Thu Dec 8, 2022
|Graduate Research Colloquium
Cosmic Topology, Conventionality, and the Constitutive A Priori
In classical general relativity, one models the physical universe with a spacetime, i.e., a 4-dimensional manifold (representing events) endowed with a particular metrical structure. Interestingly, it is possible to equip such a spacetime with a wide variety of global, qualitative properties, all of which are compatible with our best (even ideal!) observational evidence. What, then, is the epistemic status of such properties? The question is a pressing one, since some choice of global spacetime properties is required for the cogency of cosmological theorizing.
I consider, in particular, the puzzling epistemic status of the topology of space, viz., whether space is simply or multiply connected. (Extremely roughly, a multiply connected space has a “hole” or many “holes” in it, while a simply connected space does not.) A natural suggestion, building on work by Poincaré and Reichenbach, is that the topology of space is conventional. Unfortunately, though there is a sense in which calling spatial topology “conventional” is correct, conventionality of any stripe does not fully capture its epistemic status. This is because of its foundational role in cosmology: it would appear that the topology of space makes possible the application of fundamental physical concepts and subsidiary physical laws. Thus, I turn to Friedman’s work on the constitutive a priori and argue that our understanding of spatial topology requires the construction of a new epistemic category that incorporates aspects of both conventionalism and the constitutive a priori.