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Lumifer comments on Philosophy professors fail on basic philosophy problems - Less Wrong Discussion
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Because correct results or forecasts are useful and incorrect are useless or worse, actively misleading.
I can use a theory which gives inconsistent but mostly correct results right now. A theory which is consistent but gives wrong results is entirely useless. And if you can fix an incorrect theory to make it right, in the same way you can fix an inconsistent theory to make it consistent.
Besides, it's trivially easy to generate false but consistent theories.