Re: ... cosmology? KNIGHT KNAVE

2004-07-30 Thread Bruno Marchal
At 09:53 29/07/04 -0700, Hal Finney wrote: Tell me again where I am going wrong. OK. Consider each of these examples: 117. q ... 191. Bp ... 207. p - q Now, we will say that the machines believes something if it is one of its theorems, right? So we can say that the machine believes q, it

Re: ... cosmology? KNIGHT KNAVE

2004-07-30 Thread Bruno Marchal
At 12:47 30/07/04 +0200, I wrote: Oh, any accurate machine (for which Bp-p is true) is obviously normal. This is false. But an accurate stable machine will be stable. Just substitute p with Bp in (Bp - p) to get BBp - Bp. That's stability, not normality. Bruno http://iridia.ulb.ac.be/~marchal/

Re: ... cosmology? KNIGHT KNAVE

2004-07-28 Thread Bruno Marchal
Hi John, At 17:19 26/07/04 -0400, John M wrote: Bruno, (and ClassG) 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

Re: ... cosmology? KNIGHT KNAVE

2004-07-28 Thread Bruno Marchal
At 09:54 27/07/04 -0700, Hal Finney wrote: I am confused about how belief works in this logical reasoner of type 1. Suppose I am such a reasoner. I can be thought of as a theorem-proving machine who uses logic to draw conclusions from premises. We can imagine there is a numbered list of

Re: ... cosmology? KNIGHT KNAVE

2004-07-28 Thread Hal Finney
This is confusing because I believe p has two different meanings. One is that I have written down p with a number in front of it, as one of my theorems. The other meaning is the string Bp. But that string only has meaning from the perspective of an outside observer. To me, as the machine, it is

Re: ... cosmology? KNIGHT KNAVE

2004-07-27 Thread Hal Finney
I am confused about how belief works in this logical reasoner of type 1. Suppose I am such a reasoner. I can be thought of as a theorem-proving machine who uses logic to draw conclusions from premises. We can imagine there is a numbered list of everything I believe and have concluded. It starts

Re: ... cosmology? KNIGHT KNAVE

2004-07-26 Thread Bruno Marchal
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

Re: ... cosmology? KNIGHT KNAVE beyond.

2004-07-24 Thread Bruno Marchal
At 16:58 23/07/04 -0400, Jesse Mazer wrote: Bruno Marchal wrote: All right. But modal logic are (traditionaly) extension of classical logic, so that causal implication, or natural language entailment, when study mathematically are generally defined through modalities + material implication. So

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread Jan Harms
(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?Lets give a name to the sentence:S="If I am a knight then Santa Claus exists"1. If the

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread Bruno Marchal
At 16:15 23/07/04 +0200, Jan Harms 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? Lets give a name to the sentence: S=If I am a

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread Stephen Paul King
Dear Bruno and Friends, After having read Smullyan's wonderful little book and reading these posts I would like to point out a problem that I see. The notion of Knights and Knaves, as Truth and Falsehood-tellers (or reporters) respectively, tacitly assumes that these entities are

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread Jesse Mazer
Bruno Marchal wrote: Let us suppose the native is knave. Then what he said was false. But he said if I am a knight then Santa Claus exists. That proposition can only be false in the case he is a knight and Santa Claus does not exists. This only works if you assume his if-then statement was

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread Bruno Marchal
Hi George, At 22:17 22/07/04 -0700, George Levy wrote: Hi Bruno Bruno Marchal wrote: 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

Re: ... cosmology? KNIGHT KNAVE

2004-07-23 Thread John M
: ... 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

Re: ... cosmology? KNIGHT KNAVE

2004-07-22 Thread Bruno Marchal
Hi All Perhaps George Levy is right and I should explain better the strategy before proceeding. The role of the logical puzzle is to encourage you to some introspection. The puzzle are easy but at some point we will give the puzzle to the machine just for studying its psychology. You will see John

Re: ... cosmology? KNIGHT KNAVE

2004-07-22 Thread James N Rose
Bruno, Nice story and game depiction; it does help - somewhat - to explain a more expansive generalization of 'decidability' ..the bedrock on which 'logic' (at least for the traditional understanding of that term) relies. Global consistency 'permits' decidability 'which permits' logic. But

Re: ... cosmology? KNIGHT KNAVE

2004-07-22 Thread Bruno Marchal
James, You may be saying something, but the problems are not that sophisticate. There where default hypothesis, sure, like the hypothesis that the Knights and Knaves understand English ..., knows how to use a phone, and are able to survive more than a nanosecond ... There might be sense in your

Re: ... cosmology? KNIGHT KNAVE

2004-07-21 Thread Bruno Marchal
George, At 21:17 20/07/04 -0700, George Levy wrote: Bruno, John, Russell I am half-way through Smullyan's book. Nice! You will see how easy it will be to state precisely the main result and the open problems in my thesis once you grasp the whole FU. Of course, to really appreciate, there will be

Re: ... cosmology? KNIGHT KNAVE

2004-07-21 Thread John M
- Original Message - From: Russell Standish [EMAIL PROTECTED] To: John M [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; Bruno Marchal [EMAIL PROTECTED] Sent: Tuesday, July 20, 2004 7:29 PM Subject: Re: ... cosmology? KNIGHT KNAVE Russell, your solution (in your attachment) is the right one

Re: ... cosmology? KNIGHT KNAVE

2004-07-20 Thread John M
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

Re: ... cosmology? KNIGHT KNAVE

2004-07-20 Thread Russell Standish
What would your other brother say is the road to Baghdad? Then take the other direction! Cheers On Tue, Jul 20, 2004 at 06:18:43PM -0400, John M wrote: Dear Bruno, perhaps the list will forgive me a bit of distraction upon your knight and knave koan.

Re: ... cosmology? KNIGHT KNAVE

2004-07-20 Thread George Levy
Bruno, John, Russell I am half-way through Smullyan's book. It is an entertaining book for someone motivated enough to do all these puzzles, but I think that what is missing is a metalevel discussion of what all this means. Mathematical fireworks occur because we are dealing with