Jiro comments on No One Knows What Science Doesn't Know - Less Wrong
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I've tried this when arguing with utilitarians. As far as I know, it hasn't persuaded anyone.
Instead of "defending" your beliefs, you may want to try exposing those parts which seem weakest, so as to increase the probability that any errors in your web of belief will be be brought to your attention by your interlocutor.
Exposing your weaknesses increases the probability that your errors will be revealed as errors, but it also increases the probability that your correct beliefs will be falsely "revealed as errors". (In an area of weakness, your opponent could present flawed arguments whose flaws you would miss, leading you to believe them.)