  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's 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.
  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
chrono-geometry to the physics of matter and radiation);
  (ii) functionalism's idea 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; 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). 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.
