This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial hypotheses. Both of (...) these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)
This essay examines the underdetermination problem that plagues structuralist approaches to spacetime theories, with special emphasis placed on the epistemic brands of structuralism, whether of the scientific realist variety or not. Recent non-realist structuralist accounts, by Friedman and van Fraassen, have touted the fact that different structures can accommodate the same evidence as a virtue vis-à-vis their realist counterparts; but, as will be argued, these claims gain little traction against a properly constructed liberal version of epistemic structural realism. Overall, a (...) broad construal of spacetime theories along epistemic structural realist lines will be defended which draws upon both Friedman’s earlier work and the convergence of approximate structure over theory change, but which also challenges various claims of the ontic structural realists. (shrink)
This essay examines the metaphysical foundation of Leibniz’s theory of space against the backdrop of the subtantivalism/relationism debate and at the ontological level of material bodies and properties. As will be demonstrated, the details of Leibniz’ theory defy a straightforward categorization employing the standard relationism often attributed to his views. Rather, a more careful analysis of his metaphysical doctrines related to bodies and space will reveal the importance of a host of concepts, such as the foundational role of God, the (...) holism of both geometry and the material world’s interconnections, and the viability and adequacy of a property theory in characterizing his natural philosophy of space. (shrink)
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. (shrink)
This presentation will investigate the parts of space, and its relationship with metrical structure, in Newton’s natural philosophy. The historical background to Newton’s claims will form an important part of the investigation, in addition to an assessment of the recent articles by Nerlich, Huggett, Maudlin, DiSalle, Torretti, McGuire, and several others, on this subject. While various aspects of these previous contributions will prove informative, it will be argued that the underlying goals of Newton’s pronouncements on the parts of space, including (...) their ontological implications for absolute and/or substantival space, have largely eluded prior analysis. (shrink)
This essay will investigate the interrelationship between the parts of space and topological and metrical structure in Newton’s natural philosophy, as well as its influence in contemporary spacetime debates. The historical background to Newton’s claims will form an important part of the investigation, in addition to an assessment of the recent articles by Nerlich, Huggett, Torretti, DiSalle, and several others, on this subject. While various aspects of these previous contributions will prove informative, it will be argued that the underlying goals (...) of Newton’s pronouncements on the relationship among the parts of space, including their methodological and ontological implications for absolute space and contemporary spacetime theories, have largely eluded prior analysis. (shrink)
The essay examines the relationship, within spacetime theories, between contemporary structural realism, Cassirer’s neo-Kantian structuralism, and Friedman’s defense of the relativized a priori. Despite Friedman’s claim that the relativized a priori can explain the progress of science, by using invariant theoretical elements/structures, our investigation will demonstrate that his theory cannot make this guarantee, nor may Cassirer’s earlier theory. However, as will be argued, the main content of both Cassirer’s and Friedman’s theories can be retained within an epistemic version of structural (...) realism, thereby securing an account of scientific progress. (shrink)
The subject of this essay is the relationship, within spacetime theories, between contemporary structural realism and Michael Friedman’s recent defense of the relativized a priori. Despite Friedman’s claims that the relativized a priori can account for the progress and rationality of science, such that the elements and structures of past successful theories will continue to be retained in future successful theories, our investigation will demonstrate that his theory does not have sufficient resources to make this guarantee. However, by exploiting the (...) distinction between the epistemic and ontic versions of structural realism, the main content of Friedman’s relativized a priori can be retained within a structural realist position, and can thereby secure the successive progress and rationality of science without sacrificing the essential ideas put forward by Friedman. (shrink)
This essay explores structural realist interpretation of spacetime with special emphasis on the close interrelationship between, on the one hand, ontological debates in spacetime structural realism and, on the other, foundational investigations in structural realism in the philosophy of mathematics. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of General Relativity, this investigation will reveal that a structuralist approach can serve as a useful means of deflating some of the ontological and (...) metaphysical disputes regarding similarly structured substantivalist and relationist spacetimes. Our analysis only covers spacetime theories up to the standard models in General Relativity (GTR), with its extension to theories of quantum gravity left for future investigations. This presentation is based on Slowik (2005), and includes a more detailed discussion in section 2.3 (which came out a bit garbled in the earlier paper). (shrink)
This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.
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. (shrink)
This essay explores two of the more neglected hypotheses that comprise, or supplement, Descartes’ relationalist doctrine of bodily motion. These criteria are of great importance, for they would appear to challenge Descartes’ principal judgment that motion is a purely reciprocal change of a body’s contiguous neighborhood. After critiquing the work of the few commentators who have previously examined these forgotten hypotheses, mainly, D. Garber and M. Gueroult, the overall strengths and weaknesses of Descartes’ supplementary criteria will be assessed. Overall, despite (...) their ingenuity, it will be demonstrated that Descartes’ criteria cannot rescue his brand of natural laws from the inherent limitations of his strong relational account of motion. (shrink)
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. (shrink)
This paper explores the possibility of constructing a Cartesian space-time that can resolve the dilemma posed by a famous argument from Newton's early essay, De gravitatione. In particular, Huygens' concept of a center-of-mass reference frame is utilized in an attempt to reconcile Descartes' relationalist theory of space and motion with both the Cartesian analysis of bodily impact and conservation law for quantity of motion. After presenting a modern formulation of a Cartesian space-time employing Huygens' frames, a series of Newtonian counter-replies (...) are developed in order to estimate the viability of this relationalist project. (shrink)
