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MatthewB comments on Outline of a lower bound for consciousness - Less Wrong
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I can understand your worries. It doesn't actually say that you can prove a lack of consciousness; but that you can prove that, under certain conditions, the meaning of the concepts in the mind would be underdetermined; and argues that you don't need to treat such an entity as conscious.
A fuller treatment would talk about what parts of the mind are conscious, or which concepts are accessible to consciousness. I don't think consciousness is a 0/1 binary distinction for an entire brain.
Upon reading it again (and with some input from a friend who is a logician - he said that this is something that he said I should have been able to understand myself - and upon going over it with him again, I discovered he was right), I get that there is this distinction now.
I don't think consciousness is necessarily a binary distinction for any part of the brain, or any thing for that matter. This does mean that it could be 0/1, but that it is likely that most things capable of exhibiting conscious behavior lie between the two degrees.