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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Mon, 26 Jan 2009 13:37:37 -0500
Message-id: <497E02F1.6000304@xxxxxxxx>
Chris Partridge wrote:    (01)

> EB>While logic is the foundation for all of mathematics
> Is it really?
> I was taught, some time ago, that after Russell and Whitehead's failure,
> people were a little less optimistic about these kinds of claims. I have
> heard since some (maybe cynical) logicians say that they see mathematical
> logic as a branch of mathematics.
> I recall one saying that mathematical logic tended to focus on FOL as one
> could prove interesting results, but if you wanted to formalise any
> interesting mathematics, you needed to go higher order, but this was less
> tractable.    (02)

Philosophically, "logic" is the study of reasoning mechanisms -- "how to 
think".  Mathematical logic _is_ a branch of mathematics:  It is about 
formalization of logic itself as a set of theories -- reasoning about 
reasoning (and the artifacts of reasoning).  First-order logic is a 
formalization of one such mechanism, and is intentionally constrained in 
certain regards.  I didn't say that FOL was the foundation for all of 
mathematics, and I agree that it isn't.    (03)

[Pat and John will doubtless correct my less-than-well-educated 
exposition.  So I should probably have simply left the answer to them.]    (04)

-Ed    (05)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694    (06)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (07)

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