You've made a reductio of this train of philosophical thought because you have come up with statements that are entirely in contradiction with what you started your philosophical investigation on in the first place
If we knew of phenomena that couldn't be explained in terms of the few basic laws of physics (or, since physics is currently incomplete, if we had reason to believe such phenom will eventually be discovered), I would shrug and agree. But so far, it looks like everything conforms.
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Just because we are too computationally limited to do the reduction in full does not mean we have reason to believe the reduction can't be done in principle. (Bracing for your inevitable "what do you mean by "in principle" reply)
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I'll try a different tract: In the meantime, we still need to deal with these things we can't "yet" reduce as things on their own terms, existing in their own right, becuase without the reduction we have no way of establishing their reality
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