Dear Bruno, perhaps the list will forgive me a bit of distraction upon your knight and knave koan. I call it a koan, because within your conditions there is no right solution to either of the questions. IMO Problem #1 is open, #2 is subject to unlisted circumstances. (Common sense). To make the question subject to 'common sense' logic, I put some restrictions on (my)

Problem JM: "In the desert watch-tower at the fork there are two guards, twins. One tells ALWAYS the truth, the other ALWAYS lies. One way leads to Bagdad, the other to the lion-desert. You can ask ONE question: to decide which way to go to Bagdad. Which one is that ONE question getting you the right answer without knowing Which brother is on duty?" I give you a day, if nobody does so,tomorrow I will post the answer. John Mikes ----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, July 20, 2004 12:43 PM Subject: ... cosmology? KNIGHT & KNAVE > At 09:55 20/07/04 -0400, John Mikes wrote: > >It all depends what do we deem: "POSSIBLE". According to what conditions, > >belief, circumstances? If we accept the "here and now" > >as "the world", Stathis #1 may be right. > > This would mean Stathis first assumption was a first person assumption, but the > whole point of Stathis seems (to me) third person. Also what would be the > meaning of "physical" in a first person assertion. > Perhaps Stathis could comment. > > Now you are right we should agree on what we deem "POSSIBLE". > With the comp hyp I argued that POSSIBLE = arithmetically consistent, and > then we can go back asking G and G* .... > > Giving that logic is not so well known apparently > I will soon or later invite you all to Smullyan's knight > knaves Island. It is the gentlest path to G and G* which are the > propositional psychologies from which UDA shows how to > extract the quantum measure in case (comp is true). > And from which I have extract some bits of von neuman's quantum logic > (but I am just beginning opening a vast and heavy doors here). > > Why not now? The native of that Island are all either knight or knaves > and knight always tell the truth, and knaves always lie. > You go there. > Problem 1. A native tell you "I am a knight". Is it possible to deduce > the native's type? > Problem 2. You meet someone on the island, and he tells you > "I am a knave". What can you deduce? > > I would be please to get answers, or critics. > I think it will be useful if only by John Mike remark: we will not progress > if we make not clear the word "possible" in our everything context ... > Logic can help because it is the science of proofS, truthS, and possibilitieS > (note the s). > > Bruno > > > > > http://iridia.ulb.ac.be/~marchal/ >