Leibniz’ Ontology of Space: Whither Relationism?

Abstract

One of the nagging puzzles that besets both the spacetime and Early Modern communities is the problematic fit between Leibniz’ conception of space and relationism. C. D. Broad long ago hinted at the unsuitability of a spatial relationist interpretation of Leibniz (1981, 171–173), but the treatment of his spatial hypotheses in many of the canonical texts in the philosophy of space and time has continued to portray Leibniz as having sanctioned a straightforwardly contemporary version of relationism (see, e.g., Sklar 1974, 169, and, Friedman 1983, 219, all nicely recounted in Auyang 1995, 247). Sophisticated (or modal) relationism—that space is a mere relation among bodies, but that these relations may include within their scope possibilia or non-actual bodies—is still often defended (e.g., Khamara 1993, 478; Belot 2011, 184), while others promote the super-eliminative variety that insists that all spatial relations can be eliminated in favor of material relationships, so that a vacuum is impossible (see, e.g., Futch 2008, 48; and, for relationism in general, Hooker 1971, 111). Yet, in this chapter, not only will the majority of these relationist interpretations of Leibniz’ theory be revealed as inadequate to the task, but the viability of any relationist interpretation of Leibnizian space will itself be called into question. As will be demonstrated, the underlying metaphysics of Leibniz’ theory requires a different set of conceptual resources, despite the obvious fact that the aftermath of his rejection of the absolutism of his day, especially in the correspondence with Clarke, set in stone an idea of Leibnizian space that continues to mislead historians and philosophers of science. While the conclusions of this chapter may strike the reader as rather controversial, the preponderance of the evidence that will be presented has played a major role in the metaphysical investigations of Leibniz for the past several decades. Unfortunately, the lessons to be gathered from this research have not been sufficiently assimilated by spacetime philosophers in their analysis of the foundations of Leibnizian space, but neither have the subtleties of Leibniz’ concepts been properly factored into various metaphysical and historical appraisals. Part of the goal of this chapter, in short, is to remedy this unfortunate oversight.