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/
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
"
Tell me again where I am going wrong. 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
"believes Bp", and it "believes p->q", right? W
Hal,
I didn't see the whole post. So here is a sequel.
At 11:01 28/07/04 -0700, Hal Finney wrote:
BM:
> You are right. It is powerful, but rather fair also.
> let us define a machine to be stable if that is the case. When the
> machine believes Bx the machine believes x.
HAL: So in my terms, I can
At 11:01 28/07/04 -0700, Hal Finney wrote:
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.
OK. Let us call it the *intended meaning* of "I believe p" or of "Bp".
The other meaning is the
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,
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 everyth
Hi John,
At 17:19 26/07/04 -0400, John M wrote:
Bruno, (and Class)
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 be
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
'know' or 'believe' in the future. If I go to the Office of
Records, I may learn what that 'K' is.
John Mikes
- Original Message -
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Monday, July 26, 2004 12:49 PM
Subject
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 accura
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".
At 14:46 23/07/04 -0400, Stephen Paul King wrote:
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
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 in a sense, you confuse yourself by prem
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 in a sense, you confuse yourself by premature anticipation.
I know
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 na
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 tha
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
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
Omnisci
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
> (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 t
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
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 the native is a knight. Since he tells
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 r
ge-
> From: James N Rose <[EMAIL PROTECTED]>
> Sent: Jul 22, 2004 8:26 AM
> To: [EMAIL PROTECTED]
> Subject: Re: ... cosmology? KNIGHT & KNAVE
>
> Bruno,
>
> Nice story and game depiction; it does help - somewhat - to explain
> a more expansive generalization of
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 t
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 Joh
- 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 &
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 a
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
self-referenti
"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 k
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 qu
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