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Proof of Anything (Posted on 2003-12-13) Difficulty: 4 of 5
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.)
re: God's existence: | Comment 28 of 44 |
(In reply to God's existence: by Benjamin J. Ladd)

Benjamin,

Be careful, you probably do not know what you are getting yourself into. I suggest that you check out the "existence of God" discussion in the General Discussion forum and also the comments on the puzzle "Can or Can Not" in Paradoxes.


There are those among us who believe as you do and I recognize that there is no shame in wanting to share true faith (in fact I belieev the Bible enjoins a believer to do so). But remember there are also those among us who legitmaltly hold other beliefs.
I just wanted to let you know that you are setting yourself up for a lot of raised hackles, name calling and unhappiness.


I personally take accept your blessing gladly in the spirit in which it is meant and wish you the best in this holy season. May God shine his blessings upon you and keep you safe in the assurance of His love.
  Posted by FatBoy on 2003-12-17 08:35:27

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