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Nick_Tarleton comments on Reason as memetic immune disorder - Less Wrong
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It's not incoherent. There could be such a thing as Hypercomputation.
However, nobody has found any evidence that it exists so far - and maybe they never will.
Hypercomputation enthusiasts claim that its existence doesn't matter too much - and that it's a valuable concept regardless of whether it exists or not. Maybe.
I don't disagree (i.e., I don't see any positive reason to doubt the coherence of hypercomputation – though Michael sounds like he has one), but remember not to confuse subjective conceivability and actual coherence.