On Leibniz: Expanded Edition

4. Leibniz and the Plurality of Space-Time Frameworks

92 1. The Question of Distinct Frameworks Leibniz advocated a theory of space (and time) as “relative”—that is, as relative to the physical things ordinarily said to be located within space (and time). He opposed the doctrine of Newton’s Principia which cast space and time in the role of empty containers existing on their own and having a makeup that is indifferent to the things emplaced in them. For Leibniz, space and time are simply relational orders of being. Owing to the general tenor of his theory, Leibniz is sometimes seen as a precursor of Einstein and modern relativity theory. But this view is mistaken or, at any rate, misleading . Leibniz—unlike Einstein and modern relativists—is not thinking of the relativity of dynamical principles to the choice of a coordinate system within nature, so that we are involved in a situation of comparison from the perspective of various world-included frameworks. Rather, Leibniz’s thesis that “space is relative to the things in it” has regard to the perspective of various alternative possible worlds taken as a whole. The mutual attunement of whatever is included in a common world is the foundation for space and time, which have no existence apart from the concordance of the mutual “perceptions” of substances (in Leibniz’s sense of this term). “[T]here is no spatial or absolute nearness or distance between monads. And to say that they are compressed into a single point positioned in space is to use of certain fictions of our mind when we seek to visualize imaginatively that which only be understood.”1 As Leibniz saw it, the Newtonian theory of “absolute” space envisages  4 Leibniz and the Plurality of Space-Time Frameworks Leibniz and the plurality of space-time frameworks 93 this space as an entity in its own right, a content-indifferent container that would be filled up with different substantial content in the case of different possible worlds. His own view of space and time as something content relative implies—by way of contrast—that every possible world must have its own characteristic spatial (and temporal) structure. The issue comes down to a metaphysical—rather than physical—bone of contention. For in physics we study this world alone, whereas the point at issue is that of the world-transcending question, Do different “possible worlds” have their own characteristic spatial structure or should they be conceptualized as so many different ways of filling up one single common content-indifferent spacetime container? 2. Spatiality: The Conception of Space as Everywhere the Same To begin with, we have to recognize the idea or conception of space must (for Leibniz) be uniformly one and the same with respect to all possible worlds. What space is, is one (conceptually uniform) thing; what is space is another (potentially world-variable) one. This is true for space as it is for any and every concept. A possible world may or may not contain men, and its intelligent creatures may be very different from ours, but it cannot alter what humanity is. (The concept of humanity may not find application in some other possible world, but it cannot undergo alteration there.) The concept of spatiality is world-uniform because it is world-indifferent. In every world-setting space answers to the same conception: it is “the order of coexistence”—and time “the order of succession.” For Leibniz, every concept is what it is with respect to any and every possible world—the concepts of space and time included. Let us, however, look at the matter from another point of view. The ancient atomists had an interesting theory of possibility. Confronted with a question like, “Why do horses not have horns, as cows do?” they responded, “The hornlessness of a horse is just a local idiosyncrasy of our world—our own environing particular neighborhood in the universe. Somewhere else in the infinite vastness of space, there is another world, otherwise just like ours, in which horses do have horns.” The atomists thus envisaged space as one vast all-encompassing framework in which all possibilities are concurrently encompassed. 94 Leibniz and the plurality of space-time frameworks Did Leibniz hold a view of this nature? Was space for him one, all-encompassing matrix that embraced the actual and possible alike—a superspace embracing all possible worlds along with our own, actual world? Surely not. A space for Leibniz is the...