Nature of the Problem
Materialism is the doctrine that nothing exists except matter and its movements and modifications. This is the approach of those who believe science explains all that matters (scientism), however concepts like "hope" as distinct from optimism which people can possess or not as a result of logic and not physiological cause, fall outside the material category and cannot be measured. Materialism can be one of how Atheism/Scientism can become a circularly reinforced perspective, the Atheistic equivalent of "god of the gaps". A "science of the gaps" would be that anything we do not have an explanation for is simply momentarily out of reach, which is just as much of a logical jump as the "god of the gaps" is.
I was in a debate once on Twitter on whether the soul was immaterial or not. The issue seemed to "boil down" to the belief concerning whether or not immaterial realities exist. That being said it is worth reading the terrain of this issue to understand if further understanding is possible on the individual level.
Catholic Perspective on the Soul
This is a requirement if one begins from an Atheistic perspective.
God is necessarily immaterial and created material creatures, therefore it is well within the realm of possibility that other incorporeal beings exist and material beings may have immaterial aspects.
Since, God is trustworthy, being good and omniscient, anything that is properly understood in revelation (that which is given us by God as far as knowledge of the "beyond"/not our experience is concerned) cannot really even be contrary to reality.
Since science is incapable of disproving anything immeasurable and philosophy can only be theoretical concerning its approach, the ultimate epistemological (from scratch anyway) authority is our personal experience and whatever related propositions of faith can offer us.
Since the use of philosophy equipped with tenets of the faith cannot contradict necessarily intuited experience, it seems the tenets hold, and are no longer impoverished of justification.
The soul which is claimed to be immortal, and the body is claimed to be mortal, the nature of the soul must be in its way at least sufficiently incorporeal to continue existing in a way other than materially lest science be able to measure it or it being immortal.
Therefore, immaterial realities exist and may well stand behind the epistemological curtain our humanity restrains us from, concerning laws of physics, and the consistency of reality, its source, etc.
The Atheist's Response
The response to our claims was that neurology has explained everything that is attributed to the soul and therefore the souls does not exist in incorporeality but only in the material sense.
Our Rebuttal
The problem with this claim is it is impossible to prove, even if you claim science will at some point explain it if not now. The logic does not necessarily bring validity either, just because science can see the physicality does not mean there is nothing (undetectable) beyond it. Moreover, it does not necessarily use what is meant by "soul" correctly. The soul is not limited to the mind, which is what psychologists say the brain does. It assumes that what we claim to be the soul is simply the aspects of the mind/body that cannot be explained by science. This is false. In like manner, God is not that which science cannot explain. Rather, we would claim that the order that He created is what science explains. The fact there is order at all testifies to that (more on this later). Returning to the discussion of the soul, the soul is not that which neurology cannot explain, but the form of the body, which according to the tenets of faith, would consist of aspects of the rational mind and identity, which is distinct perhaps but by no means separate from the body in its functioning.
All this being said, we do not expect someone to believe in the incorporeal soul without believing it to be immortal, which several religions in various ways do, but this is only possible under some form of theism. So, we shall defer this question to the larger one of God's existence.
Other immaterial "forces"
Suppose you do not accept premise one of the above arguments, and therefore none of the above conclusions. Let us consider something else. Physics only works on the premise laws exist concerning material dynamics. All physics does is describe the tendency of things to act predictably. So, what is it that they describe happening? Why does gravity emanate from mass? Why is it consistent? Why don't things spontaneously flash in and out of existence as may be suggested in the Big Bang? If that is not what happened in the Big Bang, what change in the eternal material caused the change we still see? It is not that we must insert God into that which we cannot answer, but it should give us pause to consider that there is some reason why reality is intelligible and what is that reason? If randomness per se, and not practical randomness which remains conceivably predictable, actually existed, it would not be materially understandable. Here we could return to the Five Ways of Aquinas. In the Five Ways, we see that truth, that physical things wind up not having an explanation in themselves and so come to require a physical predecessor, and there must come a point when the material will need an immaterial cause, and this is enough to inquire more of God.
This does not have to be convincing enough to prove there is something immaterial in itself, only that it allows one to consider the problem further. We shall then continue into the 5 Ways.