Re: Name the thesis: "Formal sentences capture informal ones"

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 02/03/05 

Date: Thu, 03 Feb 2005 17:32:43 GMT

"Stephen Harris" <cyberguard1048-usenet@yahoo.com> wrote in message
news:y8tMd.196$ZZ.107@newssvr23.news.prodigy.net...
>
> "Jamie Andrews; real address @ bottom of message" <me@privacy.net> wrote
> in message news:36a8vlF4v8123U1@individual.net...
>>>> In comp.theory tchow@lsa.umich.edu wrote:
> It seems to me clear that the cardinality quantifiers E_K
> for ? uncountable belong to mathematics (specifically, set
> theory) and not to logic; they are all excluded by the
> homomorphism invariance condition, along with the E_K for
> K countable. As just remarked, the finite ones are recovered
> once one includes the identity I. The quantifier"there exist
> infinitely many", for K = Aleph_0 is a borderline case to
> which intuition and experience do not provide a clearcut
> answer as to its status. It can, however, be assimilated to
> logical notions under the homomorphism invariance criterion
> simply by restricting one's consideration to those operations
> which are invariant over infinite domains M_0, without
> thereby including the E_K for K uncountable. The
> "completeness" argument for logicality (suggested by Quine
> in the case of =) here gives quite anomalous results, since
> one has a complete logic for E_K for the case that ? = Aleph_1
> by the work of Keisler (1970) while, as is well known, there
> is no such logic for the case that ? = Aleph_0.
>

The "?" stand for K

Condensed from Sol Feferman:

'David Lewis makes a persuasive case that we do have
an independent grasp of plural quantification that
doesn't have to be explained in terms of second-order
quantification, though there appears to be an asymmetry
between existential plurals (natural) and universal
plurals (not natural) in English.'