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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.)
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I doubt I can do much to prove a lot of the 'core' concepts of rationality, but I can do a lot to point people towards it and shake up their belief that there isn't such a proof.
Here's the new thread for posting quotes, with the usual rules: