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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"
*

*>>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

Date: Fri, 23 Jul 2004 22:05:21 +0200

Hi George,

At 22:17 22/07/04 -0700, George Levy wrote:

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 ...

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

false.

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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