail. I (...) suggest that one of the two, the Borrowed Reality Argument, is philosophically more promising and has the stronger evidence for being central in Leibniz’s thought as he argues for the existence of simple substances. (shrink)

What is Leibniz’s argument for simple substances? I propose that it is an extension of his prior argument for incorporeal forms as principles of unity for individual corporeal substances. The extension involves seeing the hylomorphic analysis of corporeal substances as implying a resolution of matter into forms, and this seems to demand that forms, which are themselves simple, be the only elements of things. The argument for simples thus presupposes the existence of corporeal substances as a key premise. Yet a (...) theory of simple substances as the elements of things threatens to preclude the existence of corporeal substances for Leibniz, and the extension of the argument for forms into an argument for simples is not cogent. If nothing else rides on the simplicity of individual substances, then perhaps instead of being its most fundamental tenet, the doctrine of simples—the monadology—is something that over-extends and destabilizes Leibniz’s metaphysics. (shrink)

The sorites paradox receives its most sophisticated early modem discussion in Leibniz’s writings. In an important early document Leibniz holds that vague terms have sharp boundaries of application, but soon thereafter he comes to adopt a form of nihilism aboutvagueness: and it later proves to be his settled view that vagueness results from semantical indeterminacy. The reason for this change of mind is unclear, and Leibniz does not appear to have any grounds for it. I suggest that his various treatments (...) of the sorites do notspring from a single integrated view of vagueness, and that his early position reflects a mercenary interest in the sorites paradox---an interest to use the sorites to reach a conclusion in metaphysics rather than to examine vagueness as a subject to be understood in itsown right. The later nihilist stance reflects Leibniz’s own (if undefended) attitude towards vagueness. (shrink)

Interest in Leibniz’s early philosophical writings has been on the rise in recent years, and to the growing literature on the subject we can now add an excellent volume of papers edited by Stuart Brown. The Young Leibniz and His Philosophy collects articles from a dozen leading authors on a variety of topics, plus a substantial introductory chapter by the editor that provides an overview of Leibniz’s life and works from 1646 to 1676. The essays originate from a 1996 conference (...) at Woburn College in Bedfordshire, and they have all been polished to stand as fully articulated works of scholarship for this publication. (shrink)