Here is a nice little paradox:

Statement S: If S is true then God exists
Logically, statement S must be either true or false.

1. Suppose S is false.

2. If S if false, then any statement that starts with "If S is true..." is true *(see note)

3. Specifically, the statement "If S is true then God exists" would be true

4. This is exactly what S says, so S would have to be true

5. This is in contradiction with 1., so S cannot be false.

6. Therefore S is true.

7. So the statement "If S is true then God exists" is true.

8. By modus ponens, since S is indeed true, then the second half of that statement is true.

9. God exists.

Note of course that you can make the same argument to prove that God doesn't exist, or anything else.
What, if anything, is wrong with this proof?

*Note: This is the part that I expect most people will comment on. It is one of the standard logical rules that if something, A, is true, you can say "If (~A) then..." and that will always be true. For instance, I could say "If George Washington is alive then the moon is made of cheese" and that would be considered true in natural logic.

Sorry Sam, but I am going to do the unthinkable and agree with what a certain person said earler. (I am unable to reply to anything that person said, so I don't know who that person would be.)

The problem arises when you group a self referring sentence with another sentence by using a binary operator (like OR, or AND) Although problems can arise from a certain unary statement (This statement is false) we can prove that a statement can't refer to itself because the recursion never ends.

S = S=>X (X is the consequent that you explain after step 9)

S = S=>X

Replace S in S=>X with S=>X, and keep doing this.

...S=>S=>S=>S=>S=>S=>S=>S=>X

This obviously doesn't make sense, which is why it can't be proven true.

I will post another way to show this is false if I find it is fine. Otherwise I am still confused. I just remember you can't use the word in it's definition. Logic: Something of Logical nature.

Posted by Gamer on 2003-12-13 21:45:51