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
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/
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
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
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
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
(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
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
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
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
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
: ... 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
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
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
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
- 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
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
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.
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
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