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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Barker, Sean (UK)" <Sean.Barker@xxxxxxxxxxxxxx>
Date: Mon, 4 Feb 2008 12:10:13 -0000
Message-id: <E18F7C3C090D5D40A854F1D080A84CA4AB6CF2@xxxxxxxxxxxxxxxxxxxxxx>

This mail is publicly posted to a distribution list as part of a process of 
public discussion, any automatically generated statements to the contrary 
non-withstanding. It is the opinion of the author, and does not represent an 
official company view.    (01)

Avril,    (02)

        You cannot prove 1+1=2. You can only prove 1+1=2 in some particular 
system. In practice, the most often used system has 1+1=0, as any half-adder 
design will demonstrate. Computers use this arithmetic system all the time.    (03)

        More germanely, it is not proving 1+1=2 that is interesting, but the 
ideas that the proof illustrates. These are not part of the proof, but part of 
the human experience of the proof. A degree in mathematics is not about proving 
various facts, but illustrating interesting concepts. Understanding the 
mechanics of a proof is rarely of itself interesting. Similarly, the problems 
of formally specifying software were less around specifying correctly, but 
around specifying it in a way that meant something to the reader.    (04)

Sean Barker
BAE SYSTEMS - Advanced Technology Centre
Bristol, UK
+44(0) 117 302 8184    (05)

BAE Systems (Operations) Limited
Registered Office: Warwick House, PO Box 87, Farnborough Aerospace Centre, 
Farnborough, Hants, GU14 6YU, UK
Registered in England & Wales No: 1996687     (06)

> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of 
> Avril Styrman
> Sent: 01 February 2008 21:32
> To: Christopher Menzel; [ontolog-forum]    (07)

> I still understand Gödel's proof as a proof that you just 
> cannot govern everything. It is clear even without any proof 
> about it. One way to prove that all cannot be proved is the 
> simple fact 1+1=2 cannot be proved. Or, if you prove it in 
> some formal system, then the axioms of that formal system 
> cannot be proven true.
<snip>    (08)

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