Neuroscience is making great progress understanding the human brain, and there is no reason to think that it will not continue to do so. However, it will always have to deal with a blind spot that limits its results. What is a neuroscientist studying the brain but a brain studying? Such a study can only understand the functioning of the organ, and those functions vital to the life of the whole person: respiration, heartbeat, etc. Experiments will continue to verify or discard hypotheses concerning memory, language, the acquisition of habits and addictions, accumulating knowledge — there is no end to neuroscience as such. But why a person has become or even should become a neuroscientist is a question this science cannot and will never be able to answer.
An analogous indeterminacy exists with respect to physics, namely, the problem of frames of reference. Albert Einstein explained it thus:
Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables of the original coordinate system K, we introduce new space-time variables of a co-ordinate system K′. […]
This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory (viz., relativity of frames of reference and the constancy of the speed of light) would have been disproved. 
His theory rests on information derived from different observers, who must be equally trustworthy despite the difference in their reference frames. Einstein famously resisted the advent of quantum physics, precisely because it seems to introduce an indeterminacy in the trustworthiness of the observers’ information.
In neuroscience and physics, questions arise and answers are arrived at through observation, interpretation, formulation of hypothetical answers to questions of interpretation. Experiments are devised to judge the validity of hypotheses, and if such experiments can be repeated, facts — true statements — are said to be established.
Einstein, for instance, pointed to the now-classic experimental results as proofs of the theory of relativity: precise measurement of the orbit of Mercury, solving a contradiction of observation with classical orbital mechanics; similar precision of prediction of the size of the shadow of an eclipse; and predicting the “red-shifting” of the spectrum of light. To date, the theory has not yet been surpassed.
However, at this time of writing the contradiction between quantum physics and relativity physics also remains. That shall be resolved in some as-yet-unknown way (which may, I wonder, involve reference frames in some fashion). Yet for Einstein, the inherent indeterminacy of the quanta posed a serious challenge, not just theoretical but psychological.
The purpose of this brief excursus in philosophy of science is to point out that the scientist cannot be objective about her personal involvement in the doing of science: observation, measurement, insights that formulate questions, judgments that determine whether hypotheses are correct or not, and communicating such work with wider communities of thinkers. In other words, scientists cannot exclude their personal consciousness. The oddities both of brains studying brains and Einstein’s underlying anxiety about his theory resting on putative absolutely trustworthy observers point to this irreducible reality.
Humans are not just animals with the psychic awareness that all animals possess to one degree or another. In the famous phrase associated with Aristotle, the human is the “rational animal”, the one who is at times aware of being aware, the one who can and sometimes does feel the need to ask a question in hopes of learning something — hopes of knowing.
Science is crucial to our world. Its advancement relies on people, who are as human as any other. That objectivity comes from subjectivity is no reason to doubt the value of science. But it does mean that scientists first must attend to their own selves, their own consciousness.
 Albert Einstein, Relativity: The Special and General Theory (London: Methuen & Co., 1916, 2004), chapter XIV, interpellation mine. Accessed at http://www.gutenberg.org/files/5001/5001-h/5001-h.htm
 For a fulsome discussion, see Bernard Lonergan, Insight: A Study in Human Understanding, eds. F. Lawrence & B. Doran, (Toronto: Univerisity of Toronto Press, 2013), 159–172.
 Einstein, Relativity, Appendix III.
 Michael Polanyi, Personal Knowledge (London: Routledge and Kegan Paul, 1962), 16. “We cannot truly account for our acceptance of such theories [viz., relativity and quantum physics] without endorsing our acknowledgement of a beauty that exhilarates and a profundity that entrances us.” My interpellation.
 This is a highly contested attribution, of course. For instance, Nicomachean Ethics I.13. “Humans possess a rational principle” (λόγον ἔχον — is this a correct translation?). Hannah Arendt wrote, “Aristotle meant neither to define man in general nor to indicate man’s highest capacity, which to him was not logos, that is, not speech or reason, but nous, the capacity of contemplation, whose chief characteristics is that its content cannot be rendered in speech.” The Human Condition (Chicago : University of Chicago Press, 1998), 27.