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 0p -> 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/
