Szent-Giorgi, the Nobel laureate biologist, said, …"I went through my entire scientific career searching for life, but now I see that life has somehow slipped through my fingers and all I have is electrons, protons, and particles, which have no life at all. So in my old age I am forced to retrace my steps." 
So I think the great advantage of discussing the notion of the conscious self within our scientific paradigms is that we can actually enlarge our framework. In order to do that we need help, and I don't think that anyone can deny that the Vedic literatures are the single most vast body of literature that seriously deals with this topic. From page one to the end it is conscious(ness) all the way.

Science, as long as it remains bound to empirical reductionism, can say nothing about the conscious self. Many in the contemporary world have tried to define perception such that it fits into their existing paradigms, but this has only made our problems more acute. Time has come to redefine scientific procedures such that they explain the conscious self. We need as many new ideas as we can get. If we are so foolhardy as to reject the entire wisdom preceding us, such as the Vedic paradigm I have presented, then what assurance do we have that our present-day knowledge will not similarly be rejected by future generations?

Science is rooted in observations, and our conscious self is the very tool by which we observe. Even the strongest giant cannot lift the platform on which he stands. As great as scientific knowledge is, it cannot explain the conscious self within its present observational framework. To experience it is to observe it.