The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the (...) assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

From recent writings of Brent Mundy and Michael Friedman we reconstruct two different representation-theoretic or embedding accounts of space-time relationalism, involving two different conditions on embeddings: respectively, uniqueness up to symmetry and uniqueness up to indistinguishability. We discuss the properties of these two accounts, and, with respect specifically to Friedman's projects, assess their merits and demerits.

All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (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)

ABSTRACT Let wF, wC+, and wC− be three distinct worlds, each of which contains only a single point-sized material particle, and in each of which spacetime is: uniformly flat, constantly positively curved, and constantly negatively curved, respectively. By the relationist’s lights, these worlds seem to be qualitatively identical. Nevertheless, for each world, there are propositions concerning possible arrangements of material points that are true in that world, but false in the other two. I argue that, surprisingly, the relationist can ground (...) these differences in the distinct non-modal and intrinsic relations that are instantiated in each of wF, wC+, and wC–. (shrink)

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)

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)

Scientific realism is dead, or so many philosophers believe. Its death was announced when philosophers became convinced that one can accept all scientific results without committing oneself to metaphysical existence claims about theoretical entities (Fine 1986, 112). In addition, the inability of self–proclaimed scientific realists, despite recurrent demands, to distinguish themselves from their rival anti–realists (Stein 1989) didn’t exactly help their cause. If realists cannot identify the key feature or features that set them apart from their opponents, then there is (...) really no need to conduct a debate on scientific realism, is there? (shrink)