Re: Propositions (Pat Hayes)
Date: Thu, 12 May 1994 12:08:21 -0500
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From: (Pat Hayes)
Subject: Re: Propositions
Cc: interlingua@ISI.EDU
>1. There is no special difficulty about propositions provided you
>don't demand a characterization of what a proposition is.  The
>philosophical problems are to be evaded by limiting ambitions.  We
>need to decide what properties of propositions as distinct from sentences
>are desirable and attainable.

But there *are* special problems with propositions, because they have a
special status with regard to the sentences of our language. No other kind
of thing is supposed to be what sentences (as opposed to terms) express:
but our standard model theory doesnt seem to allow sentences to express
them properly. So even if we managed to do a good CYC job on propositions
(ie, treating them as another ontological category like fish or kitchen
implemens and coming up with a convincingly rich set of intuitively
plausible axioms), we would still be left with the task of relating these
things to our language in an adequate way. 

>2. It seems to me that my 1979 "First order theories of individual concepts
>and propositions" was ok as far as it went and could serve as a basis for
>Interlingua.  What it didn't do, because I didn't know a good way of doing it,
>was to handle quantifiers with propositions in a good way.

Nobody knows a good way to do it; and not just becuse of lack of
creativity, but because there are some very general theorems that show that
whole classes of approach won't work. 

And this difficulty illustrates my point. Quantifier scope is a syntactic
notion. Why dont we get 'quantifying in' difficulties in describing, say,
kitchen implements? They arise in trying to describe propositions just
because we want to be able to say things like 'Joe believes ....' where the
'...' space is filled by an expression whose structure is supposed to both
fit into our formalism's syntactic rules AND denote the proposition that
Joe believes. The language has to be both stating and describing
propositions. And the quantifying-in snags happen when we try to bridge
this gap by a quantifier in the 'stating' part of the language binding a
variable in the 'describing' part. If we face up to this starkly by having
Joe believe quoted sentences, then quantifying-in becomes ill-formed; but
then we don't regard the formalism as being expressive enough.


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