And am sorry at this time the "consciousness" in the OP, which some of us think we a) have and b) objectively demonstrate cannot be handled by the mathematics that describes and bounds your world of matter.
I would be very interested to see that objective demonstration, so please go ahead and present it.
This is an interesting idea to contemplate. What form could such a mathematical description take? How would you go about demonstrating that it isn't possible? Hmmm. Maybe using the uncertainty principle? Maybe using the incompleteness theorem?
More on this later.
I think this is a key question.
While I think not. Why do I feel that way? Basically because I think it's simply too much of a stretch of the term physical. What about numbers? Will you call numbers physical too? I just can't do it. Such things are not physical to me. Things less substantial than rainbows and sunshine don't count as physical to me. Think of it as a cultural bias on my part. One I am unable or unwilling to discard.
Do you suggest that we will eventually just run all these semantic (but iyo physical) constructs through the system:
"Is is consistently observable? Is it measurable? Could there be a testable hypothesis about it? Could it be described by some mathematical model?
If so then it is physical."
and answer all questions "correctly" with the logical systems of math and physics?
If not, why not?
The problem isn't that we can't do that, the problem is that we can't do so satisfactorily.
I could define consciousness = 1 and dead = 0 and asleep = .5. That's a mathematical model of consciousness. It's just a very poor one.
We should eventually be able to get what engineers call "close enough". Right now, only folks like RD and Pixy think we're there. We're certainly developing better and more useful artificial intelligences.
On the other hand, I find it quite plausible that we'll never get all the way there. It might be possible to prove it mathematically. It's an interesting question. If our neural system turns out to make use of quantum theory in some way (which is possible - I read an article a week or so ago about how plants were making use of it to extract energy from the sun) I think that would establish it as fact quite nicely.