### An Illogical Argument ( from a friend )

In light of Beck's recent post, I have dug up the following illogical proof. I think he and I spent a some 52 hours trying to parse this and convert it to more formal logic. We vowed never to touch this stuff again :

The statement that there is no absolute truth is in and of itself an absolute, and if the statement were true, it would be self contradictory, and hence the statement is itself false.

Therefore, there is no such truthful statement. the statement that there is an absolute truth is also an absolute, and if the statement is true, it is not self contradictory. hence this statement by itself is not necessarily true nor false. if we assume that this statement is neither true nor false then we arrive at a contradiction, because the negation of the statement that there is absolute truth is the statement that there is no absolute truth.

Therefore, if one is true, the other must be false since both are absolute statements about truth or falsity. the statement that an absolute truth exists which is both true and false is false since we have shown that the negation of there existing an absolute truth is false. so, it must be that there is at least one absolute truth.

I.e., any theory in modal logic which is powerful enough to emulate itself contains at least one true statement.

ReplyDeleteBut wait. Emulating itself means has_proof("blah")=>blah is a true statement. So we knew that already, and your proof is useless.

This reminds me of a bit of sophistry I emailed Beck a couple weeks ago involving truth and Truth and noodles.

Not to mention A=>A.

ReplyDeleteI mean, most of the trouble I had with this was translating the vague english into logic. Also, if I recall correctly, the notion of truth in your axiom system is undefinable from within your axiom system ? And for some reason we thought he was illegally using excluded middle a few times and had to sort that out.

ReplyDeletewhat is the truth about Truth and noodles ?

Sounds like you've hit on Godels incompleteness theorem / Entscheidungsproblem / Church–Turing thesis, any system powerful enough to describe itself can't make conclusive statements about itself.

ReplyDelete