What are the arguments that speak against that the mind or human
consciousness emerged from the properties of the underlying systems?
There are arguments based in the explanatory gap of our incomplete understanding of how consciousness might depend upon a nonconscious substrate, especially a physical substrate. And there are arguments based in the structure of scientific explanations and understanding.
The basic gap claim admits of many variations in generality and thus in strength. In perhaps its weakest form, it asserts a practical limit on our present explanatory abilities; given our current theories and models we can not now articulate an intelligible link. A stronger version makes an in principle claim about our human capacities and thus asserts that given our human cognitive limits we will never be able to bridge the gap. An even stronger version of the gap claim removes the restriction to our cognitive nature and denies in principle that the gap can be closed by any cognitive agents.
Some neodualists have tried to use the existence of the gap to refute physicalism. Dualist conclusions are often supported by appeals to the supposed impossibility in principle of closing the gap. If one could see on a priori grounds that there is no way in which consciousness could be intelligibly explained as arising from the physical, it would not be a big step to concluding that it in fact does not do so: Given the inherently spatial nature of both our human perceptual concepts and the scientific concepts we derive from them, we humans are not conceptually suited for understanding the nature of the psychophysical link. Facts about that link are as cognitively closed to us as are facts about multiplication or square roots to armadillos. They do not fall within our conceptual and cognitive repertoire. To creatures cognitively like us, it must remain a residual mystery. An even stronger version of the gap claim removes the restriction to our cognitive nature and denies in principle that the gap can be closed by any cognitive agents.
But it is difficult to assume, without begging, this metaphysical result, without assume a metaphysical principle too. Those who wish to use a strong in principle gap, to claim refute physicalism must find independent grounds to support it, without assuming metaphysical principles at start. Such arguments without metaphysical principles will avoid begging the anti-physicalist question, but they themselves rely upon claims and intuitions that are controversial and not completely independent of one's basic view about physicalism.
Therefore, for example, some have appealed to conceivability arguments for support, such as the alleged conceivability of zombies molecularly identical with conscious humans but devoid of all phenomenal consciousness. Other supporting arguments invoke the supposed non-functional nature of consciousness and thus its alleged resistance to the standard scientific method of explaining complex properties in terms of physically realized functional conditions. Such arguments avoid begging the anti-physicalist question, but they themselves rely upon claims and intuitions that are controversial and not completely independent of one's basic view about physicalism.
Maybe science is able, in principle, to close the gap and solve the hard problem of consciousness in an analogous way that we now have a very good understanding for why “water is H2O” or “heat is mean molecular kinetic energy” that was lacking centuries ago. Maybe the hard problem isn’t so hard after all – it will just take some more time. After all, the science of chemistry didn’t develop overnight and we are relatively early in the history of neurophysiology and our understanding of phenomenal consciousness. Our present inability to see any way of closing the gap may simply reflect the limits of our current theorizing rather than an unbridgeable in principle barrier.
The hard problem of consciousness is why or how does some particular brain process produce that particular taste or visual sensation? It is difficult to see any real explanatory connection between specific conscious states and brain states in a way that explains just how or why the former are identical with the latter. There is therefore an explanatory gap between the physical and mental. This difficulty in explaining consciousness is unique; that is, we do not have similar worries about other scientific identities, such as that “water is H2O” or that “heat is mean molecular kinetic energy.” There is an important sense in which we can’t really understand how physicalism could be true. The existence of a "hard problem" is controversial and has been disputed by some philosophers. For philosophers who assert that consciousness is nonphysical in nature, there remains a question about what outside of physical theory is required to explain consciousness.
Consciousness is especially resistant to explanation in physical terms because of the inherent differences between our subjective and objective modes of understanding. There are, for example, unavoidable limits placed on our ability to understand the phenomenology of bat experience by our inability to empathetically take on an experiential perspective like that which characterizes the bat's echo-locatory auditory experience of its world. Given our inability to undergo similar experience, we can have at best partial understanding of the nature of such experience. No amount of knowledge gleaned from the external objective third-person perspective of the natural sciences will supposedly suffice to allow us to understand what the bat can understand of its own experience from its internal first-person subjective point of view. Maybe the bat is not good example why they probably will not pass through the mirror test, a test of self-awareness, but dolphins and elephants pass. The dolphin has sonar and the elephant can hear infrasounds, and we cannot understand what they can understand of its own experience from its internal first-person subjective point of view.
But why we must be deluded by schizophrenic and LSD hallucinations to empathetically take on an experiential perspective understanding? Is subjective understanding necessary to make objective science? Some physicists, argue that an interpretation is nothing more than a formal equivalence between sets of rules for operating on experimental data, thereby implying that the whole exercise of interpretation is unnecessary, for example in quantum physics. Any modern physic's scientific theory requires at the very least an instrumentalist description that relates the mathematical formalism to experimental practice and prediction. By abuse of language, a bare instrumentalist description could be referred to as an interpretation, although this usage is somewhat misleading since instrumentalism explicitly avoids any explanatory role; that is, it does not attempt to answer the question why.
Most of the laws of physics themselves as we experience them today appear to have emerged during the course of time making emergence the most fundamental principle in the universe and raising the question of what might be the most fundamental law of physics from which all others emerged. Chemistry can in turn be viewed as an emergent property of the laws of physics. Biology (including biological evolution) can be viewed as an emergent property of the laws of chemistry. Finally, psychology could at least theoretically be understood as an emergent property of neurobiological laws.
But Science must, as a practical matter, work with high-level principles in dealing with complex systems, and that these principles are confirmed independently of the emergence of, or evidence for, our best fundamental theories. For example there is a rapid rate at which quantum descriptions become more complicated as the size of a system increases. There are a practical impossibility of directly deriving predictions from quantum mechanics for systems containing more than ten particles. Sciences can be arranged roughly in a linear hierarchy — particle physics, many body physics, chemistry, molecular biology, cellular biology, physiology, psychology, social sciences — in that the elementary entities of one science obeys the laws of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it and reduces it. At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry. There is a limitation in the reductionist/emergentist view of consciousness as emergence of, or reduced to, neurons and chemistry.