🚀 go-pugleaf

In article <1992Dec31.171138.18363@guinness.idbsu.edu>
holmes@opal.idbsu.edu (Randall Holmes) writes:

>In article <1hteqjINN85h@tamsun.tamu.edu> 
>cmenzel@kbssun1.tamu.edu (Chris Menzel) writes:

>>holmes@opal.idbsu.edu (Randall Holmes) writes:

RH:
>>>First-order logic does not commit one to abstract objects at all.

CM:
>>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.

RH:
>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.

Good.  And what does the semantics for set theory involve?

RH:
>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).

Nonsense.  ZFC^2 is consistent, and has no countable models.

RH:
>				    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).

That's precisely my point: the true semantics of ZFC presupposes a
proper class theory, which likewise presupposes a proper super-class
theory, and so forth.  May I assume that you have conceded my point?

>>--Chris Menzel
>>  Philosophy Department
>>  Texas A&M University

>-- 
>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

cordially,
mikhail zeleny@husc.harvard.edu
"Le cul des femmes est monotone comme l'esprit des hommes."