Consciousness and the Proportionate Indeterminacy of Knowledge
One of the strange themes that you will run across amongst the New Atheists is a type of ana-Positivism or an inerascinable faith in the ability of empirical scientism to provide explanations for reality, especially over-against any type of "religious" thematic. I call it "ana-Positivism" not because it fundamentally differs from positions put forward by the Vienna Circle and their epigones (hence why it would be difficult to call it "neo-Positivism"), but simply because it appears to be an attempt (an incredibly myopic one, in my opinion) to re-positivize the sciences (hence the prefix ana) despite the hefty amount of evidence weighed against pure empiricism (linguistic theory, hermeneutical theory, Kuhn's "paradigm shift" theory etc...). For those unfamiliar with positivism it is, loosely put, the theory that all true knowledge must be able to be proved 1.) empirically or 2.) be true analytically (i.e. by definition: "all bachelors are unmarried men.") A later addition was that knowledge is acceptable that in theory will eventually meet one of these two criteria (e.g. we may not know exactly what a planet in another galaxy is made of, but in principle this could be provable by one of the two postulates in the future). This of course rules out any talk about God or metaphysics, which was one of its prime intentions.
I dont want to here go over the oft-repeated hermeneutical and philosophical objections to positivism (e.g. that it, as a theory, does not meet its own criteria), except one. The assumption seems to be that we are being given a more and more comprehensive view of reality based upon scientific or empirical description that is giving us the ability more and more to "explain" events. Now I dont want to contradict the truism that certainly scientific knowledge of the world is advancing, or that our technological expertise is increasing. What seems bizarre to me is the almost utopian (or even post-Hegelian) ideal that one day all "facts" about the universe could even be known. It seems to be a fundamentally undergirding ideal that there is a set quantity of information (even if this quantity is theoretically infinite) the "unknown" quantity of which is progressively shrinking as we continue our scientific investigations of the world. Even if this quest for scientific knowledge understands itself as an essentially endless quest (as there could be an infinite number of finite aggregates of knowledge to be known) nonetheless in theory this scientism presupposes that all aggregates composing this infinite are knowable via scientific inquiry. That is to say, even if in theory we will never comprehend the whole of the totality, it is nonetheless feasible that we will never run into an object that is not fundamentally comprehensible by scientific standards.
But this empiricism is of course based on the thoroughly un-empirical theory of materialism. In order for everything to be theoretically knowable in this matter, it must be able to be understood quantitatively, and hence be "material" of some sort. This is not a new critique of course. But what seems to me to be a fundamental aporia is that it seems to exclude a fundamental non-exhaustibility of the human. All acts of our scientific comprehension are, of course, acts done by humans. But in the very act of cognition of data there is a proportionate increase in the unknowable. What I mean is that our acts of comprehension themselves cannot be comprehended except by an additional act of comprehension. E.g. Me knowing "this apple is red," or "water is two hydrogen and one oxygen atom" is, tautologically, different from me knowing that I know the apple is red or the molecular makeup of water. But the immediate act of cognition is a datum that would be a necessary component to our "set" of all knowledge. This means (strangely parallel to Cantorian set-theory) that the knowledge of the set [x] which includes all currently known facticity does not include the act of cognition which knows of set [x]. But then ironically the set of all sets of knowledge is in principle unobtainable. I hesitate to use the word, but our consciousness, or our ability to cognize, remains a "transcendental" over against empirical quantification in this manner because it always reflectively exceeds the ability to categorize information.
Moreover the act of immediate cognition remains aloof from categorization because it can only be known by a second act of knowledge. As Sartre put it in the Transcendence of the Ego, critiquing Descartes' famous formulation "I think, therefore I am" that that the entity putatively referred to by the item of consciousness, be it the "I" in "I am conscious" or the red apple in "this apple is red" can only appear as an item within consciousness and is not an awareness of the consciousness itself. This same fact appears in William James' Principles of Psychology where the focus point of consciousness remains a mere postulate which cannot be verified introspectively. He says "Introspecting with maximum exigency, we discover no subject of experience at all but only a collection of objective phenomena at the level of the material self" which remains distinct from the act of cognition. As Robert Jenson puts it in the second volume of his Systematic Theology: "There is the transcendental unity of consciousness, necessarily posited but not describable as anything I can find in myself."
In this sense we might say that the human remains fundamentally beyond total empirical quantification, and in humanity resides a fundamentally non-manipulable transcendence (in theory).
I dont want to here go over the oft-repeated hermeneutical and philosophical objections to positivism (e.g. that it, as a theory, does not meet its own criteria), except one. The assumption seems to be that we are being given a more and more comprehensive view of reality based upon scientific or empirical description that is giving us the ability more and more to "explain" events. Now I dont want to contradict the truism that certainly scientific knowledge of the world is advancing, or that our technological expertise is increasing. What seems bizarre to me is the almost utopian (or even post-Hegelian) ideal that one day all "facts" about the universe could even be known. It seems to be a fundamentally undergirding ideal that there is a set quantity of information (even if this quantity is theoretically infinite) the "unknown" quantity of which is progressively shrinking as we continue our scientific investigations of the world. Even if this quest for scientific knowledge understands itself as an essentially endless quest (as there could be an infinite number of finite aggregates of knowledge to be known) nonetheless in theory this scientism presupposes that all aggregates composing this infinite are knowable via scientific inquiry. That is to say, even if in theory we will never comprehend the whole of the totality, it is nonetheless feasible that we will never run into an object that is not fundamentally comprehensible by scientific standards.
But this empiricism is of course based on the thoroughly un-empirical theory of materialism. In order for everything to be theoretically knowable in this matter, it must be able to be understood quantitatively, and hence be "material" of some sort. This is not a new critique of course. But what seems to me to be a fundamental aporia is that it seems to exclude a fundamental non-exhaustibility of the human. All acts of our scientific comprehension are, of course, acts done by humans. But in the very act of cognition of data there is a proportionate increase in the unknowable. What I mean is that our acts of comprehension themselves cannot be comprehended except by an additional act of comprehension. E.g. Me knowing "this apple is red," or "water is two hydrogen and one oxygen atom" is, tautologically, different from me knowing that I know the apple is red or the molecular makeup of water. But the immediate act of cognition is a datum that would be a necessary component to our "set" of all knowledge. This means (strangely parallel to Cantorian set-theory) that the knowledge of the set [x] which includes all currently known facticity does not include the act of cognition which knows of set [x]. But then ironically the set of all sets of knowledge is in principle unobtainable. I hesitate to use the word, but our consciousness, or our ability to cognize, remains a "transcendental" over against empirical quantification in this manner because it always reflectively exceeds the ability to categorize information.
Moreover the act of immediate cognition remains aloof from categorization because it can only be known by a second act of knowledge. As Sartre put it in the Transcendence of the Ego, critiquing Descartes' famous formulation "I think, therefore I am" that that the entity putatively referred to by the item of consciousness, be it the "I" in "I am conscious" or the red apple in "this apple is red" can only appear as an item within consciousness and is not an awareness of the consciousness itself. This same fact appears in William James' Principles of Psychology where the focus point of consciousness remains a mere postulate which cannot be verified introspectively. He says "Introspecting with maximum exigency, we discover no subject of experience at all but only a collection of objective phenomena at the level of the material self" which remains distinct from the act of cognition. As Robert Jenson puts it in the second volume of his Systematic Theology: "There is the transcendental unity of consciousness, necessarily posited but not describable as anything I can find in myself."
In this sense we might say that the human remains fundamentally beyond total empirical quantification, and in humanity resides a fundamentally non-manipulable transcendence (in theory).

Comments
But what about all the Christians who use left-brained reason to try to prove the existence of "God".
Left-brained reason being the very mode of thinking which is itself the method using by reductionist scientism to investigate reality--or rather reduce everything to mere unconscious molecules
Plus the same very reasonable Christians argue that there is a pre-given objective world "out there".
Which is again one of the dogmatic positions ardently promoted and defended by left-brained scientism.
And speaking of Consciousness, it is a word which is seldom used in Christian theology or apologetics.
Meanwhile it is more or less common knowledge at the present time that we do not merely see what is external to us. Our seeing is in fact an electronic apparition, developed in, and projected by, the nervous system and brain.
We thus have no direct connection to the gross objects that we are seeming to view at any given present time. In other words we are always experiencing a psychically projected vision. We are not merely seeing a gross environment, but are having a vision of a gross environment.
Likewise, our sense of being physically embodied is communicated to us through the electronics of our nervous system. WE are thus always experiencing an apparition, an electronic sense of being identified with a gross physical body. The position in which we experience perceptions is an extremely subtle position which is in Truth a shapeless thoughtless feeling.
Mind is not merely "in" the brain. And mind is not less than the brain.
Mind is universal, infinite in its extent.
Such is also who and what we are in Truth and Reality
Again this last proposition is not something you will find by reading the usual Christian apologetics or theology.