This essay explores Kant’s concept of absolute space in the Metaphysical Foundations from the perspective of the development of the relationist interpretation of bodily interactions in the center-of-mass reference frame, a strategy that Huygens had originally pioneered and which Mach also endorsed. In contrast to the interpretations of Kant that stress a non-relationist, Newton-inspired orientation in his critical period work, it will be argued that the content and function of Kant’s utilization of this reference frame strategy places him much closer (...) to Huygens’ relationism than the absolute notions of space and motion favored by Newton and Euler. (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)

Mundy (1983) presented the formal apparatus of certain relationist theories of space and space-time taking quantitative relations as primitive. The present paper discusses the philosophical and physical interpretation of such theories, and replies to some objections to such theories and to relationism in general raised in Field (1985). Under an appropriate second-order naturalistic Platonist interpretation of the formalism, quantitative relationist theories are seen to be entirely comparable to spatialist ones in respect of the issues raised by Field. Moreover, it appears (...) that even if accepted as sound, Field's general line of criticism would not diminish the significance of relationism for philosophy of science, since this derives primarily from its connection to physical rather than to mathematical or philosophical ontology. (shrink)

Relationist theories of space or space-time based on embedding of a physical relational system A into a corresponding geometrical system B raise problems associated with the degree of uniqueness of the embedding. Such uniqueness problems are familiar in the representational theory of measurement (RTM), and are dealt with by imposing a condition of uniqueness of embeddings up to composition with an "admissible transformation" of the space B. Friedman (1983) presents an alternative treatment of the uniqueness problem for embedding relationist theories, (...) developed independently of RTM. Friedman's approach differs from that of RTM in securing uniqueness by adding new primitives to the physical system A in contrast to the RTM approach which adds new axioms. Friedman's proposal has recently been developed and defended by Catton and Solomon (1988). This method of solving the uniqueness problem is here argued to be substantially inferior to the RTM method, both in practice and in principle. In practice we find that in none of the concrete examples offered to illustrate the method is the uniqueness problem actually solved in general. Moreover we find that in the most interesting case (addition to the system A of a finite number of relations of finite degree) the method is in principle incapable of success for mathematical reasons. In addition to these technical difficulties there are compelling methodological reasons for preferring the RTM method to the method of adding primitives. (shrink)

A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...) emerge from the latter in living systems. Thus, several relational theories of living systems can be represented by natural transformations of organismic, relational structures. The ascent of man and other living organisms through adaptation, is viewed in novel categorical terms, such as variable biogroupoid representations of evolving species. Such precise but flexible evolutionary concepts will allow the further development of the unifying theme of local-to-global approaches to highly complex systems in order to represent novel patterns of relations that emerge in super- and ultra-complex systems in terms of compositions of local procedures. Solutions to such local-to-global problems in highly complex systems with ‘broken symmetry’ might be possible to be reached with the help of higher homotopy theorems in algebraic topology such as the generalized van Kampen theorems (HHvKT). Categories of many-valued, Łukasiewicz-Moisil (LM) logic algebras provide useful concepts for representing the intrinsic dynamic ‘asymmetry’ of genetic networks in organismic development and evolution, as well as to derive novel results for (non-commutative) Quantum Logics. Furthermore, as recently pointed out by Baianu and Poli (Theory and applications of ontology, vol 1. Springer, Berlin, in press), LM-logic algebras may also provide the appropriate framework for future developments of the ontological theory of levels with its complex/entangled/intertwined ramifications in psychology, sociology and ecology. As shown in the preceding two papers in this issue, a paradigm shift towards non-commutative, or non-Abelian, theories of highly complex dynamics—which is presently unfolding in physics, mathematics, life and cognitive sciences—may be implemented through realizations of higher dimensional algebras in neurosciences and psychology, as well as in human genomics, bioinformatics and interactomics. (shrink)

Kant's argument from incongruent counterparts for substantival space is examined; it is concluded that the argument has no force against a relationist. The argument does suggest that a relationist cannot give an account of enantiomorphism, incongruent counterparts and orientability. The prospects for a relationist account of these notions are assessed, and it is found that they are good provided the relationist is some kind of modal relationist. An illustration and interpretation of these modal commitments is given.

I argue that the conviction, widespread among philosophers, that substantivalism enjoys a clear superiority over relationalism in both Newtonian and relativistic physics is ill-founded. There are viable relationalist approaches to understanding these theories, and the substantival-relational debate should be of interest to philosophers and physicists alike, because of its connection with questions about the correct space of states for various physical theories.

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present (...) features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation. (shrink)

We should see the debate over the existence of spacetime as a debate about the fundamentality of spatiotemporal structure to the physical world. This is a non-traditional conception of the debate, which captures the spirit of the traditional one. At the same time, it clarifies the point of contention between opposing views and offsets worries that the dispute is stagnant or non-substantive. It also unearths a novel argument for substantivalism, given current physics. Even so, that conclusion can be overridden by (...) future physics. I conclude that this debate is a substantive one, which the substantivalist is currently winning. (shrink)