On the Plurality of Spaces in Leibniz

Abstract

According to a famous Leibnizian dictum, space is nothing but “an order of situations, or an order according to which situations are disposed”. This so called “spatial relationism” is sometimes understood as a form of relativism (space is relative to the possible dispositions of bodies), which seems to entail the possibility of a spatial pluralism (possible worlds with non-equivalent dispositions of bodies might have non-equivalent spatial structures). An overly exclusive focus on the exchange between Leibniz and Clarke, considered to be the locus classicus for understanding Leibniz’s views on space, did much to lend credence to such a conception. In addition, in several passages, Leibniz talked of other possible worlds as lacking this or that spatial property. In the exchange with De Volder, for example, he explained that God could have been pleased with a phenomenal world with gaps in it. In this description, as in other passages, it seems that we can imagine without contradiction a world with a geometrical structure different from ours. This stance was supported, as we will see, by influential scholars who concluded, without much trouble, that a plurality of spaces was conceivable for Leibniz. Yet this idea runs counter to two other no less famous Leibnizian dicta: first, that geometrical truths are absolutely necessary (one cannot deny them without contradiction); second, that geometry should be considered as the science of space and that we can specify various properties of geometrical space (such as tridimensionality, homogeneity, isotropy or continuity). Combined together, these last two claims tend to prevent any form of pluralism: space is the object of a science which describes its essential properties and these properties are truths which are absolutely necessary. These eternal truths apply to all possible worlds. Our goal in this paper is to confront this tension in Leibniz’s description of space.