Leibniz and the Sorites

Abstract

The sorites receives its most sophisticated early modem discussion in Leibniz's writings. In an important early document Lcibniz holds that vague terms have sharp boundaries of application, but soon thereafter he comes to adopt a form of nihilism about vagueness: 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 ap­ pear to have any grounds for it. I suggest that his various treatments of the sorites do not spring 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 conclu­ sion in metaphysics rather than to examine vagueness as a subject to be understood in its own right. The later nihilist stance rei1ects Leibniz's own (if undefended) attitude to­ wards vagueness. A term that is vague in the philosopher's sense-such as 'rich', 'poor', 'bald', 'heap' -characteristically admits of borderline cases, lacks a clearly defined extension, and is susceptible to the sorites or paradox of the heap.' Take 'poor' for example. Someone with only a small amount of money may appear to be neither poor nor not poor, but on the borderline, even in the estimation of a competent language user fully informed about the amount of money the person has, the relative distributions of wealth in the community, and so on. The term 'poor' imposes no clear boundary between the poor and the not poor-it fails to single out a least number n such that anyone with at least 11 pennies is not poor while anyone with fewer than n pennies is poor-with cases seeming instead to fall into a spectrum across which poverty shades off gradually. And of course 'poor' can figure as a predicate for a sorites argument in the classical way; a stan­ dard version of the sorites for 'poor' might run as follows. Someone with zero pennies is poor. For any n, if someone with n pennies is poor, then someone with n+ 1 pennies is poor. So, someone with one billion pennies is poor.