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.
The title of this puzzle is "Proof of Anything." As the author has used the example of George Washington and the moon being made out of cheese, I gathered (this may be difficult for you to believe) that this problem wasn't merely about God's existence and was of a more general nature--"...find the problem in the logical conclusion derived from these set of statements." Fine, that's easily accepted all good and well. Still, there they are--those words "then God exists..." glaring at me from the computer screen and begging me to reply to them...
Here's my real fault with the problem and not at all from a religious standpoint--although it certainly does have its application. I believe that logic and reason must ultimately halt at fundamental statements that are either true or untrue and go no further. For example: God exists, I exist, I have brown hair. There we may conjecture some statement about reality if we assume that S is true or we may conjecture another statement if S is false. Faith, really then in the truth of one or the other of those statements is what enables us to make intelligible assumptions about this universe. As the faculties we employ in determining our faith in these fundamental assumptions are derived solely from our senses, our moral conscience, and our reason (others of varied faiths and occult practices would also include supersensual or spiritual revelation), it would seem pointless to begin at the statements themselves as any grounds for a proof. In fact, those assumptions that we hold dearest to us are still in fact unprovable assumptions and we've decided by faith alone to accept their truth.
My point is this: logic and reason are subordinate to faith and at bottom logic is merely a tool employed by faith to determine the truth of this universe. That truth is of course by no means "proven," it's entirely accepted by faith. By postulating sentences such as "if x is true, then pink elephants float in space..." and watching mystified at a two page discourse on a paradox arising from this inconsistency...
Well, my good friends, give me my faith.
Edited on December 17, 2003, 4:39 pm
No Subject
