FOM: {n: n notin f(n)} - anaphora

[Dean Buckner]

> >     Some people were at that bar.  Some of them were drunk.  Some other
> >     people at the bar were laughing at them.

Chris Menzel writes

> I'm not sure if certain notable aspects of the grammar of your story whose
>difficulties are well-known -- viz., plural quantification and unbound
anaphora -- are > among the things you want preserved.  (For instance,
because the
> anaphoric references run across sentences, we can't expect to provide a
translation > of the story into  three distinct sentences using the standard
apparatus
> of  quantification.)

There are exactly the things I want preserved & as Chris writes the
difficulties are well-known to those whom they are well-known.  I'm not sure
how well known in FOM circles as I raised similar problems earlier this year
& met in the main with blank incomprehension.  The difficulty is that
anaphora is on boundary of philosophy and linguistics, and unlikely to be of
interest to mathematicians - metaphysica sunt, non leguntur, whereas
philosophers like myself find the jargon of set theory quite impenetrable -
mathematica sunt non leguntur.

I have a hunch there's a very deep connection between problems of
cross-sentential anaphora and set theory, a flavour of which as follows:

    Some people were at the bar.  The people were laughing.

There's a copious literature on the "expected completion" approach to
descriptions which do not satisfy a unique individual,  as Russell's theory
requires if his analysis is not to assert falsely that only one individual
satisfies the description.  Neale summarises this literature in Chapter 3 of
Neale [1] and himself argues for such an approach.  The difficulty is how to
complete the second sentence above to make the description unique.  Assuming
the two sentences are all we have, there is no extra information that would
allow this.  We're not saying the people who were laughing were the _only_
people at the bar.

Sommers [2] proposes a device that he calls the U-term.  This is a term that

"has restricted application so some given individual under consideration"
(p. 103 my emphasis).  Other writers have suggested a similar approach.
Clearly, this allows a Russellian analysis - only one bunch of people are
"under consideration".  But what is this property of being under
consideration, of being "mentioned".  There's another idea you meet in the
linguistics literature of conversational "salience".  You say one set of
people are "salient" whereas another maybe isn't.  It's quite incoherent if
you so much as scratch the surface.

My hunch is it's connected with the equally clumsy things Cantor and
Dedekind get into when they start off about sets

"By a "set" I understand each gathering-together (Zusammenfassung) into a
whole of determined well-distinguished objects ... of our intuition or of
our thought"

"Various things a,b,c, . comprehended from any cause under one point of
view".

That sort of thing.  As though the flashlight of the mind sort of
illuminates these things and  temporarily unites an otherwise disparate
collection of objects into a collection that is in some way not disparate.
You're tempted to ask, how does it do this, how does it get together these
disparate things? - the horse in America, the horse in Germany?

But then you realise that the expression "these disparate things" has
already done what you wanted to explain.

There must be a very deep connection between set theory and these kinds of
things, and it's mostly because of this that I'm generally hostile (as
everyone knows) to the Cantorean way of looking at things.  But I'm unable
to say any more on this at the moment.  (Which sounds portentous, but
actually I've got to and see to the children upstairs).


Dean

P.S.  Glad to see another philosopher (Chris Menzies) with a discography on
his website.  Sadly no dance music.


[1] Neale, S., Descriptions London/Cambridge Mass. 1990
[2] Sommers, F.  The Logic of Natural Language, Oxford 1982