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

[Chris Menzel]

> My position is that there are two
> radically different kinds of predication, as follows:
> 
>     Some people were at that bar.  Some of them were drunk.  Some other
>     people at the bar were laughing at them.
> ...
> As an exercise I'd challenge Richard or any other FOM'er to translate the
> simple 3-sentence story above into formal set-theoretical terms, in a way
> that preserves the logic of the story.

I'm not exactly sure what would count as preservation of the logic for
you.  In particular, 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.)  If not, and in particular, if you'll allow that to
laugh at a group is to laugh at each member of the group, how about:

  (EX)[(x)(Xx -> AtTheBar(x)) & (EYZ)(~Y = 0 & ~Z = 0 & Y U Z subset X &
  Y intersect Z = 0 & (y)(Yy -> (Drunk(y) & (z)(Zz -> LaughingAt(z,y)))))]

Chris Menzel