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" <[EMAIL PROTECTED]> To: "Everything List" <[EMAIL PROTECTED]> 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/ >
