Re: propositionsChris Menzel <firstname.lastname@example.org>
Subject: Re: propositions
From: Chris Menzel <email@example.com>
Date: Tue, 10 May 1994 17:08:48 -0500
Cc: genesereth@cs.Stanford.EDU, interlingua@ISI.EDU, kr-advisory@ISI.EDU,
In-reply-to: <199405101959.AA24456@dante.cs.uiuc.edu> from "firstname.lastname@example.org" at May 10, 94 09:59:52 am
X-Mailer: ELM [version 2.4 PL23]
Pat Hayes 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.
I think that's too strong, Pat. First of all, there surely are
formalizations of the notion of 'proposition' that have been
successful by at least a number of measures, e.g., Montague's
definition of a proposition as a function from possible worlds to
truth values. For some purposes, this notion is quite adequate (cf.,
e.g., Montague himself, Cresswell's work, or David Lewis's *On the
Plurality of Worlds*), though its shortcomings, e.g., for the analysis
of propositional attitudes, are well known. These shortcomings have
spawned a number of more fine-grained (as well as type-free) analyses
from, e.g., Ray Turner, Ed Zalta, George Bealer, and others that are
much more successful in dealing with the challenges on which the
possible worlds account founders. (Propositions on these accounts,
BTW, are all a special case of n-place relation (n=0, obviously)).
> 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.
Careful not to overgeneralize; the accounts of Turner and Bealer both
permit the construction of a term for every sentence, yet both are
provably consistent (relative to some fragment of ZF, of course).
> 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.
On Bealer's approach, for example, one can define a sort continuum of
granularity with a nearly 1:1 relationship of sentences to
propositions at one end and Montague-like propositions at the other.
This suggests the idea of a variety of normal forms depending the
one's preferred granularity.
> 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?
On a fine-grained approach, what proposition the sentence "The person
standing behind you is female" expresses is going to depend on context
and on your intentions as the speaker. If you are using the
description as a mere tag to pick out a certain individual (so that
the correctness of the description doesn't really matter), then (on
the "Russellian" view, at least) you are expressing a singular
proposition containing the person in question as a constituent (what
you're calling a de re proposition, I take it), the proposition itself
the result of a certain sort of predication operator that takes an
n-place relation and n individuals as arguments.
If you're using the description to pick out whoever it is who
satisfies it, then there are a couple of options. One is simply to
eliminate the description by means of a standard Russellian analysis
(There is one and only one person x such that x is standing behind you
and x is female), which then can be taken to be denoting a complex
"quantified" proposition (arising from a quantification operator from
simpler propositions). The other is to introduce a primitive
"description" operator that takes a property P to a property Q that
holds of m just in case m is the only P, and carry out the analysis Q.
Both approaches are discussed in the relevant literature.
> >(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.
This is owing in part to the fact that different conceptions seem
appropriate for different contexts. However, if we agree on a
particular conception, e.g., the idea of very fine-grained, singular
propositions with a structure that reflects the sentences that express
them, then there should be a very plausible set of axioms for this
conception (e.g., among others in this case, [Pa] = [Qb] iff P=Q and
a=b). But in other contexts we might want Montaguovian propositions,
and hence we'll need very different first principles. But we can
axiomatize them as well.
> 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'.
Agreed, it would be sheer hubris to propose *the* standard account of
propositions. What might more modestly be hoped for, however, is for
several conceptions of proposition to be isolated and, drawing upon
existing literature and powerful new formal techniques, theories
corresponding to each of these conceptions to be made available as
Christopher Menzel Internet -> email@example.com
Philosophy, Texas A&M University Phone ----> (409) 845-8764
College Station, TX 77843-4237 Fax ------> (409) 845-0458