Overcoming Metaphysics (Again!): Cassirer, Weyl, and Carnap on the Ontology of Spacetime

James Mattingly, Georgetown University

Many discussions of the 3d/4d issue focus on the theory of relativity in attempting to evaluate the truth of metaphysical claims about the nature of time. Insofar as these discussions move beyond the theory of relativity, they tend to look toward theories that attempt to mirror the empirical claims of the theory while proposing physical conceptions of space and time supporting the metaphysical presuppositions of those who are attempting to effect the move beyond relativity. Exchanges between adherents to basically relativistic views and those who propose, in effect, new scientific theories are legion. Janssen and Balashov (2002, 2003), for example, are responding to Craig's (2000ab, 2001ab) attempt to make just such a move, and they do so by ruling out the possibility of moving beyond relativity in the way that Craig does. The first part of the paper is an argument that such responses can never prove entirely effective, and for three reasons. First, they cannot predict the range of possible theories that are not relativity, and yet appear to respect the basic evidence for the theory. Nor, secondly, can their straightforward account of scientific methodology be expected to influence those who are motivated by a priori convictions in favor of a largely Newtonian cosmology, in the sense in which Newtonian cosmology is accepted as 3+1 dimensional. What is required instead is an account of scientific methodology that is at once more nuanced than theirs (in the sense that it is sensitive to Kuhnian style theses regarding the cognitive status of theory choice) and more radical (in the sense that it uncovers implicit commitments held by those who would attempt to use metaphysics to drive theory formation in physics in order to support a metaphysical view). The second half of the paper is an exploration of the 3d/4d debate in the foundations of spacetime theories from a novel perspective that attempts to provide a sketch of just such an account of scientific methodology. Naturally a full account is beyond the scope of a discussion in the ontology of spacetime. Here the basic view will be outlined in the context of the spacetime ontology debates. Toward that end the "debate" between Carnap and Weyl on the foundations of geometry and the space problem is rehearsed in relation to Cassirer's contribution. (Michael Friedman, has considered this debate in another context, but here I will consider the explanatory theses employed in the debate.)

Carnap in his dissertation, Space, argues that since the fact that a choice of metric may be arbitrarily chosen makes any choice of metric arbitrary, there are no facts about the geometry of space beyond the topological. Weyl (in Space, Time, Matter and Die Einzigartigkeit der Pythagoreischen Massbestimmung) on the other hand suggests that the facts of geometry follow from our basic commitments to what is to count as something subject to a measure procedure. I will argue that while Weyl has the better of the argument over the facts, his metaphysical commitments do not follow. After briefly introducing the version of functionalism Cassirer outlines in Einstein's Theory of Relativity, I will claim that he has the right blend of facts vs. things: The facts are to be accounted as nothing more than a reflection of our most comprehensive functional characterization of the world. But we do not have to deal with things, and "things" here is broadly enough construed to include spacetime. I outline a broadly Cassirerian account of scientific methodology that meets the desiderata outlined above. The moral I will attempt to draw should be obvious: those arguing against the necessity to accept relativity theory in its present form and attempting to draw ontological comfort therefrom are to be identified with the thoroughgoing conventionalism of Carnap's view; those arguing that the correct account of the empirical evidence is relativity theory in its spacetime form and attempting to support their metaphysics that way are to be identified with Weyl; finally I propose that Cassirer convincingly shows that we ought to accept the theory of relativity and make no pronouncement whatever regarding the metaphysical nature of spacetime.

At the end, some very basic problems facing the proposed view of scientific methodology will be aired and ignored.

James Mattingly
Philosophy Department
221 New North
Georgetown University
Washington, DC 20057