From: zeleny@husc10.harvard.edu (Michael Zeleny)
Newsgroups: rec.arts.books,sci.philosophy.tech
Subject: Re: A note on Modal Logic that has nothing to do with Ikky Sex
Date: 26 Dec 92 20:35:15 GMT
Organization: The Phallogocentric Cabal

In article <1h84e6INNhq@cat.cis.Brown.EDU> 
PL436000@brownvm.brown.edu (Jamie) writes:

>>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.

J:
>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.

Correct, on the assumption that it is limited to Hilbertian positive
logic.  (I feel some qualms about this attribution, -- exactly how
much of the work in logic, historically associated with his name, was
actually done by Hilbert himself?)

J:
>(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....)

As in the case of G\"odel's results, the expressive power of
arithmetic can be dispensed with, in favor of the quotation function.

J:
>>>A figurative circumlocution, huh? Well, I'll wait until I have
>>>a chance to do my assigned reading before following up on this.

MZ:
>>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.

J:
>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.

Bentham's theory of fictions played a cardinal role among the
influences of modern philosophy of language, from Russell to Quine.
See the monograph by C.K.Ogden, or Quine's "Ontological Relativity"
for more tedious details.

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."

J:
>With the apparent exception: That it does not exist.

The grammatical form of Church's phrase does not support reification.

MZ:
>>(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.

J:
>(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.)

This being a metalinguistic statement, the range of its quantifiers is
fixed accordingly.

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

J:
>Explain "any".

Regard it in the same manner as any reference to the universal
totality, as relative to a background linguistic theory.

MZ:
>>Snicker if you must.

J:
>Barely containing it.

I commend your forbearance.

J:
>>>I am nothing if not a dedicated amateur. Professional, too, but
>>>amateur nonetheless.

MZ:
>>Well, no one is paying me for this, so I must be a pure amateur.

J:
>Bravo.

Don't be so liberal with your praise, -- I mostly use my status as a
license to hurl abuse at paid professionals.

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.

J:
>Logic will do that.

Not really; but Kripke will.

J:
>The connections between Lob's theorem and Existentialism have
>been insufficiently explored.

If you say this sort of thing long enough, it is bound to end up in
somebody's .sig file.  Is that why you don't sign with your last name?

>Jamie

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