Functionalism as a Species of Reduction

Abstract

This is the first of four papers prompted by a recent literature about a doctrine dubbed spacetime functionalism. This paper gives our general framework for discussing functionalism. Following Lewis, we take it as a species of reduction. We start by expounding reduction in a broadly Nagelian sense. Then we argue that Lewis' functionalism is an improvement on Nagelian reduction.This paper thereby sets the scene for the other papers, which will apply our framework to theories of space and time. (So those papers address the space and time literature: both recent and older, and physical as well as philosophical literature. But the four papers can be read independently.)Overall, we come to praise spacetime functionalism, not to bury it. But we criticize the recent philosophical literature for failing to stress:(i) functionalism's being a species of reduction (in particular: reduction of chronogeometry to the physics of matter and radiation);(ii) functionalism's idea, not just of specifying a concept by its functional role, but of specifying several concepts simultaneously by their roles;(iii) functionalism's providing bridge laws that are mandatory, not optional: they are statements of identity (or co-extension) that are conclusions of a deductive argument, rather than contingent guesses or verbal stipulations; and once we infer them, we have a reduction in a Nagelian sense.On the other hand, some of the older philosophical literature, and the mathematical physics literature, is faithful to these ideas (i) to (iii)-as are Torretti's writings. (But of course, the word 'functionalism' is not used; and themes like simultaneous unique definition are not articulated.) Thus in various papers, falling under various research programmes, the unique definability of a chrono-geometric concept (or concepts) in terms of matter and radiation, and a corresponding bridge law and reduction, is secured by a precise theorem. Hence our desire to celebrate these results as rigorous renditions of spacetime functionalism.

Humeanism in Light of Quantum Gravity

“…For discussion on spacetime functionalism seeKnox (2013);Read and Menon (2019);Baker (2020);Butterfield and Gomes (2020);Lam and Wüthrich (2020).26 Baker (2020) suggests that our concept of spacetime is a cluster concept, and that Knox (2013)'s criterion is only one of the possible alternative criteria for what counts as spacetime structure.…”