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Desrtopa comments on Philosophical Landmines - Less Wrong
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Have you ever come up with what appeared (to you) to be a knock-down argument for your position; but only after it was too late to use it in whatever discussion prompted the thought? Have you ever carried that argument around in the back of your skull, just waiting for the topic to come up again so you can deploy your secret weapon?
I have. Hypothesis: At least some of the landmines you describe stem from engaging someone on a subject where they still have such arguments on their mental stack, waiting not for confirmation or refutation but just for an opportunity to use them.
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.