🚀 go-pugleaf

In article <1hteqjINN85h@tamsun.tamu.edu> cmenzel@kbssun1.tamu.edu (Chris Menzel) writes:
>holmes@opal.idbsu.edu (Randall Holmes) writes:
>: First-order logic does not commit one to abstract objects at all.
>
>Seems hasty, Randall.  Don't you think the semantics for first-order
>logic (or better perhaps, a first-order language) commits you to
>(among other things) the semantic entities that interpret the
>constants and predicates of the language?  If so, then you're at least
>committed to sets or classes or, for friends of the forms, properties
>and relations as the meanings of predicates.
>
>--Chris Menzel
>  Philosophy Department
>  Texas A&M University

First-order logic doesn't commit one to the semantics for first-order
logic, either.  The semantics for first-order logic certainly does
involve some set theory.

Personally, I am committed to set theory, and so to semantics for
_some_ interpretations of first-order logic (all consistent theories
have countable models, after all).  But the intended interpretation of
Cantorian set theory _cannot_ have semantics in the sense indicated.
Its domain of discourse is _not_ a set, and most of its predicates are
_not_ sets or relations (all are "too large").  This is not specific
to Cantorian set theory; the same holds for the set theories derived
from NF.  If one tries to get around this by using proper classes,
super-classes, and so forth, one still has the same problem at a
higher level (the theory of the classes, super-classes, and so forth).
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu