Pat Hayes schrieb:
> Is there any utility in seeking a *definition* of proposition?
> Propositions are not after all a natural kind: (01)
As soon as one leaves Quine's view that there is only one kind of
abstract objects (sets) behind, then one can talk about natural kinds
even among abstract objects. Four comes immediately to mind: sets,
mathematical numbers, meanings, and propositions. And of these, I would
say, only propositions can lay claim to be truth-value bearers. (02)
> 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.
>> 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.
> Why not? It seems to me that as long as the equivalence is
> truth-preserving, (03)
But then you have already presupposed that there is some entitiy that is
a truth-value bearer, haven't you? (04)
> that way of defining them works quite well. Not perfectly, but it is a
> very good start.
> In our IKL formalism we extend FOL (actually CLIF, but that is not
> important) with a proposition-naming construction (05)
If these constructions do not name something that can be true or false,
then I think you have given them a bad name; more about this in my next
> written (that <sentence>), so for example
> (that (forall (x)(implies (P x)(R x a))))
> is the proposition which is true just when the sentence
> (forall (x)(implies (P x)(R x a)))
> 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.
> So, is this what propositions *really are*? I have no idea, nor of how
> one could answer such a question. (07)
I have taken for granted that there is consensus among philosophers that
in whatever way 'propositions' are to be defined or characterized, they
should have the feature of being truth-value bearers. In the
propositional calculus, we have variables for propositions, and as soon
as we insert a specific proposition we insert an entity that is either
true or false. (08)
> 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.
>> 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
> You seem to be under the impression that formality and truth are
> somehow incompatible. I find this position ridiculous. (09)
No, not at all. True propositions (as well as false) can of course have
a formal structure. And of course I belive in the inference rules of
deductive logic. What I meant comes in my next comment. (010)
>> You exemplify with FOL, but I wouldn't say that sentences
>> in FOL are truth-value bearers; they are forms for truth-value bearers.
> Pfui. Nonsense. What is your basis for this kind of a claim? (011)
I can't ascribe any truth-value at all to sentences such as 'there is an
x such that Fx' and 'for all x, if Fx then Gx'. Can you? (012)
>> 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?
> See above.
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