From: PL436000@brownvm.brown.edu (Jamie)
Newsgroups: rec.arts.books,sci.philosophy.tech
Subject: Re: A note on Modal Logic that has nothing to
Date: Tue, 22 Dec 1992 17:22:15 EST
Organization: Brown University - Providence, Rhode Island  USA
NNTP-Posting-Host: brownvm.brown.edu
News-Software: BNN via BNN_POST v1.0 beta

>Posted on 22 Dec 1992 at 16:30:47 by Michael Zeleny

MZ:
>In fact, I glossed over an important detail in my argument.  A language
>may be semantically closed, in the sense of containing intensional
>meaning predicates applying to (the senses of) its own expressions, and
>yet remain consistent.

Well, actually, I would have thought it was fairly obvious that
a language can do that. So long as it doesn't have TOO many
of those predicates. For example, a language could contain
its own truth predicate but not its own falsity predicate.
(It is a popular misconception that Tarski showed a language
cannot contain its own truth predicate. Even for smooth,
stratification-free languages, it is pretty obvious that
he showed only that none can contain its own FALSITY
predicate. Even then, of course, only that no language
with at least the expressive power of arithmetic cannot....)

>J:
>>A figurative circumlocution, huh? Well, I'll wait until I have
>>a chance to do my assigned reading before following up on this.
>
>No need to wait: chances are that I am merely blabbering.  No relation
>to Hallett's book, anyway.  Instead of "figurative circumlocution", you
>may read "contextually eliminable Benthamian fiction".  Same difference.

A Benthamian fiction?

Hmm.
Let's see. Why Benthamian?

Well, perhaps one Benthamian fiction is "the greatest number."
Bentham wrote about the greatest happiness of the greatest number,
right? That MUST have been a fiction. Unless he's a finitist.

>J:
>>I can't resist adding this before I do my reading:
>>
>>It appears that no sentence of the type "We cannot quantify over
>>everything at once" is true. And yet, it also appears that we
>>cannot quantify over everything at once.
>>How odd.

MZ:
>To cite Church summarizing Frege, "nothing can be said truly of what
>does not exist."

With the apparent exception: That it does not exist.

>(i)     We cannot quantify over everything at once.
>
>will come to be analyzed as:
>
>(ii)    In any language L, the range of each quantifier is limited in
>        virtue of not containing any items of type T.

(I wasn't going to object to the quantification over languages. I
was going to ask what the range of the SECOND "any" is supposed to be.)

>process.  So I claim that the propositions expressed by the sentences of
>*any* language, are in fact infinite abstract objects.

Explain "any".

>Snicker if you must.

Barely containing it.

>>I am nothing if not a dedicated amateur. Professional, too, but
>>amateur nonetheless.
>
>Well, no one is paying me for this, so I must be a pure amateur.

Bravo.

>J:
>>One last bit:
>>I have to agree that the Kripke theory of truth does not ultimately
>>avoid a Tarskian hierarchy. Kripke himself says something like,
>>"The ghost of the Tarski hierarchy still haunts us."

MZ:
>It makes me wonder about the point of it all.

Logic will do that.
The connections between Lob's theorem and Existentialism have
been insufficiently explored.

Jamie