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.
- Please post all quotes separately, so that they can be voted up/down 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- Do not quote yourself.
- Do not quote comments/posts on LW/OB.
- No more than 5 quotes per person per monthly thread, please.
I don't really follow. How is arbitrarily divisible not the same as infinitely divisible? If there is some limit to the arbitrariness then it's just atomism discussed. If there is no limit, then it seems like infinity to me.
(Most of the arguments against continuity use this sort of induction; continuity causes problems at this level, and it logically causes problems on n+1 levels; therefore it causes problems on all levels.)
If atomism is false, then for any matter and any n, the matter can be divided into n parts (whatever that may mean); this is a finite division, so if we started with a nonzero amount of "stuff" (whatever that may mean), the parts we divided it into should also comprise nonzero amounts of "stuff" that total to the original amount of "stuff". No problem there.
The apparent problem (which I would say isn't one really, but that's not the point, because there's no way the Greeks could have been expected to come up with why not) app... (read more)