> I would almost be interested to see your model of the real world without
> mathematics. (01)
If you are raising concerns about how this could be done, then Pat might
like to point you to Hartry Field's book - Science Without Numbers - for an
example, but this may not be what you are looking for. (02)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rob Freeman
> Sent: 18 February 2010 07:55
> To: cmenzel@xxxxxxxx; [ontolog-forum]
> Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
>
> Chris, Pat, Azamat,
>
> On Thu, Feb 18, 2010 at 9:30 AM, Christopher Menzel <cmenzel@xxxxxxxx>
> wrote:
> > On Wed, 2010-02-17 at 11:32 +1300, Rob Freeman wrote:
> > ...
> >> I'm happy you agree the axiomatic set theories of mathematics are
> >> such incompatible theories.
> >
> > I agree with no such thing
>
> You don't agree the axiomatic set theories of mathematics are
incompatible?
>
> >> 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".
> >
> > There isn't really anything to dispute, as if there are two sides to
> > the issue. "logic" is simply the wrong word.
> >
> >> And you dispute second authors their proud claim of precedence for
> >> Thoralf Skolem.
> >
> > They never claimed precedence for anything. And again there is
> > nothing to dispute. The authors simply gave an incorrect informal
> > characterization of the L-S theorem.
>
> So you dispute my use of the words "dispute" and "precedence", as well as
the
> first author's use of the word "theories" instead of "logics", and the
second
> authors' "characterization of the L-S theorem."
>
> Additionally in this thread I think Azamat Abdoullaev is calling me
"naive"
> because I am asking for information about Thoralf Skolem.
>
> More interesting is the argument you are developing Pat, in this and the
other
> threads. I'll try and enlarge on this a bit.
>
> Pat, you seem to be proposing a vast breach between mathematics and the
real
> world, so that you can separate yourself from the demonstrable
impossibility of
> a complete theory of mathematics, and keep your preconceptions about
> universal meaning alive in some non-mathematical realm of the "real
world",
> defined mostly by its non-mathematicality.
>
> It's an ambitious effort. You deserve more credit than Chris, because you
are
> absorbing arguments and responding to them creatively. Chris just disputes
> interpretations. Honestly, I respect ambitious and creative efforts.
>
> I can understand why you want to take such a radical step in a way.
> Intuitively the real world does ground our intuitions. It is something
objective. It
> makes sense you should be able to relate meanings based on it. If
mathematics
> refuses to match this expectation, the temptation to abandon mathematics
> must be strong, despite the enormous utility of mathematics in every
> constructive interpretation of the real world since... Stonehenge?
>
> I would almost be interested to see your model of the real world without
> mathematics.
>
> It is a lot to abandon just so that you can keep your preconceptions about
> universal meaning though.
>
> Anyway, thanks for asking for more detail on my own ideas:
>
> Pat C: 'Perhaps you could provide more detail for your alternative method
of
> achieving general accurate semantic interoperability? The sentence above
> conjures up nothing concrete in my imagination. How does one "implement
> interoperability based on overlaps between sets [of observations]"???'
>
> Actually, what I am proposing is not so very far from your "real world
without
> mathematics". It is just that this universal arbiter won't be a
(non-mathematical)
> theory about the real world. It won't be a theory at all, not a single
one. What I
> think can be the objective arbiter are *observations* about the real
world. The
> only trick is we must accept these same observations can lead to
different,
> contradictory, theories.
>
> We can keep mathematics. Mathematics just becomes another (ultimately
> contradictory) interpretation of real-world observations.
>
> On one level, to provide something concrete to relate the discussion to,
you can
> think of what I am proposing as case-based reasoning.
> There are differences with the way case-based reasoning is usually
practiced
> today. We would not assume a finite, non-contradictory solution set for a
start.
> But as an initial intuition for how such a model would work, case-based
> reasoning gives you some idea.
>
> But I'll step back and let you attack that before I say more.
>
> It may be moot anyway, because John's "catch-all" project may be
sufficiently
> broad to resolve most of the disputes of interest to Ontolog members.
>
> If the entire list is willing to get behind a project which takes as its
grounding
> principle that there is no single complete theory, that may be the best we
can
> hope for at this stage, and I would like to encourage that.
>
> On the topic. I recall Doug F. mentioned some weeks back that
microtheories
> were largely dropped from Cyc:
>
> Doug F, Feb. 2:
>
> 'This separation is something that Cyc worked on for years through its
> "microtheory" (context) system, but then (for reasons of philosophical
> purity) to a great extent discarded.'
>
> I didn't want to be distracted by this at the time, but can you clarify
Doug? What
> were the "reasons of philosophical purity" which caused Cyc to discard
> microtheories? Did they work, but get discarded because of the expectation
> there should be a single theory, or did they not work? If they didn't
work, why
> didn't they work?
>
> -Rob
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/ Community Wiki:
> http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-
> bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> (03)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (04)
|