[...] but we have no guarantee at all that our formal system contains the full empirical or quasi-empirical stuff in which we are really interested and with which we dealt in the informal theory. There is no formal criterion as to the correctness of formalization.
-- Imre Lakatos, "What Does a Mathematical Proof Prove?"
ETA: When I first read this remark, I couldn't decide whether it was terrifying, or just a very abstract specification of a deep technical problem. I currently think it's both of those things.
Link appears to be broken.
This is our monthly thread for collecting these little gems and pearls of wisdom, rationality-related quotes you've seen recently, or had stored in your quotesfile for ages, and which might be handy to link to in one of our discussions.