### Re: ... cosmology? KNIGHT KNAVE

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

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

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

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

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

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

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.

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

(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

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

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

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

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

: ... 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

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

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

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

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

- 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

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

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

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