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)
<snip>
>
> 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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