Eliezer: There are an infinite number of truths of euclidean geometry. How could our finite brains know them all?
This was not meant to be a profound observation; it was meant to correct Silas, who seemed to think that I was reading some deep significance into our inability to know all the truths of arithmetic. My point was that there are lots of things we can't know all the truths about, and this was therefore not the feature of arithmetic I was pointing to.
A decision procedure is a finite specification of all truths of euclidean geometry; I can use that finite fact anywhere I could use any truth of geometry. I suppose there is a difference, but even so, it's the wrong thing to say in a Godelian discussion.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).
ETA: It would seem that rationality quotes are no longer desired. After several days this thread stands voted into the negatives. Wolud whoever chose to to downvote this below 0 would care to express their disapproval of the regular quotes tradition more explicitly? Or perhaps they may like to browse around for some alternative posts that they could downvote instead of this one? Or, since we're in the business of quotation, they could "come on if they think they're hard enough!"