Bruno,
"If I am a Knight..." is definitely Knave: a Knight would not make it a
condition of his stating whether S.Cl is 'true' upon HIS status in the
world. Such wishy-washy statement is Knavish.
It would be better put so: Since I am... - but still not Knightish (although
we did not hear about the logical prowess of Knights).
What difference would it make on S.Cl. if 'he' is anything else?
Bad proposition I think (PC).
John Mikes
----- Original Message -----
From: "Bruno Marchal" <marchal.domain.name.hidden>
To: "Everything List" <everything-list.domain.name.hidden>
Sent: Friday, July 23, 2004 9:09 AM
Subject: Re: ... cosmology? KNIGHT & KNAVE
> Hi George,
>
> At 22:17 22/07/04 -0700, George Levy wrote:
>
>
> >>(problem 4)
> >>You get a native, and asks her ........if Santa Claus exists.
> >>The native answers this: "If I am a knight then Santa Claus exists"
> >>What can you deduce about the native, and about Santa Claus?
> >
> >First let's assume that the native is a knight. Since he tells the truth,
> >then Santa Claus must exist. That's all,... we cannot go any further.
> >
> >Now let's assume that the native is a knave. Then the statement he made
is
> >false. The corresponding true statement is: "If I am a knight then Santa
> >Claus does not exist." However we assumed that the native is not a
knight.
> >Therefore the statement does not apply. No information can be obtained
> >from this statement.
> >
> >We still don't know if the native is a knight or a knave, and we still do
> >not know if Santa exists or not.
>
>
>
>
> Does everybody agree with George?
> Well, if everybody agree then ... everybody should think twice!
>
> (It *is* a little bit tricky, but that trickiness is really what we need
> to understand Godel, Lob, and then, as you can
> suspect, the derivation of physics from logic/arithmetic through Godel,
> Lob, ...).
> For the fun, I let everybody think twice!
> (Actually you really need to think "twice". This is a hint.
> Another hint: the reasoning toward the solution will look a little bit
> circular, but only "look"; appearance can be deceiving.
> Things will be more tricky when we will introduce the modal "know" or
> "believe",
> but that's premature. We are still in pure PC. (PC = Propositional
Calculus).
>
> George, thanks for your attempt. There is no shame to be wrong of course,
> on the contrary it is the *only* way to learn. Note that some professional
> mathematician have criticize my thesis by doing similar error!!!
> (most acknowledge at time, but not all!!!).
> It is my revelation of the last ten years, logic is not well known even
> by "scientist".
> ... and the problem 4 is somehow tricky, I let you enjoy thinking
> twice.
> If nobody solves the problem 4, I will give the solution tomorrow,
> unless someone asks for having more time ...
>
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
>
Received on Fri Jul 23 2004 - 16:12:37 PDT