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From: gawilson@watdragon.UUCP (Graham Wilson)
Newsgroups: net.puzzle
Subject: New Puzzle (honestly...)
Message-ID: <423@watdragon.UUCP>
Date: Sat, 22-Feb-86 04:50:39 EST
Article-I.D.: watdrago.423
Posted: Sat Feb 22 04:50:39 1986
Date-Received: Mon, 24-Feb-86 08:27:56 EST
Reply-To: gawilson@watdragon.UUCP (Graham Wilson)
Organization: U of Waterloo, Ontario
Lines: 23

I have read the last two or three hundred articles in new.puzzle, and I 
have not seen this one (or any variations).  Credit goes to me (Graham
Wilson) and Peter Fruchter.  We originally thought it up as an analogy
to explain Godel's Incompleteness Theorem...

Consider a machine which is used to create true sentences (for example,
the sentence "A dog is a dog" is true).  If the machine is "complete",
then it could, given time, produce the set of ALL true sentences.  If the
machine is "consistent", then all the sentences that it produces will be
true.

Question:  Can such a machine exist (even in theory)?

Note that your answer must involve an iron-clad proof (i.e. like a math
theorem.

Persons who have read "Godel, Escher, Bach, An...." by D.H. should consider
disqualifying themselves.

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Graham Wilson
University of Waterloo
gawilson@watdragon