Chris, (01)
On Wed, Feb 17, 2010 at 6:50 AM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
>
> ...
> As for charge #3 that you direct at Pat above, Pat has never claimed that a
>FO would include a complete, consistent, recursive axiomatization of
>arithmetic. You should be more careful about lecturing others about what they
>don't understanding. (02)
This reduces the debate, once again, to a definition of the words
"foundation ontology". (03)
Pat's exact words were (Feb. 1): (04)
"If you doubt that incompatible theories can be described in terms of
common, more basic elements, try presenting some incompatible theories
(and show how they are logically incompatible) and I will show how it
can be done." (05)
I'm happy you agree the axiomatic set theories of mathematics are such
incompatible theories. (06)
If Pat will now include the caveat, "not mathematics" (or anything
based on manipulations of symbols?) I suppose that is progress of a
sort. (07)
BTW Pat went on to say: (08)
"... (but if you do that, gird up your loins like a man and be
prepared to *admit* that the general principle holds, and don't run
off and bring up some orthogonal objection or keep adding more
examples ad infinitum - I don't want to waste time for no productive
purpose)." (09)
Your other arguments are with the authors of my references. As I
understand it you dispute the first author's use of the word
"theories" instead of the word "logics". And you dispute second
authors their proud claim of precedence for Thoralf Skolem. (010)
>> By the way, my alternative is to work directly with observations of
>> different kinds, perhaps indexed by labels, and implement
>> interoperability based on overlaps between sets of these, as the task
>> demands.
>
> Your alternative to *what*? (011)
FO, Pat C, Feb 14: (012)
Pat C: "In these discussions of the principles of an FO and a proposed
FO project,
not only has there been no technical objection to the feasibility of an FO
to serve its purpose (just gut skepticism), but there has also been a
notable lack of suggestions for alternative approaches that would achieve
the goal of general accurate semantic interoperability" (013)
-Rob (014)
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