Theorem: false is true
Let P be the statement, "If P is true, then false is
Lemma: P is true.
Proof: In order to prove the implication of P, we
assume the premise and try to derive the
conclusion. So assume the premise of P,
namely, that P is true. Since P is true,
and premise of P, "P is true" is true, then
we know that the conclusion of P, "false is
true." is true. This proves the lemma.
Now, since P is true, and the premise of P, "P is
true" is true, the conclusion of P must be true, so
therefore false is true. This concludes the proof.
Of course you can substitute
for "false is true" in the above proof, but I thought this would be the most interesting
So what is going on here? Can we easily just prove any arbitrary claim? Of course, this proof contradicts our notion of truth... it can't be that C is true for any statement C. Well, it's as simple as that. Our notion of truth is just not well defined, and leads to contradiction.
Guess we won't be needing that Cause-Effect Nullifier...