free association proof theory

[fancybred]

"Proofs are the marks of concurrence", Steven Ericsson-Zenith wrote on the
FOM mailing list, in response to a post by Regien Stomphorst about stuff including "I would like to know when do mathematicians understand their subject matter? Do they agree on when something is understood and on what is understood?" The reason why this was funny was

Comments

[self_referent]

What's a "catch-22" in PL terms? ;) Logically, I suppose it's a decorated version of a one-step "Strange Loop" (from _G.E.B._), such as "This statement is false" or something.

[self_referent]

Catch-22: If you fly bombers, then you are crazy. If you are crazy, then you should not fly bombers. You can only be classified as crazy if you declare yourself as such to Doc X. But as soon as you've declared yourself to be crazy, you have revealed yourself as sane. And then you have to go back to flying bombers(...which means you must be crazy.)

At the heart of this construct is something like "this statement is false" (flipping between crazy and sane instead of between true and false), with the effect that you are trapped as a bomber pilot. I guess it can be represented as a Markov chain, such that with some probability, as a bomber, you go to Doc X and tell him you're crazy instead of flying another bombing run.

[fancybred]

yep, the PL equivalent is probably the lambda term omega = (\x.x x)(\x.x x)