Three Essays about Problems of Space in the Early Modern Period

Given that we cannot perceive space via the senses, how do we arrive at the representation of space in the first place? Why do we tend to attribute certain properties to space – for instance, that it is infinite, empty, continuous, immutable, and so forth? My dissertation, consisting of four chapters, investigates two early modern accounts, which have suffered relative scholarly neglect, despite proposing to answer these time-honored questions: Locke’s account in his An Essay Concerning Human Understanding, and Du Châtelet’s account set out in in her Foundations of Physics. While Locke’s views concerning the idea of space prompted animated responses from early modern philosophers, it seems to have fallen into relative neglect in contemporary scholarship. In the first chapter, I engage with Locke’s controversial distinction between simple and complex ideas, as applied to the simple idea of space. In particular, I take up two objections that have been raised against Locke: that Locke’s criterion of simplicity fails (Aaron 1955) and that Locke’s use of ‘idea’ is ambiguous (Woolhouse 1970). I show that appealing to the method of strict interpretation is an effective means to defuse these difficulties, allowing us to appreciate Locke’s views with a greater degree of analytical confidence. The second chapter is devoted to analyzing Du Châtelet’s chapter on space, in order to identify her singular contributions to the absolute-relative debate about space which animated the scientific body at the time. To begin with, I demonstrate that contrary to the received view, Du Châtelet’s account is neither Wolffian nor Leibnizian. Instead of deriving the representation of space from perceptions of spatially related objects, Du Châtelet argues that we obtain this representation by conceiving extension as occupiable by possible coexisting objects. Next, I argue that by means of this proposed account, Du Châtelet not only defends the Leibnizian idea of space as the order of coexisting objects, but further succeeds in explaining why the Newtonian idea of absolute space is so attractive, viz. the idea that space is an independently-existing, empty, infinite, and immutable entity. The third chapter, “A Deeper Investigation of Du Châtelet’s Uses of the Term “External-to””, identifies three distinct uses of the term ‘external-to’ in Du Châtelet, and argues that each of them denotes a relation obtaining among different kinds of relata: simple substances, composite bodies, and objects of imagination. At the outset of the chapter, I challenge a recent interpretation by Jacobs (2019), which construes “external-to” as an ontological relation, pointing out that this interpretation is in tension with (1) Du Châtelet’s division of labor between the faculty of imagination and the faculty of understanding, and (2) her considered view that we cannot perceive simple substances as distinct individuals, owing to the weakness of our sensory organs. This significant chapter lays the groundwork for future research by seeking to distinguish three tiers of created reality in Du Châtelet’s ontology: the elementary (inhabited by simple substances), the phenomenal (by material bodies), and the ideal (by entities such as space and time). The last chapter turns to another issue intimately related to the ontological problem of space in the same period: the problem of gravity. This chapter starts with a response to George E. Smith’s “Newton’s numerator in 1685: A year of gestation”, Studies in History and Philosophy of Modern Physics 68 (2019) 163-177. I offer this response from the perspective of Euler scholarship. First, I challenge Smith’s claim that Euler dismisses gravity’s proportionality to the mass of the attracting body. Rather than rejecting this proportionality from the numerator of Newton’s law of gravity, I will show that Euler is opposed to Newton’s appeals to the third law of motion to derive this term. Second, I provide a reconstruction of Euler’s elastic ether mechanism of gravity, whereby he “recovers” all three proportionalities in Newton’s law of gravity without appealing to the third law, but to the material properties of the ether and contact action (i.e., fluid pressure). Third, I proffer a critical assessment of Euler’s mechanism. My analysis reveals that, while Euler is right to point out the lack of direct evidence for gravity being a force of interaction governed by the third law of motion, his alternative falls far short of its Newtonian rival on grounds of empirical adequacy and fruitfulness for future research.