Grice on second-order set theory -- and why we need it

By J. L. Speranza
---- dedicated to R. B. Jones
------- for the Grice Club, etc.

I WAS RECENTLY DISCUSSING some of Grice`s points re: the analysis, or subanalysis, rather, of propositions (or propositional complexes, out of simplexes). Grice relies, explicitly on second-orde set theory:


"[W]e associate with the subject-expression of a canonically
formulated sentence [expressing a proposition, bearer of truth] a set of

at least second order."

--- He considers three cases:

First case: singular entities (as in "France", or "South of France")

"[1] If the subject-expression is a singular name, its ontological
correlate will be the singleton of the singleton of the entity which bears
that name. ..."

Second case: indefinite phrases (like "Somewhere in the South of France").

"[2] If the subject-expression is an indefinite quantificational phrase ..., its ontological correlate will be the set of all singletons whose sole element if an item belonging to the extension of the predicate to which the indefinite modifier is attached." ...

Third case: universal quantification (as in "All of France")

"[3] If the subject-expression is a universal quantificational [all-together, rather than one-at-a-time] phrase, ... its ontological correlate will be the singleton whose sole element is the set which forms the extension of the predicate to which
the universal quantifier is attached."
(Reply to Richards, p. 77ff).

The essay is not easily distributed, since it is in a festschrift, and who buys festscrhifts, but hey.

R. B. Jones may wonder about the technicality here of a second-order set theory.

In any case, it struck me as an intersesting case of Grice relying on some useful formalism (as per the philosophy or theory of mathematics and computer science) to deal with, er, the vernacular.

I suppose second-order set entities are no mystery to most, but it may do to revisit Grice´s motivations in so doing. On a longer day, though!