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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: ( You must be logged in to post comments.)
  Subject Author Date
False implies anythingMath Man2011-01-04 18:01:32
re: another solutionSam2005-03-09 10:30:43
another solutionLogan2005-02-18 10:40:13
Equivocation of S and (S --> G)?Matthew Pianalto2004-03-09 20:29:07
Comment on solutioncogitater2004-02-02 03:27:52
This statement is false.Jeff2003-12-23 19:46:02
re(2): Partial disproofTristan2003-12-18 22:51:38
SolutionSolutionDJ2003-12-18 22:43:01
re:donnmike2003-12-17 22:07:15
Kripke solved it a long tome ago, Tristan.Penny2003-12-17 21:40:20
re: Partial disproofSilverKnight2003-12-17 20:10:18
Some ThoughtsPartial disproofTristan2003-12-17 19:27:29
No Subjectstephen ocone2003-12-17 18:03:06
re:SilverKnight2003-12-17 16:49:26
No SubjectBenjamin J. Ladd2003-12-17 16:38:44
re(2): God's existence:SilverKnight2003-12-17 13:35:07
re: God's existence:FatBoy2003-12-17 08:35:27
re: God's existence:donnmike2003-12-16 21:03:57
Hints/TipsGod's existence:Benjamin J. Ladd2003-12-16 18:40:33
re(3): statement 2donnmike2003-12-16 02:05:07
No Subjectdonnmike2003-12-16 02:04:22
re(2): statement 2donnmike2003-12-15 23:02:37
re: statement 2Sam2003-12-15 20:03:01
statement 2donnmike2003-12-15 12:24:14
re: The error; re: assumptionSam2003-12-15 04:43:13
assumptionmanuel2003-12-15 02:51:36
my thoughtsdonnmike2003-12-15 02:11:29
SolutionThe errorFederico Kereki2003-12-14 19:35:24
HEY, THEY JUST CAUGHT "GAMER" IN IRAQ !!Penny2003-12-14 15:16:07
re: Self-referential logic saved my life.Gamer2003-12-14 14:31:21
Self-referential logic saved my life.Eric2003-12-14 02:46:32
Some ThoughtsHas self-referential logic ever achieved anything?Penny2003-12-14 01:14:03
re(2): Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!Penny2003-12-14 00:37:42
re: Poor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!Sam2003-12-13 23:01:44
SolutionPoor Sam...Trying to be a philosopher while ignoring the Ancient Greeks !!!!Penny2003-12-13 21:54:10
Penny was right?!?!??!Gamer2003-12-13 21:45:51
re: Welcome to Logic 101Sam2003-12-13 18:09:09
Penny, you missed a chance to impress us...TomM2003-12-13 18:08:35
proof of anythingwinnie2003-12-13 15:58:06
SolutionUntying the Gordian KnotPenny2003-12-13 15:32:40
re(2): Welcome to Logic 101Penny2003-12-13 12:29:47
hm..Victor Zapana2003-12-13 12:24:00
re: Welcome to Logic 101Gamer2003-12-13 10:48:04
SolutionWelcome to Logic 101Penny2003-12-13 08:58:51
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