"Science Without Numbers" is out of print at Amazon. Any
other sources? (01)
-John Bottoms
FirstStar Networks Inc. (02)
David Leal wrote:
> Dear Chris,
>
> The book sounds interesting, but "without numbers" is not necessarily
> "without mathematics".
>
> Best regards,
> David
>
> At 16:18 18/02/2010 -0000, you wrote:
>
>>>I would almost be interested to see your model of the real world without
>>>mathematics.
>>
>>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.
>>
>>
>>>-----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
>
>
> ============================================================
> David Leal
> CAESAR Systems Limited
> registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
> registered in England no. 2422371
> tel: +44 (0)20 8857 1095
> mob: +44 (0)77 0702 6926
> e-mail: david.leal@xxxxxxxxxxxxxxxxxxx
> web site: http://www.caesarsystems.co.uk
> ============================================================
>
>
>
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