> Glenn wrote:
>>OK, let me explain this. First, Goedel's theorem says that within any logical
>>system, there are statements that you can KNOW to be true but you can't prove
>>to be true. There are technical limitations on the type of logical system.
>>Goedel's theorem does not apply to arithmetic with only +/- operations, (See
>>Tipler, Physics of Immortality p 193 (I think, my book is at home and this is
>>from memory)).
>
>Well, maybe we need to find a mathematician on the list to referee (since
>Glenn didn't like the opinion of the one I consulted). But I'm pretty sure
>the statement of Godel's theorem above is just plain wrong. Let me repeat
>my friend's version:
[ snipped, as it is stated above ]
I believe Glenn is agreeing with Allan's mathematician friend here about the
strength of the formal system: it must have axioms that postulate the existence
of the natural numbers and the operators thereupon.
However, with Allan I'm having trouble understanding how the undecidability of
theorems in formal systems bears on the question of SETI. Penrose has used
Godel to postulate that the current type of computing systems will never
reproduce human thought. That makes some sense to me, but I'm not seeing the
connection of Godel and SETI. Could you please elaborate Glenn?
Steve Anonsen
Erstwhile but no longer math student