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.

"A conditional statement is false if and only if the antecedent (the IF part) is true and the consequent (the THEN part) is false. ("If George Bush is President, then the U.S. is at peace" is a false statement). It is true if both antecedent and consequent are true. ("If the Pope is Polish, then the moon is smaller then the earth" is a true statement.) It is also true if the antecedent is false and the consequent is true. ("If Ireland is more populous than India, then Tokyo is the capitol of Japan" is a true statement.) It is even true if both antecedent and consequent are false. ("If smoking cigarettes is good for your health, then drinking beer improves your driving skills" is, believe it or not, a true statement !!) "

We already know this. That's what the note says.

The way this proof works, is it says the statement is true, and then says the antecedent is true. Obviously in order to prove a statement, you need to actually prove it.

The part that you read is correct. We don't care about the consequent until the very end except for saying the original statement is true. This is possible by doing what is listed in the proof.

Posted by Gamer on 2003-12-13 10:48:04