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Re: [ontolog-forum] Search engine for the ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 28 Feb 2008 14:23:11 -0600
Message-id: <p06230909c3ecc7a50d88@[]>
At 2:12 PM -0500 2/28/08, John F. Sowa wrote:
>PH> The term 'foundations' is well chosen. When building a house...
>The analogy with houses is misleading because gravity creates
>a preferred direction of building (although there are many cases
>where builders jack up a house to construct a new foundation
>under it).  For mathematics, there is no inherent directionality.    (01)

What has that got to do with my point? I didn't speak of directions. 
If foundations were built in the air and houses hung from them (which 
does happen in rare cases) the point, and the analogy, would apply.    (02)

>PH> Similarly with mathematics and formal logic.
>Not really.  ....  no single system is the "foundation'.
>Instead, you have an open-ended collection of systems, and
>you can show relative consistency of one system in terms
>of another.  That is very different from the idea of a
>single, privileged, universal foundation for everything.    (03)

I agree. If you knew more about concrete foundation work, you would 
know that this applies to real buildings also :-)    (04)

But more seriously: in fact, in actual practice, there is a 
privileged universal foundation for virtually all of mathematics, to 
wit, ZFC.    (05)

Pat    (06)

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