Here's another installment of rationality quotes. The usual rules apply:
- Please post all quotes separately, so that they can be upvoted or downvoted separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote from Less Wrong itself, Overcoming Bias, or HPMoR.
- No more than 5 quotes per person per monthly thread, please.
This is often a good idea in mathematics. Two concepts that are equivalent in some context may no longer be equivalent once you move to a more general context; for example, familiar equivalent definitions are often no longer equivalent if you start dropping axioms from set theory or logic (e.g. the axiom of choice or excluded middle).
Outside of mathematical logic, some familiar examples include: