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Desrtopa comments on Philosophical Landmines - Less Wrong
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Of course, since you're not the person who actually believes in the position you're trying to refute, it's much harder to judge what would actually seem like a knockdown argument to someone who does believe it.
I've stood by watching lots of arguments where people hammered on the same points over and over in frustration, "how can you not see this is irrefutable!?" that I had long ago filed away for future notice as Not Convincing.
If I ever had this tendency it was knocked out of me by studying mathematics. I recommend this as a way of vastly increasing your standard for what constitutes an irrefutable argument.
I'm not even an amateur at math, but yes yes yes. Doing a few proofs and derivations and seeing the difference between math-powered arguments and not is huge.