[SCL] Quantifying over propositions

[John F. Sowa]

Bill,

Yes, that is certainly true:

 > A sentence can be treated as a 0-ary relation if it appears
 > at the top level
 >
 >   (city nyc)
 >
 > but if you have instead, say
 >
 >   (believes john (city nyc))
 >
 > then it doesn't seem as if you have any way to tell if
 > you intend  '(city nyc)' to denote a proposition or
 > to denote some non- propositional object.

Yes, we definitely need a quoting mechanism -- that plus
the ability to refer to propositions by quantified
variables.  For example,

    (forall (p)
       (if (= p '(city nyc))
           (iff (p) (city nyc)) ))

In this notation, I'm assuming the Lisp conventions for
quote and eval:

  1. In (= p '(city nyc)), p refers to the proposition,
     which is asserted to be equal to the quoted expression.

  2. In (iff (p) (city nyc)), the truth values of p and
     the expression are asserted to be identical.

 > Plus, wasn't this point about the denotation  of 0-ary
 > relations settled in the model theory - in the way that
 > you  suggest?  I may be misremembering.

I thought it was, but in recent notes, the question came up
again, and the current draft of the proposed standard isn't
clear on this point.  We have to clarify these issues in
the ISO standard.

John