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 Proof of Anything (Posted on 2003-12-13)
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.

 See The Solution Submitted by Sam Rating: 3.6250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 False implies anything Comment 44 of 44 |
You can actually prove that God exists without saying that a false proposition implies anything.
S:If S is true, then God exists.
1. Suppose S is true.
2. Then, if S is true, then God exists.
3. From 1 and 2, God exists.
4. We have just proven that if S is true, then God exists.
5. That is what S says, so S is true.
6. We know that S is true, and if S is true, then God exists.
7. Therefore, God exists.

Edited on January 4, 2011, 6:02 pm
 Posted by Math Man on 2011-01-04 18:01:32

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