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Leibniz and Clarke’s theories of space play

Leibniz and Clarke’s theories of space play

What role do Leibniz and Clarke’s theories of space play in their view of the nature of God?

For this exercise you want to complete the following steps:

1. List the relevant considerations and supporting passages from the reading, focusing on the fourth letter from both Leibniz and Clarke, including the Appendix sections cited in footnotes, but drawing, where necessary, from previous letters. For the sake of brevity (shortness), pick the most important THREE considerations from your complete list and include them here. How to choose? SEE NEXT:

2. Step back and look at the two elements of the question: (a) a theory of space (meaning the view of space each figure has) and (b) the nature of God (ditto re God). See if you can start to see how the theories of space help each philosopher argue for his view of the nature of God.

One of several nagging puzzles that vexes Leibniz scholars, regardless of whether through the space–time or Early Modern communities, may be the challenging suit between relationism and his awesome getting pregnant of place. Long ago, C.D. Broad hinted at the unsuitability of a spatial relationist interpretation, but the treatment of Leibniz’s spatial hypotheses in many canonical texts (in the philosophy of space and time) has continued to portray Leibniz as having sanctioned a straightforwardly contemporary version of relationism.1 One of these modern forms of 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,2 while others promote the more traditional and restrictive conception of relationism, which insists that all spatial relations are directly grounded within material bodies, such that there are no spatial relations that are external to, or between, material bodies. Leibniz’s denial of a vacuum (empty space) might lend support to this reductive relationist interpretation.3 Yet, in this essay, not only will the majority of the relationisms typically offered as interpretations of Leibniz’s theory be revealed as inadequate to the task, but the very viability of relationism will be called into question with respect to Leibnizian space. As will be demonstrated, the underlying metaphysics of Leibniz’s theory requires a different set of conceptual resources, despite the obvious fact that the aftermath of the debates with the absolutists of his day (e.g. the Leibniz–Clarke correspondence) set in stone an idea of Leibnizian space that continues to mislead philosophers. While the conclusions of this essay may strike the reader as rather controversial, the preponderance of the evidence that we will present has played a major role in the metaphysical investigations of Leibniz for, roughly, the past 25 years. Unfortunately, the lessons to be gathered from this research have not been sufficiently assimilated by the space– time crowd in their analysis of the foundations of Leibnizian space, but neither have the subtleties of Leibniz’s concepts been properly factored into various metaphysical and historical appraisals. Part of the goal of this essay, in fact, is to remedy this unfortunate oversight. In the first section, the various brands of relationism are compared and contrasted with Leibniz’s spatial hypotheses, with the surprising result that most are either entirely inadequate, or, at best, only tangentially relevant to his deeper metaphysical design. In the second section, God’s foundational role as the ontological basis of space will be revealed, along with an analysis of the substance/accident dichotomy, quantity and order of situations, and the holism or monism of both geometry and the material world’s interconnections. In essence, a case will be made that the most plausible form of spatial theory consistent with Leibniz’s spatial hypotheses is a unique form of property theory, albeit a property theory that resembles relationism on a few important issues. Furthermore, throughout this essay, we will largely confine our analysis to the metaphysical level of material bodies, and substance/accident/relation metaphysics, since a thorough treatment of the intricacies of the monadic component of Leibniz’s theory requires a separate investigation. Yet, various hints as to how the monadic realm connects with the material realm will be briefly considered in the concluding third section. This choice, to specifically focus upon the level of bodies, is in keeping with both the traditional substantival/relational dispute in ontology, and, more importantly, with the form of the debate as manifested in the Leibniz–Clarke correspondence, his most significant and detailed contribution to the philosophy of space. In short, the late correspondence with Clarke fails to bring into play the underlying monadic foundation of Leibniz’s philosophy, thus partly justifying our exclusive investigation of the more commonplace ontological themes associated with material substances, accidents, and God. Nevertheless, a complete account of Leibniz’s views on space must ultimately explicate the monadic basis, and thus the ensuing analysis is but the first half of this larger story.

Supplying a exact definition of substantivalism and relationism can be a overwhelming process in its own correct, but, for our own purposes, we will consider substantivalism, or absolutism, since the see that area is undoubtedly an independently existing entity of some type, in a way that the geometry of room is self-sufficient of bodies (e.g., length interaction are in between the areas of place, using the distance interaction among body supervening on these self-sufficient geometric facts). A central tenet of relationism is the rejection of substantivalism (or absolutism), thus, at least on this point, Leibniz’s philosophical inclinations side with the relationists. In many writings, Leibniz clearly rejects the view that space is an entity that exists separate or apart from material things, but, unlike Descartes, he rejects the thesis that space is identical with matter: ‘I do not say that matter and space are the same thing. I only say that there is no space where there is no matter and that space in itself is not an absolute reality’. 5 Nevertheless, other approaches to space and time, such as the property theory, also deny the substantivalist creed (as will be explained below), so the rejection of substantivalism does not necessarily equate with relationism. Furthermore, relationism comes in many flavors, and so the question remains as to which type Leibniz subscribes, if any. One version is a strictly reductive, non-modal relationism, the main feature being the reduction of spatial facts to material facts and relations, whether those spatial facts possess a quantitative/geometric component or not. Another way to view this option is to claim that all spatial facts are necessarily obtained within matter, so that there can be no materially unsupported spatial facts that are external to the confines of corporeal existents, as in a vacuum. Descartes was the foremost proponent of this view, denying that a vacuum was possible whether internal or external to the terrestrial realm.6 Yet, on several occasions, Leibniz insists that the vacuum is a possible, although not actual, state of affairs: ‘I don’t say that the vacuum, the atom, and other things of this sort are impossible, but only that they are not in agreement with divine wisdom’. 7 Nevertheless, in explaining away the possibility of a vacuum, Leibniz provides other, more potent, rationales, besides divine wisdom, to guarantee the fullness of space, the most important being that a vacuum would violate the principle of the identity of the indiscernibles (PII), because the empty parts of space would be intrinsically identical: ‘Space being uniform, there can be neither any external nor internal reason by which to distinguish its parts and to make any choice among them’. 8 Yet, if one assumes that the structure of space is Euclidean, and hence infinite, as Leibniz presumably did (see footnote 70), then his admission that the material world could be finite if God had so desired raises obstacles for any non-vacuum version of reductive relationism, e.g. ‘[a]bsolutely speaking, it appears that God can make the material universe finite in extension […]’. 9 Likewise, the various hypothetical scenarios envisaged in the New Essays, which discuss indirect methods of measuring a vacuum within the material world (as opposed to outside the world; see, once again, footnote 70), would also seem to refute a non-vacuum reductive relationism.