# Re: ... cosmology? KNIGHT & KNAVE

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Fri, 23 Jul 2004 22:05:21 +0200

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"
>
>First let's assume that the native is a knight. Since he tells the truth,
>then Santa Claus must exist. That's all,... we cannot go any further.

Do you see now that we can go further? You just showed true that if he is a
knight Santa
Claus exists, but that is what he said so he said something true, meaning
he *is* a knight
and then ...

>Now let's assume that the native is a knave. Then the statement he made is
>false. The corresponding true statement is: "If I am a knight then Santa
>Claus does not exist."

False statement you mean? I mean "p -> q" is false when p is true and q is
false.

>However we assumed that the native is not a knight. Therefore the
>statement does not apply. No information can be obtained from this statement.

All right somehow you make a point, but, as Stephen deplores, we are in
Platonia.
Do you agree that, (with x number):

"for all x, if x is bigger than 10 then x is bigger than 5".

If you agree you are in platonia giving that you have accepted that
the (admittedly vacuous) truth of all the following propositions:

if 1 is bigger than 10 then 1 is bigger than 5
if 6 is bigger than 10 then 6 is bigger than 5
if 100 is bigger than 10 then 100 is bigger than 5

So you accept the truth table of p -> q
1 1 1
1 0 0
0 1 1
0 0 0

p -> q is the same as -p v q, or -(p & -q)

So if a *knave* say (A -> B), it means really means -(A -> B) = (A and -B)
(the second row).

OK?

Bruno

http://iridia.ulb.ac.be/~marchal/
Received on Fri Jul 23 2004 - 16:02:41 PDT

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