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 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