RE: SUO: RE: Re: More KIF-ified Ontology Content
Pat,
I agree that looking for deep metaphysical differences in the
various notations for FOL is a waste of time. The best you can
find is improvements in computability and certain aspects of
human factors.
>Yes, I entirely agree. In fact there is a way to transcribe all of
>Hobbs' axioms and schemas (he has all this stuff worked out in
>enormous detail) into a slightly odd version of FOL (one that ought
>to appeal to Jon Awbry) in which every open sentence can be seen as a
>relation name (so you can write things like
>(R & Q)(a,b) to mean R(a,b) & Q(a,b) ), and all the 'things' in
>Hobbs' ontology become ways of talking about the things you or I
>would think were really there. (The cute part of this mapping is that
>one gets *exactly* the same conclusions, somewhat undercutting the
>ontological claims being made. Sorry, couldn't help a bit of public
>gloating there.)
That "odd" version of FOL is based on Boole, who applied his
algebra to propositions, sets, and monadic predicates. Frege
considered that a weakness, but that was primarily because
he was trying to drum up support for his own pet notation,
which everybody treated with all due respect -- they ignored it.
In 1870, Peirce generalized the Boolean approach to an algebra
of dyadic relations (much like what Hobbs is doing). Later,
Ted Codd, a former student of Arthur Burks (who edited vols.
7 & 8 of Peirce's Collected Papers), dusted off Peirce's
relational algebra as a foundation for his database theory,
which has been swallowed up (in a rather degraded form) as
the SQL query language -- which is in the Boole-Peirce-Codd
tradition.
Bottom line: Don't expect to find deep metaphysical insights
in the notations for FOL, since they can all be translated
from one to the other, salva veritate.
John Sowa
PS: That conclusion, however, does not apply to the various
versions of higher-order, modal, and metalevel languages,
which are very far from being intertranslatable.