How far down into philosophy does the mysterian attitude penetrate? I realize it's nothing new, since Christian and other religious philosophers have thrown in the towel when it comes to describing Deity. The problem of consciousness is now producing the same helplessness. When is a problem decreed beyond human competence and when is it just beyond your and my current competence? Is continued frustration the deciding factor?

What you seem to mean by "the mysterian attitude" is captured by your later phrases, "throwing in the towel" and "helplessness". In this sense, I don't know that there are any philosophers who count as mysterians, though I suppose Colin McGinn, who holds the view that our mind just cannot entertain the concepts necessary to solve the mind-body problem comes closest. He calls his view "cognitive closure". The idea is that human minds, like those of other animals, have an innate restriction on the range of concepts available to them. But one needn't go as far as McGinn's idea of cognitive closure to acknowledge that the concepts available for framing theoretical hypotheses concerning conscious mental activity - whether based in neuroscience or computational psychology - don't seem adequate to capture the character of conscious experience. But rather than throw up our hands out of frustration, most philosophers, whether they agree with this assessment or not, are continually trying to articulate ever more precisely just where the problem lies, and only in this way can a solution be achieved. In the end there is no generally agreed criterion for when a problem is hopeless. So long as someone is willing to work on it, it isn't.

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