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Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 8 Feb 2010 11:18:17 -0600
Message-id: <C050A748-76F7-4EDA-B783-907BF742ED5B@xxxxxxxx>
On Feb 8, 2010, at 10:43 AM, Cory Casanave wrote:
> ...
> Considering the "Pat Axiom": That if 2 theories can be shown to be 
>incompatible they must share some concepts - intuitively obvious but I have 
>never seen it made explicit, thanks!    (01)

Actually, the "Pat axiom" needs a couple small qualifications.  First, each of 
the two theories in question has to be consistent.  An inconsistent theory is 
incompatible with every theory, regardless of any concept overlap.  Second, the 
theories must not put incompatible conditions on the number of things that 
exist.  In first-order logic (with identity), it is possible to express that 
there are only N things, for any natural number N.  So if T1 says "There are 
exactly three things" and T2 says "There are exactly four things", they will be 
incompatible even if they share no concepts (though I suppose one could say in 
this case that they share the concept of identity).    (02)

Yours in excruciating correctness,    (03)

Chris Menzel    (04)

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