All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
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(3): statement 2 | Comment 25 of 44 |
(In reply to re(2): statement 2 by donnmike)

and if the conclusion about the scenario that i described involving tomorrows weather is technically correct, that both statements are true, then clearly the problem with the original paradox about the existence of god is one of semantics. saying that the statement is "logically true" means something quite different than saying that the antecedent and consequent of the statement are factually true. so the argument fails at line #8 when the logical truthfulness of the statement is extended to the factual truthfulness of its parts.

like i mentioned, i don't know much about logic so i realize that what i just said might not make any sense, and might reveal my ignorance and make me sound arrogant, but i don't see a problem with it.

also, i'm still sticking with my original comment that a statement can't be contingent on itself.
  Posted by donnmike on 2003-12-16 02:05:07

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information