metametameta
I was reading this list of proofs of God — which is really entertaining, but you’ve probably already seen it — when I came over this really clever argument:
META-PROOF
(1) This is a proof of God’s existence.
(2) If the reader finishes reading this proof, the existence of God will be proven to him/her.
(3) If the existence of God is proven, then God exists.
(4) Therefore, God exists.
The cleverness lies in the fact that it’s actually pretty difficult to pinpoint the trick the argument uses. What (I think) is about right is that it assumes its own soundness, and then deduces that since it’s sound, its conclusion is true, therefore, its conclusion is true. This is sort of like the (even stronger, even more puzzling) argument called Curry’s paradox — I’ve mentioned it before. Both the meta-proof and Curry’s paradox can be used to prove anything, so, inserting “God’s existence” for “anything”, here’s Curry:
If this sentence is true, then God exists.
Curry’s paradox is both shorter and harder to refute than the meta-proof. It seems completely obvious that if the antecedent of a conditional is true (in this case, “the sentence is true”), then so is the consequent (in this case, “God exists”). But that’s what the sentence says, so it’s true. So its conclusion is true; hence, God exists. But we can use this to prove anything, and the whole point of logic is to draw lines between valid and invalid arguments, true and untrue conclusions!
Head asplode seems appropriate. Bonus point: logicians are still undecided as to how to resolve this.
