Re: propositions (Pat Hayes)
Date: Thu, 12 May 1994 12:08:59 -0500
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To: Chris Menzel <>
From: (Pat Hayes)
Subject: Re: propositions
Cc: interlingua@ISI.EDU, kr-advisory@ISI.EDU

>>.... 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)).

OK, I agree. I still think its true that nobody has formalised the notion
of 'proposition' well enough to satisfy themselves. But I have to confess
to a lack of scholarship here in not being closely acquainted with the work
you mention. (I guess I am using the Fermats Last Theorem heuristic: this
is a sufficiently difficult and long-standing problem that anyone solving
it satisfactorily would cause a sufficiently big fuss that I would have
heard about it ;-))

>>...... 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).
I said 'skirting close', not necessarily 'inside'. 

>> 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.

But on what grounds should one prefer one granularity over another? I was
objecting to the idea that there was a theory of propositions. To be told
that we are free to construct one is not like having one constructed.

>> 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.

This is what I had in mind. Unless I completely misunderstand this (quite
possible), such a de re proposition, having physical objects as
constituents, could not possibly be anything of a syntactic nature.

>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). 

But who is "you" ? If we take it as a description then when I say "You have
a nice hat" I am apparently asserting "there is one and only one person I
am talking to and he has a nice hat". But that doesnt seem right. Its more
like a comment I might make into a tape-recorder; its not addressed TO you.

Im not saying that we have to get all this stuff clear in order to make
progress in knowledge representation, only that if someone says they are
going to describe propositions, they had better be able to account for it.

> 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.

This seems to have the same inadequacy, although I confess I dont know it well.

>...., 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.

Im not convinced you can. By all means lets try, but Im not persuaded that
any nontrivial account of proposition has yet been axiomatised. In
particular, the most fine-grained account essentially identifies
propositions with sentences, so the whole concept can be happily abandoned
in favor of a much clearer and better-understood one.

But let me finish by agreeing with you:

>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
>separate ontologies.

Pat Hayes

PS. No more from me to Interlingua on propositions. 

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