Why I believe that 1≠2 more than I do the existence of God
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Loading ...Well, personally I am agnostic/atheist, but I’ve heard from several people that believe in God, that they believe “he exists” more than they believe that 1≠2.
Please put aside for one moment the exact meaning of the sentence “God exists”. All knowledge is, to an extent, subjective. I know that 1≠2 because it is a mathematical theorem, but also is a theorem that Zorn’s Lemma is provable from the Axiom of Choice – my level of confidence in these two theorems being true is rather different.
I claim that anyone (if he understands logic), even if he believes that “God exists”, should place more confidence in the statement “1≠2” than in his belief in God *. Why? Let’s assume 1=2, and prove God does not exists:
- Assume 1=2, and suppose by negation that God exists
- 1≠2 (from standard arithmetic axioms and inference rules)
- If God exists, then 1=2 and 1≠2 (from 1 and 2)
- Therefore, God does not exist (from 3, by Proof by Contradiction)
Q.E.D
So, one can prove from 1=2 that God exists, but I doubt you’ll find a proof that 1=2 from the assumption God exists. So believing 1=2 requires more faith, and provides more information, than believing God exists (because it implies God exists, but the other way around does not hold).
* Of course, there is at least one flaw in the above argument. Can you find it?
Anna:
Hey Ron,
There is something here that sounds fishy to me.
Lets change your statement 1 to:
Assume 1=2, and suppose by negation that “The sky is blue” (or any other statement).
This way you can prove/disprove anything (no matter if it is true or not).
On the other hand, if you assume that “God exists and created the world as it is” (I think that the standard definition in religion is that god created the world, and therefore can control the way it works), you can infer that since logic as we know it is part of the world, god made it so that 1=2. On other worlds, it could be different (for example: 1=3 in some worlds – group theory flashback – depending on our assumptions).
20/4/09, 22:20Eli:
Line 3 is just wrong. 2 negates the first assumption in 1, there’s nothing relating to the second assumption.
21/4/09, 18:03Sam:
As my Algebra lecturer would say: 1 DOES equal 2, but that is so if the world we’re talking about is Z1, which (as he would also note to the class) is a trivial and boring field, and therefore we shall not mention it any further…
22/4/09, 14:12