Chris, Pat, Azamat, (01)
On Thu, Feb 18, 2010 at 9:30 AM, Christopher Menzel <cmenzel@xxxxxxxx> wrote:
> On Wed, 20100217 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 (02)
You don't agree the axiomatic set theories of mathematics are incompatible? (03)
>> 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 LS theorem. (04)
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 LS theorem." (05)
Additionally in this thread I think Azamat Abdoullaev is calling me
"naive" because I am asking for information about Thoralf Skolem. (06)
More interesting is the argument you are developing Pat, in this and
the other threads. I'll try and enlarge on this a bit. (07)
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
nonmathematical realm of the "real world", defined mostly by its
nonmathematicality. (08)
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. (09)
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? (010)
I would almost be interested to see your model of the real world
without mathematics. (011)
It is a lot to abandon just so that you can keep your preconceptions
about universal meaning though. (012)
Anyway, thanks for asking for more detail on my own ideas: (013)
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]"???' (014)
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 (nonmathematical) 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. (015)
We can keep mathematics. Mathematics just becomes another (ultimately
contradictory) interpretation of realworld observations. (016)
On one level, to provide something concrete to relate the discussion
to, you can think of what I am proposing as casebased reasoning.
There are differences with the way casebased reasoning is usually
practiced today. We would not assume a finite, noncontradictory
solution set for a start. But as an initial intuition for how such a
model would work, casebased reasoning gives you some idea. (017)
But I'll step back and let you attack that before I say more. (018)
It may be moot anyway, because John's "catchall" project may be
sufficiently broad to resolve most of the disputes of interest to
Ontolog members. (019)
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. (020)
On the topic. I recall Doug F. mentioned some weeks back that
microtheories were largely dropped from Cyc: (021)
Doug F, Feb. 2: (022)
'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.' (023)
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? (024)
Rob (025)
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