FOM: In defense of vagueness_2.

[Jon Barwise]

Sol Feferman writes about vagueness and CH:
>
>I don't understand Tennant's alternative (2): "it has a precise sense, but
>it involves certain predicates (such as '...is bald') whose (precise)
>sense is such that they admit 'borderline cases'."
>
>In that case, I would say of a statement that it does not have precise
>sense...

It seems to me that (2) is coherent and that many of terms of ordinary
language are vague in this way.   The color term "blue" seems a case in
point; it has a precise sense, but the sense is a property with borderline
cases.  The cover Kleene's IM is blue. No doubt about it.  Kleene's
undergraduate text is grey, not blue.  "Smart" is another. Harvey is smart,
Dan Quale isn't.  But there are borderline cases, things where we are not
sure whether to call them blue or not, smart or not.  My copy of Lewis
*Counterfactuals* is sort of blue, maybe.   Bill Clinton is sort of smart,
maybe.

I doubt that this issue of vague_2 has anything AT ALL to do with CH.  IF
CH is vague, then it is surely not in this sense. The property of being a
set of natural numbers is not a property with borderline cases, surely.
Still, I do think it is interesting to try to see how to model vague
predicates in a mathematically precise way. I suggested one in a recent
message about infinitesimals.  I take a very different approach in a
chapter of by book *Information Flow* with Seligman.   There we looked at
vague predicates (short, tall, and the like) in terms of shifting
perspectives.  The sorites paradox turns into a neat little theorem, one
whose statement you will have to look at the book to read.  (Anything for a
sale!)

Jon

p.s. If YOU call me a charming guy and I will call you smart, too.