[SCL] Quantifying over propositions

[Chris Menzel]

On Wed, Aug 10, 2005 at 09:04:58PM -0400, Bill Andersen wrote:
> John,
> 
> Seems you have a problem, unless I'm missing something.  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.  

The way the model theory currently works, "(city nyc)" is treated as a
functional term, and its denotation would be the value of whatever is
paired with whatever "nyc" denotes in the functional extension of
"city".  That's fine for now, since we don't have structured
propositions in the current model theory, just structurally simple,
0-adic relations.*  This example shows that, when we add such
propositions (as an extension to the standard, or whatever), we need
something like the square bracket notation to ensure we get the right
reading in intensional contexts. 

-chris

ps: Briefly and roughly, by "structured proposition" I simply mean a
notion of proposition rich enough to enable us to assign denotations to
proposition-denoting terms that vary in truth value systematically in
accordance with the syntactic structure of those terms, e.g., the
proposition denoted by "[and p q]" should be true iff the propositions
denoted by "p" and "q" are both true.