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From: franka@mmintl.UUCP (Frank Adams)
Newsgroups: talk.philosophy.misc,sci.philosophy.tech
Subject: Re: Counting Statements
Message-ID: <2464@mmintl.UUCP>
Date: Thu, 8-Oct-87 17:53:03 EDT
Article-I.D.: mmintl.2464
Posted: Thu Oct  8 17:53:03 1987
Date-Received: Sun, 11-Oct-87 14:01:20 EDT
References: <2340@mmintl.UUCP> <8641@mimsy.UUCP> <2402@mmintl.UUCP> <881@sjuvax.UUCP> <171@yetti.UUCP>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Followup-To: sci.philosophy.tech
Organization: Multimate International, E. Hartford, CT.
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Xref: mnetor talk.philosophy.misc:728 sci.philosophy.tech:518

[I am moving this discussion to philosophy.tech, since it seems to have
become a philosophy of mathematics issue as much as anything else.]

In article <171@yetti.UUCP> peter@yetti.UUCP (Peter Roosen-Runge) writes:
|However, if you do feel convinced that infinite sets actually exist and
|that natural languages as sets are or can be infinite, why stop
|at the countable?  It turns out that the arguments for stopping at that
|cardinality aren't as strong as people used to think -- a beautiful hatchet
|job on the countability restriction has been provided by
|Langoeden and Postal in THE VASTNESS OF NATURAL LANGUAGE, Blackwell: 1984
|They argue that languages are far larger than countable and flit loftily up
|into the rarified stratosphere of transfinite cardinals and mega classes.
|
|The authors state that one does not have to be a platonic realist to accept
|their arguments but it sure helps!  At the very least, the book is extremely
|helpful in making clear what is at stake in allowing non-constructive
|descriptions of infinite classes.

It is a hazardous enterprize to argue against an argument which has not been
stated, but I am going to attempt it anyway.  I am assuming that Messers.
Langoeden and Postal are arguing that a sentence like:

"Consider a real number x."

has uncountably many meanings, since x can be any of uncountably many
values.  I think this is wrong; it has only one meaning, about an
incompletely specified value x.

Allowing non-constructive descriptions of infinite classes does not commit
us to believing that we can refer to particular non-constructive objects.
-- 

Frank Adams                           ihnp4!philabs!pwa-b!mmintl!franka
Ashton-Tate          52 Oakland Ave North         E. Hartford, CT 06108