Re: Dementia Redux
That was just a Quip Ersatz Demonstrandum in response
to a current bit of expressivist looniness that I've
been running across on the web of late. It gave me
a feeling of deja vu back to the days when people
were puzzled over the notion that you could put
very different sorts of spaces in one-to-one
correspondence with each other, for example,
spaces that ought to be different on some
intuitive natural measure of complexity
like dimension or differential order.
This always turned out to symptomize
the fact that the people in question
were confusing cardinality with the
measure in question and most likely
lacked an adequate definition of
the natural property at issue.
By way of an object example, a lot of mathematical category theory
got invented in order to bring formal clarity to the distinction
between "natural" isomorphisms and the other kind.
So I think I detect something analogous going on with all this
talk about "expressiveness", as if the job of logic ended with
mere expression or representation. That was of course the big
issue in AI thirty years ago, but folks who cut their teeth on
effective syntax way back then have long since learned that it
will take a bit more in the way of practical performance if we
want our syntax to get any kind of bite on real world problems.
It will take efficient equational inference, just for starters.
Dawidowicz, Edward RDECOM CERDEC C2D wrote:
> Interesting proof, but how do you define 'expressive'?
> *********1000 0111 -0111***********
> Edward Dawidowicz
> US Army, RDECOM, CERDEC
> Command and Control Directorate (C2D)
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> -----Original Message-----
> From: owner-standard-upper-ontology@LISTSERV.IEEE.ORG
> On Behalf Of Jon Awbrey
> Sent: Friday, April 09, 2004 12:11 PM
> To: SUO
> Subject: Dementia Redux
> Theorem. Two dimensions (as in the space R^2) are not
> more expressive than one dimension (as in the space R).
> Proof. They have the same cardinality.
> Yeah, right.
> Jon Awbrey
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