Hi John,
At 17:19 26/07/04 -0400, John M wrote:
>Bruno, (and Class<G>)
>
>We have an overwhelming ignorance about Ks and Ks. We don't know their
>logical built, their knowledege-base, their behavior.
Indeed.
>Is the K vs K rule a physical, or rather human statement, when - in the
>latter case there may be violations (punishable by jail - ha ha).
Neither physical, nor human ... (see below).
>Do K & K abide by 100.00% by the ONE rule we know about them, or ~99.999%,
>when there still may be an aberration?
100,00%
>Are they robots or humans? Looks like
>machines. Are machines omniscient?
Interesting question (not addressed by Smullyan!). But easy though.
From Godel's incompleteness (which we have not yet proved,
except in the diagonalisation post some time ago, but on which
we will come back: it is the "heart of the matter" in FU's term),
it will be easy to prove that:
- Machine cannot be omniscient.
- Both knight and knaves are omniscient, and so they cannot
be machine.
I expect, but will not argue now, that knights cannot exist at all,
even in platonia (and this with or without comp).
Does this throws doubts on what we can infer from FU's puzzles?
No, because the KK island is just a pedagogical tool for building
a fictive but easily imaginable situation where reasoners must
believe some self-referential propositions. But with the "diagonalization
lemma" (alias the heart of the matter) we will eliminate the need of the
KK island. It is the logical fate of the correct machine to meet
inescapably true and believable (provable) self-referential propositions,
from which we can derive true but unbelievable propositions,
... and much more.
Bruno
PS: "Thanks" to those who have send me hard puzzles! I will try to solve
them after 16 August. I will be busy until then. I will just answer Hal
Finney KK Posts, and then finish my paper. I hope I will get the authorization
to make it public soon for it will be a good base to proceed on. It is a
step toward the "English paper" I promised to Wei Dai, a long time ago.
http://iridia.ulb.ac.be/~marchal/
Received on Wed Jul 28 2004 - 05:54:18 PDT