Re: SUO: Re: Propositions
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