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Let's refer to emotion, for example. Say you feel happy. The state of being "happy" can be measured and quantified in terms of neurological impulses in our brains. But such a description in itself is insufficient to describe "happiness", because it is a state of mind that emerged out of an interaction between various neurons in our brains and external stimuli that we cannot fully catalogue. To fully describe the state of "happiness", we would require a whole new class of measurements, and not just those derived from brain scans.
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You are describing the concept of
qualia there, which indeed is a baffling concept once we realize the full implications of something that is seemingly so simple, however as much as I share your enthusiasm I do not see why do you automatically assume that such a thing is not measurable or synthesized down into its basic parts. Are you coming from an incompleteness theorem POV?
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Key word here being "model", an approximation of the actual thing, namely conscious thought.
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Well yeah, human understanding itself is a model of reality, and as human beings we are limited by our own perceptions and thoughts. I had already agreed that free will is real for all practical purposes given that its impossible for a human to completely understand another human (even himself), and as such its impossible to predict another person with a 100% accuracy. As such I thought we were discussing things on a more philosophical plane, no need to play with words and nuances. i'm just stating that there are no mistical qualities to human thought or the human mind problem that would hamper its possible study and break down. :/
I will read your link on emergence and come with my thoughts alter...