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Re: [ontolog-forum] what is a proposition?

To: Ingvar Johansson <ingvar.johansson@xxxxxxxxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 24 May 2007 21:13:44 -0700
Message-id: <p06230904c27c0cc77e90@[]>
>Dear John and all others interested,
>I would like to switch from "truth and reality" to "what is a
>proposition?" Here is what one of my philosophical dictionaries says:
>"In philosophy, but not in business and sexual activity, a proposition
>is whatever can be asserted, denied, contended, maintained, assumed,
>supported, implied, or presupposed. It is that which is expressed by a
>typical indicative sentence. The same proposition may be expressed by
>different sentences."
>John F. Sowa schrieb (but italics mine, IJ):
>>  But I would like to restate
>>  them in terms of propositions, although the word 'proposition' is
>>  also considered to be in some *need of clarification*.  The definition
>>  of proposition that *I prefer* is one I stated in
>>      http://www.jfsowa.com/logic/proposit.htm
>>  The basic idea is summarized in the abstract of that paper:
>>      Informally, different statements in different languages may mean
>>      "the same thing." Formally, that "thing," called a proposition,
>>      represents abstract, language-independent, semantic content.
>>      As an abstraction, a proposition has no physical embodiment that
>>      can be written or spoken. Only its statements in particular
>>      languages can be expressed as strings of symbols. To bring the
>>      informal notion of proposition within the scope of formal treatment,
>>      this paper proposes a formal definition:  a proposition is defined
>>      as *an equivalence class of sentences in some formal language* L
>>      under some meaning-preserving translation (MPT) defined over the
>>      sentences of L. This paper defines a series of six MPTs f0,...,f5
>>      and recommends f4 as the most useful for most purposes.
>I have read your paper, understood (I think) your constructions, and
>have no objections to your views - apart from the fact that I find it a
>misnomer to call any of your six constructions a definition of
>"proposition".    (01)

Is there any utility in seeking a *definition* of 
proposition? Propositions are not after all a 
natural kind: they are not concrete entities like 
inscriptions: they are a theoretical construct 
invented to help give an account of meanings of 
languages. So the best approach to 'defining' 
them, it seems to me, is to emulate what 
mathematicians did to the various mathematical 
constructions about a century ago, and 
reconstruct a formally precise construction which 
has the same intuitive properties as our 
theoretical notion, to declare that these precise 
constructions 'are' the notion itself, or at any 
rate can be taken to be for purposes of precise 
theory, and proceed from there. Looked at in this 
light, John Sowa's constructions serve quite well.    (02)

>Earlier in the discussion, I got the impression that both
>of us were of the opinion that propositions are the primary truth-value
>bearers, but "an equivalence class of sentences in a formal language"
>cannot be a truth-value bearer.    (03)

Why not? It seems to me that as long as the 
equivalence is truth-preserving, that way of 
defining them works quite well. Not perfectly, 
but it is a very good start.    (04)

In our IKL formalism we extend FOL (actually 
CLIF, but that is not important) with a 
proposition-naming construction written (that 
<sentence>), so for example    (05)

(that (forall (x)(implies (P x)(R x a))))    (06)

is the proposition which is true just when the sentence    (07)

(forall (x)(implies (P x)(R x a)))    (08)

is true, in any interpretation. Thus, the 
proposition that is denoted by the naming 
expression depends on the interpretation of the 
nonlogical symbols in the embedded sentence, as 
one would expect. In order to construct a model 
theory, we needed to give a precise account of 
what it is that these proposition names denote. 
It has to be something which 'has' a truthvalue, 
and which obeys the same structural conditions on 
truth of subexpressions that sentences do. Other 
than satisfying those conditions, its exact 
nature is irrelevant. Several suitable 
constructions can be given, including a purely 
algebraic construction originally due to Tarski, 
but we chose an intuitively clearer notion based 
directly on the sentence syntax, which is 
essentially a sentential construction with all 
its free names interpreted in a domain of 
interpretation. For details see
and the 'guide' linked from there. The definition 
follows John's equivalence exactly, but treats it 
as an equivalence relation on these *interpreted* 
sentences rather than sentences themselves.    (09)

So, is this what propositions *really are*? I 
have no idea, nor of how one could answer such a 
question. Can one treat this construction as 
being an adequate mathematical model of 
propositions? I would suggest that one can; or at 
any rate, if anyone has a better idea, I'd love 
to hear about it. It certainly satisfies all the 
conditions listed in your philosophical 
dictionary.    (010)

>I have noted that you call your
>definition a "formal definition" of proposition, but I  think a more
>adequate label would be "definition of the formal-logical counterpart to
>propositions".    (011)

You seem to be under the impression that 
formality and truth are somehow incompatible. I 
find this position ridiculous.    (012)

>You exemplify with FOL, but I wouldn't say that sentences
>in FOL are truth-value bearers; they are forms for truth-value bearers.    (013)

Pfui. Nonsense. What is your basis for this kind of a claim?    (014)

>That is, you bring out something in your paper, but you do not, as you
>claim, *clarify* the traditional philosophical concept of "proposition".
>What do you (or someone else) say?    (015)

See above.    (016)

Pat    (017)

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