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.
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).
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? Are they robots or humans? Looks like
machines. Are machines omniscient?

To your present 2 problems:
none of them CAN be a knight, because in all fairness, nobody knows what may
a person 'know' or 'believe' in the future. If I go to the Office of
Records, I may learn what that 'K' is.

John Mikes

----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
Sent: Monday, July 26, 2004 12:49 PM
Subject: Re: ... cosmology? KNIGHT & KNAVE

> Hi,
> At 19:47 23/07/04 +0200, I wrote:
> >Big Problem 5:
> >
> >Could a native tell you "You will never know that I am knight"  ?
> >
> >Very Big Problem 6:
> >
> >Could a native tell you "You will never believe that I am knight" ?
> It was perhaps not pedagogical to say "big" and "very big".
> Here John Mikes would be accurate to say those are not problems,
> but koans. So you can *meditate* on it ...
> My intent in the use of the word "big" was more to point on the fact
> that ,going from the preceding problems to those new one is,
> as you can guess, the passage from  ordinary logic
> to  modal  logic, giving that "knowing" and "believing" are modalities.
> Still we do have intuition on what knowledge and believe can be, and
> we can try to get some conclusion.
> Let us try the problem 5. Just to be sure let me know if you agree
> that the proposition:
> You will not know that Lance Amstrong has win the "Tour de France",
> is false. I mean the negation of "You will not know p" is "you will know
> OK then. Suppose the native is a knave. Then it means he is lying when
> he say that "you will never know I am knight". But that means I will know
> he is a knight. But I cannot *know* he is a knight if he is a knave, so he
> cannot be
> a knave, and thus he is a knight. But having reach that conclusion I know
> he is a knight, but then he was lying (giving he told me I will never
> know that. So he is a knave, yes but we have already show he cannot
> be a knave. It looks like we are again in an oscillating state of mind.
> Is it a tourist again? No. I told you it is a native and all native are,
> by the definition of the KK island, either knight or knave. So what?
> I will give many critics later on some "less good" chapter of FU, (ex:
> the chapter "the heart of the matter" is too short, or when he identify
>   a reasoner with a world in his possible world chapter, etc.)
> But Smullyan's discussion on the problem 5 is really quite instructive.
> Its attack of the problem 5 is quite alike my attack on the mind body
> problem, Smullyan will interview "reasoner" (actually machine) on those
> questions. And he goes on very meticulously by defining a hierarchy
> of type of  reasoner, making those problem, mainly the problem 6 more
> and more interesting.
> Indeed, with the problem 5, we are  quickly done, giving that the
> problem 5 leads toward a genuine contradiction even with the reasoner
> of lowest type: the one Smullyan calls the "reasoner of type 1".
> A reasoner, or a machine, or a system (whatever) will be said to be
> of type 1 if by definition the following conditions hold:
> 1) he believes all classical tautologies (our lowest type of reasoner
>      is already a platonist!)
> 2) if the reasoner ever believes both X and X ->Y, he will believe Y.
> I will also say, following Smullyan and ... Theaetetus, that a reasoner
> know p, in the case the reasoner believes p and p is true, that is when
> the reasoner correctly believes p.
> There is nothing metaphysical in our use of the word "believe". You can
> substitute it by "prove" or even just "print". That would mean you are
> in front of a sort of theorem prover which will, for any classical
> print it one day or an other (condition 1), and, in case it prints X and
> it will, soon or later, print Y. That is he prints a proposition if and
> only if he believes it.
> To transform the "koan 5" into a genuine problem, I must explain what it
> means for a reasoner to believe in the rules of the island. It means that
> if he met a native asserting a proposition p, then he believes the
> "the native is a knight if and only if p is true".
> We will write Bp for the reasoner believes p, and Kp for the reasoner
> knows p.   For exemple we have Kp <-> p & Bp
> problem 5' (ameliorated version):
> A visitor of type 1 meets, on the KK island, a native telling him
> "you will never know I am a knight". Convince yourself that this
> really cannot happen. Derive a contradiction.
> Problem 6' (new version):
> A visitor of type 1 meets, on the KK island, a native telling him
> "you will never believe I am a knight". Convince yourself that this
> can happen. Derive as many conclusions as you can (note that
> all FU will follow, and even my thesis!!! (if you are patient enough).
> The idea is to give more and more self-awareness to the visitor ...
> Curiously enough that path converges.
> Bruno
> PS Those who feels overwhelmed can wait I come back on problem 4,
> when I will recall a little bit more matter on propositional logic.
Apology for
> my post to Jesse which could look a little bit "advanced" for many
> (it presupposes FU and a little bit more). Actually writing this stuff
helps me
> for my paper. I thank you in advance.

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