SUO: Semes To Be The Truth
John F. Sowa wrote:
>
> Jon,
>
> No, no, no!!!! Absolutely not:
>
> > > but it seems to me like, on the output side of things,
> > > anyway, that if something is indeed a theorem, then the
> > > canonical representative of its equivalence class ought
> > > to be just the value true.
>
> Some logicians made the mistake of identifying
> a proposition with the set of all possible worlds
> in which it happens to be true. But that identification
> collapses all theorems to just T. Such an idiotic collapse
> would cause Fermat's last theorem and "2+2=4" to be identified
> as "the same proposition". That definition utterly fails to
> capture the informal notion of a proposition as the "meaning"
> of a sentence. No mathematician in his or her right mind
> would ever say that Fermat's last theorem and "2+2=4"
> have the "same meaning".
>
> The definition I gave makes a much finer distinction of
> meaning, which I claim is much closer to the informal notion.
> Please reread the excerpt from Ch 5 that I put on the web:
>
> http://www.bestweb.net/~sowa/logic/meaning.htm
>
> John Sowa
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John,
Here's a statement to think about:
| Finally, and in particular, we get a Seme of that
| highest of all Universes which is regarded as the
| Object of every true Proposition, and which, if we
| name it [at] all, we call by the somewhat misleading
| title of "The Truth".
|
| C.S. Peirce, 'Collected Papers', CP 4.539.
Now, if every true proposition denotes the same object --
and here I think that Peirce ('Monist', 1906?) concurs
with what Frege also says, though I think that this is
just the very model of a typical mathematical attitude --
then all true propositions have ultimately one and the
same referential meaning, at least. Since Peirce uses
the term "proposition", unless he has in mind a design
to play it equivocally, for the "syntactic expression",
or the "sentence" as we more often prefer to say, then
I would have to say that this propositional expression,
say, "e", denotes a function e : X -> B, with the type
of e being left indefinite for the present moment, not
yet run time, nor even compile time, but only IOU time.
This semes to suggest that the type of the proposition,
to be e-nunciate, is a co-notation that e-fects itself
not in the mediate but only in the ultimate denotation.
I belive that Peirce would fairly call that a "symbol".
Jon Awbrey
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