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Date: Tue, 10 May 1994 14:59:52 +0000
To: genesereth@cs.Stanford.EDU (Michael R. Genesereth), interlingua@ISI.EDU,
Subject: Re: propositions
At 10:50 AM 5/2/94 -0700, Michael R. Genesereth wrote:
>(1) From what I have heard on the interlingua mailing list and in private
>conversations, propositions CAN BE HANDLED via an ontology, just as we
>handle other important concepts....
Where does your optimism come from? As far as I am aware, every attempt to
formalise the notion of 'proposition' has failed, and all the technical
results which might be relevant to the possibility are negative.
There is one important difference between propositions and other kinds of
thing. In a logical language of the usual kind, things are denoted by
terms; but propositions seem to correspond to sentences. The complexity
comes in getting the nature of this correspondence clear. One can't
(usually) say that sentences denote propositions. But it is hard to see
what, other than sentences, should be considered to convey or describe
propositions. One can always enrich the term structure of (a theory in) the
language so as to make it have a term for every sentence, but then one is
skirting close to the paradoxical territory of self-reference: see
McCarthy's old theory for a well-worked-out example which didnt work.
Another other source of complication is that the relationship of sentence
to proposition is not 1:1. Several different sentences can express the same
proposition, everyone agrees (eg permute a few conjunctions). So the
natural idea would be to define a normal form which eliminates the
variation. If anyone is aware of a plausible candidate for such a normal
form, I'd love to hear why it is plausible.
And another famous source of complication comes from de re propositions. Is
this a proposition: the person standing behind you is female? If not, why
not: if so, how could it possibly be expressed in a formalism?
>(2) I have not yet gotten the sense that there is a consensus on the nature
>of propositions, i.e. the axioms that characterize them.
The finest minds in Western civilisation havn't come to a consensus on this
in hundreds of years. We should be very sceptical of a committee of even
the *very best* computer scientists claiming it has a 'standard'.
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