(The dialogue between Cody, a Codicalist, and Tony, a Platonist, continues.)
CODY: Are all relations physical, or are some relations nonphysical?
TONY: I’d say yes. Being uncountably infinite is a property (one-place relation), but it’s not physical. Being the sidekick of Sherlock Homes is a relation, but it’s not physical. Do you count “linguistic” relations, e.g. as physical.
CODY: There is only an uncountably infinity if physical hypercomputing (of a sufficient Turing level) can be found to occur in nature or in a machine we make.
– Hyperarithmetical sets and iterated Turing jumps: the hyperarithmetical hierarchy
– Reverse mathematics, countable and uncountable: a computational approach
– Effective Mathematics of the Uncountable
“The sidekick of Sherlock Homes” (or all “linguistic” things for that matter) is physical: It’s print in books, magnetic states on disks, chemicals on films, neuronal states in brains, … .
TONY: Relations, per se, are neither physical nor nonphysical. Relations can be between physical things; or nonphysical things; or, even between physical and nonphysical things.
CODY: An ontology of physical + nonphysical is Platonism or Dualist Mentalism (which physicalism rejects).
The confusion between “linguistics” and “physics” — between (mathematical/formal) models/languages and (physical) reality/substrate — is what Victor Stenger defined as “platonism”.