What we saw about theories and reduction is that in the case of reducibility we have a theory that enables the proof of definitions enabling the reduction. reference can be determined by reference in structures and it can also be the case that no term in is (even accidentally) co-extensional with a term in the vocabulary, . This means that determination of reference (Det-R) does not imply physical reductionism (PR) in cases where the set in Det-R is substituted by the singleton of some member of .
The upshot is that the link between theories as syntactic entities and reductionism doesn’t carry over to determination of reference and even accidental co-extensiveness between terms is ruled out.
This concludes my notes on Hellman’s “Physicalism: Ontology, Determination, and Reduction”. In the next update I’ll summarize what has been covered and give some examples and clarifications from another paper by Hellman, “Physicalist Materialism”, that appeared in Noûs in the late ’70s.