'Caught in the Net of our Concepts': Spacetime Ontology and the 'Constraints' of Objectivity
Edward Slowik
This presentation will investigate the concept of objectivity in spacetime theories, with special emphasis placed on (1) the relationship between objectivity and ontology, and (2) the problem of a subjectivist/relativist interpretation of spacetime theories that would either deny any form of objectivity, or, less drastically, claim that the objective features of spacetime theories are relative to the conceptual framework utilized by the particular theory. (As used in this context, “relative” pertains to a relativism concerning truth, ontology, etc., and not the Theory of Relativity, of course.) In fact, whether or not this second form of subjectivism/relativism, i.e., that objectivity is dependent on the theoretical construction of a particular theory, really does constitute a species of relativism (and if it does, what form of relativism) will be a central concern of our examination. In investigating both points (1) and (2), the importance of “constraints” within particular mathematical constructions of spacetime theories will prove beneficial in striving to understand (1), for it suggests that the underlying ontology has been “caught within the net of our (theory’s) concepts”. More specifically, given the conceptual apparatus and structures stipulated by a given theory, certain conclusions (or pathways for obtaining a range of possible conclusions) are open to the theorist, and others foreclosed—it is in this sense that a “constraint” has been imposed, and it is possible that these constraints can provide information on the underlying ontology. The use of constraints has been investigated by Galison (e.g., “Context and Constraints”, 1995), although our investigation will explore its usefulness in a different ways. Overall, it will be demonstrated that the relativism associated with (2) might still remain, although in a much weaker variety, since different theoretical constructions of the same physical phenomena or events can be interpreted as confirming the essential context-dependence of the underlying ontology. Nevertheless, this context-dependence does not threaten the objectivity of the different theoretical spacetime formulations, or, at least, it does not threaten a modest type of objectivism: as will be argued, constraints (even if dependent on the context of a given theory) are too weak to mount a successful challenge to objectivism, since it would need to be shown that the constraints imposed by competing theoretical constructions are directly contradictory, which is highly implausible if not impossible to prove. Overall, the manner by which the concept of constraints aligns with the further notions of invariance and structure, besides objectivism and subjectivism/relativism, will also figure prominently in the discussion.
The early attempts at examining these issues, especially in the “structuralist” literature of Weyl, Eddington, Russell, and Cassirer, will be explored, along with the recent discussions by Nozick (Invariances, 2001), Earman (“Laws, Symmetry, and Symmetry Breaking”, 2002), and others.