Edward Slowik

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism.

This essay critically examines Joseph Rouse's arguments against, what he dubs, the "legitimation project", which are the attempts to delimit and justify the scientific enterprise by means of global, "a priori" principles. Stipulating that a more adequate picture of science can be obtained by viewing it as a continuously transforming pattern of situated activities, Rouse believes that only by refocusing attention upon the actual practice of science can philosophers begin to detach themselves from the irresolvable epistemological problems that have remained the primary byproduct of the traditional philosophical approach. On closer inspection, however, Rouse's project appears susceptible to the criticism that it is either too relativistic to do the work he envisioned for it, or that it participates in the very same legitimation venture that it was intended to replace (in addition to its own brand metaphysical/epistemological problems). This unexpected outcome, moreover, suggests that such legitimation projects may be an integral component of the very practice of science, contrary to Rouse estimate.

This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a third-way between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A non-substantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional substance/accident dichotomy concerning space. Nevertheless, our analysis of the metaphysical foundations of Newton’s spatial theory will strive to uncover its unique and innovative characteristics, most notably, the distinctive role that Newton’s “immaterialist” spatial ontology plays in his dynamics

This paper examines Descartes' problematic relational theory of motion, especially when viewed within the context of his dynamics, the Cartesian natural laws. The work of various commentators on Cartesian motion is also surveyed, with particular emphasis placed upon the recent important texts of Garber and Des Chene. In contrast to the methodology of most previous interpretations, however, this essay employs a modern "spacetime" approach to the problem. By this means, the role of dynamics in Descartes' theory, which has often been neglected in favor of kinematic factors, is shown to be central to finding a solution to the puzzle of Cartesian motion.

Do theories of quantum mechanics and quantum gravity require spacetime to be a basic ground-level feature, or can spacetime be seen as an emergent element of these theories? While several commentators have raised serious doubts about the prospects of forgoing the standard spacetime backdrop, we will argue that a defence of these emergent spacetime interpretations of quantum mechanics and quantum gravity hypotheses can be made whether as an inference as to what the best explanation is or using another strategy. Furthermore, the idea that space and time can arise from a quite different, non-spatiotemporal level of reality will be shown to have various historical precedents, especially in the seventeenth and eighteenth centuries. This realization may help dispel some of the mystery associated with these types of hypotheses.

This essay explores theories of place, or lived-space, as regards the role of objectivity and the problem of relativism. As will be argued, the neglect of mathematics and geometry by the lived-space theorists, which can be traced to the influence of the early phenomenologists, principally the later Husserl and Heidegger, has been a major contributing factor in the relativist dilemma that afflicts the lived-space movement. By incorporating various geometrical concepts within the analysis of place, it is demonstrated that the lived-space theorists can gain a better insight into the objective spatial relationships among individuals and within groups—and, more importantly, this appeal to mathematical content need not be construed as undermining the basic tenants of the lived-space approach.

In the Principles of Philosophy, Descartes attempts to explicate the well-known phenomena of varying bodily size through an appeal to the concept of "solidity," a notion that roughly corresponds to our present-day concept of density. Descartes' interest in these issues can be partially traced to the need to define clearly the role of matter in his natural laws, a problem particularly acute for the application of his conservation principle. Specifically, since Descartes insists that a body's "quantity of motion," defined as the product of its "size" and speed, is conserved in all material interactions, it is imperative that he explain how solidity influences the magnitude of this force. As a means of resolving this problem, Descartes postulated an idealized condition of "perfect solidity" which correlates a body's "agitation" force (a forerunner of Newton's concept of non-accelerating, or "inertial" motion) with the interplay of its volume, surface area, and composition of minute particles. This essay explores this often misunderstood aspect of Descartes' physics, as well as the special function of idealized conditions in his collision rules. Contrary to those commentators who regard "perfect solidity" as a stipulation on bodily impact, this notion, it will be argued, is primarily concerned with the internal composition of macroscopic bodies, and only indirectly with their collision characteristics. Along the way, many of Descartes' hypotheses will be shown to display a level of sophistication and intricacy that, despite their essential incompatibility, belie several of the common misconceptions of Cartesian science.