the complexity is the rise of consciousness and the qualia of sensory experience and others.
Here are a few cases and philosophers who give their arguments why things such as consciousness will be too hard to explain in physical science terms.
What it's like to be Problem:
Thomas Nagel (1974) argues that conscious experience is subjective, and thus permanently impossible to objective scientific understanding. He invites us to ponder ‘what it is like to be a bat’ and urges the intuition that no amount of physical-scientific knowledge (including neuroscientific) supplies a complete answer. Nagel's intuition pump has generated extensive philosophical discussion. At least two well-known replies make direct appeal to neurophysiology. John Biro (1991) suggests that part of the intuition pumped by Nagel, that bat experience is substantially different from human experience, presupposes systematic relations between physiology and phenomenology. Kathleen Akins (1993a) delves deeper into existing knowledge of bat physiology and reports much that is pertinent to Nagel's question. She argues that many of the questions about bat subjectivity that we still consider open hinge on questions that remain unanswered about neuroscientific details. One example of the latter is the function of various cortical activity profiles in the active bat.
Explanatory Gap by David Chalmers
More recently philosopher David Chalmers (1996) has argued that any possible brain-process account of consciousness will leave open an ‘explanatory gap’ between the brain process and properties of the conscious experience.[10] This is because no brain-process theory can answer the "hard" question: Why should that particular brain process give rise to conscious experience? We can always imagine ("conceive of") a universe populated by creatures having those brain processes but completely lacking conscious experience. A theory of consciousness requires an explanation of how and why some brain process causes consciousness replete with all the features we commonly experience. The fact that the hard question remains unanswered shows that we will probably never get a complete explanation of consciousness at the level of neural mechanism. Paul and Patricia Churchland (1997) have recently offered the following diagnosis and reply. Chalmers offers a conceptual argument, based on our ability to imagine creatures possessing brains like ours but wholly lacking in conscious experience. But the more one learns about how the brain produces conscious experience--and a literature is beginning to emerge (e.g., Gazzaniga, 1995)--the harder it becomes to imagine a universe consisting of creatures with brain processes like ours but lacking consciousness. This is not just bare assertion. The Churchlands appeal to some neurobiological detail. For example, Paul Churchland (1995) develops a neuroscientific account of consciousness based on recurrent connections between thalamic nuclei (particularly "diffusely projecting" nuclei like the intralaminar nuclei) and cortex.[11] Churchland argues that the thalamocortical recurrency accounts for the selective features of consciousness, for the effects of short-term memory on conscious experience, for vivid dreaming during REM (rapid-eye movement) sleep, and other "core" features of conscious experience. In other words, the Churchlands are claiming that when one learns about activity patterns in these recurrent circuits, one can't "imagine" or "conceive of" this activity occurring without these core features of conscious experience. (Other than just mouthing the words, "I am now imagining activity in these circuits without selective attention/the effects of short-term memory/vivid dreaming/...").
Qualia problem
A second focus of skeptical arguments about a complete neuroscientific explanation of consciousness is sensory qualia: the introspectable qualitative aspects of sensory experience, the features by which subjects discern similarities and differences among their experiences. The colors of visual sensations are a philosopher's favorite example. One famous puzzle about color qualia is the alleged conceivability of spectral inversions. Many philosophers claim that it is conceptually possible (if perhaps physically impossible) for two humans not to differ neurophysiologically, while the color that fire engines and tomatoes appear to have to one subject is the color that grass and frogs appear to have to the other (and vice versa). A large amount of neuroscientifically-informed philosophy has addressed this question. (C.L. Hardin 1988 and Austen Clark 1993 are noteworthy examples.) A related area where neurophilosophical considerations have emerged concerns the metaphysics of colors themselves (rather than color experiences). A longstanding philosophical dispute is whether colors are objective properties existing external to perceivers or rather identifiable as or dependent upon minds or nervous systems. Some recent work on this problem begins with characteristics of color experiences: for example, that color similarity judgments produce color orderings that align on a circle (Clark 1993). With this resource, one can seek mappings of phenomenology onto environmental or physiological regularities. Identifying colors with particular frequencies of electromagnetic radiation does not preserve the structure of the hue circle, whereas identifying colors with activity in opponent processing neurons does. Such a tidbit is not decisive for the color objectivist-subjectivist debate, but it does convey the type of neurophilosophical work being done on traditional metaphysical issues beyond the philosophy of mind.

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