How our mental states -- that is to say our experiences, thoughts, beliefs and so on --- are related to our bodies, is known as the mind-body problem. There are two general positions, materialism and dualism, and many varieties of each (although my own position is neither materialism nor dualism, but rather idealism).
What does materialism mean? It means broadly that the totality of all that exists is exhausted by both everything that we directly perceive through our five senses, and also what we can sense or detect through the use of scientific instruments. Such scientific instruments include microscopes and so on that simply extend the range of things we are able to sense or infer.
Should materialism be true then this means we are purely material beings; that is, we are nothing but our material bodies. Hence, under this view, consciousness is typically considered to be a physical thing or process, or perhaps even purely illusory. This implies that ultimately we are merely sophisticated biological robots operating according to the laws of physics. If true this would seem to pretty much rule out the prospect of a soul residing in any type of afterlife realm.
The movement away from belief in a soul over the past 400 years or so can be laid squarely at the door of the ascendency of materialism. But what accounts for this ascendancy? Is it because materialism is obviously correct? I would argue most definitely not. Indeed, I and many others have made the argument that materialism cannot be correct. How so?
To understand why we have to go back to the scientific revolution in the 17th Century that heralded the birth of modern science. This revolution was precipitated by the concept of material reality that both Galileo and Descartes advanced. They proposed that the material realm is wholly quantitative. That is to say that the external world is wholly composed of things and processes that can in principle be detected by our measuring instruments and thus can be measured. The consequence of all this was that science could describe the whole of the external material world; no aspects of the external world lay beyond its scope. Once we have made all appropriate measurements of this material reality and then mathematically described the patterns found and codified them into the laws of nature, then nothing more need be investigated.
But, what of the qualitative aspects of reality such as colours, sounds, and smells? These aspects of reality are not detectable by our measuring instruments and hence are not measurable. The only option was to stipulate that they simply weren't part of the furniture of reality at all (note the word stipulated, this was in no shape or form a scientific discovery). Instead, colours, sounds, and smells were redefined to stand for those measurable aspects of reality which were deemed to cause these qualitative experiences. Thus, colours were redefined to refer to the respective specific wavelengths of light that objects reflect. Sounds were redefined to refer to rarefactions and compressions of the air. Smells redefined to refer to various molecules in motion. It was acknowledged that colours, sounds, and smells, as we experience them, still existed. But they only existed in the mind. Hence, an experience of greenness was a creation by the mind fashioned from the purely quantitative light entering the eyes. In short, from the birth of modern science onwards, the external material world, including our bodies and brains, was supposed to be wholly quantitative and devoid of anything qualitative. Thus a very much emaciated conception of the material external world was advanced. Compared to the commonsensical conception of the material world, this was a bare skeletal outline of reality denuded of the flesh of the qualitative.
I now need to stress that carving up reality in this manner seems to entail a form of dualism. The material external world was defined to be wholly quantitative and hence measurable. The qualitative aspects of reality -- colours, sounds, smells and so on -- were extracted from this external reality and were supposed to have subsistence only within the mind. But it then follows there are two different types of existent. On the one hand, there is the material world that is composed exclusively of the quantitative. On the other hand, there is the mind, which is responsible for both the qualitative aspects of reality as well as our mental states such as our experiences, thoughts, beliefs and so on. Note that even if the mind-brain correlations force the conclusion that consciousness is created by the brain, this still doesn't entail that consciousness is material -- remember, to be material means it has to be detectable, and we can only detect the neural correlates of consciousness, not consciousness itself.
Thus materialism seems to be ruled out. But, in that case, why did the birth of science lead to materialism rather than the obvious dualism it suggests? And why is it that today the vast majority of scientists and philosophers are materialists?
The answer is this. Science investigates the quantitative or measurable. Material reality had been defined as exclusively consisting of the quantitative. It then follows that science is the investigation of this material reality. Now, science has been astoundingly successful in furnishing us with knowledge of this material reality as well as being an extraordinarily fruitful one in terms of the manipulation of our environment and in the creation of our technology. So, a leap of “logic” was made. It was simply assumed that since science was so successful, it must describe the whole of reality, including the mind.
Since this is so important, let me put it another way. Material reality was stripped of all its qualitative aspects – colours, sounds, smells and so on. These qualitative aspects of reality were relegated to being creations of the mind rather than actually existing out there. This left material reality consisting exclusively of all the measurable elements that science could then successfully describe. Minds, on the other hand, could not be so described since they consist of thoughts, pains, emotions and so on, in addition to what were hitherto considered to be the qualitative aspects of reality such as colours, sounds, and smells. Hence the mind, by definition, did not come under the purview of science. However, since science has been so incredibly successful, it was supposed that it simply must describe the entirety of reality, including minds. In order to square this circle, the solutions advanced were to stipulate that consciousness is either illusory, or that it is one and the very same thing as a material process, or that it is one and the very same thing as the functions carried out by such material processes.
Here is a splendid analogy used by the philosopher Edward Feser to illustrate this type of reasoning. It’s as if someone were to declare that since metal detectors are so successful at detecting metal, they must detect everything that exists. Hence, anything that appears to be made out of plastic, rubber, or wood and so on, must somehow either be illusory, or really be metal in disguise. This is of course silly. But, in a similar way in which metal detectors are only designed to detect metal objects and have nothing whatsoever to say about the existence, or otherwise, of objects made of other substances, so too are the methods of current science limited to the quantitative aspects of reality, and cannot have anything to say about aspects of reality not amenable to this approach. And these aspects of reality not amenable to this approach are consciousness and the qualitative aspects of reality such as colours, sounds, and smells. So, appealing to the success of science is simply a complete irrelevancy.
As an aside, this tactic of declaring consciousness is one and the very same thing as a material process or thing, does not seem to me to be meaningful in any case. On the one hand, we have physical processes whose reality is wholly cashed out in terms of physical properties – mass, electric charge, velocity and so on. On the other hand, we have a conscious experience, perhaps a sensation of greenness, or of pain. There is no commonality whatsoever between such physical properties on the one hand, and qualia on the other, so it seems straightforwardly false to declare they’re one and the very same. Arguing over this though is to miss the much deeper point that we simply have no reason to suppose consciousness is a physical thing or process in the first place.
Edited to add:
Now, if consciousness can in principle be measured -- not just aspects of it, but wholly so -- this is to deny that consciousness has any qualitative elements. Instead, consciousness, like the rest of material reality, is wholly quantitative. Any experience can hence, at least in principle, be wholly conveyed by units of measurement(s).
Regarding "c", namely that modern materialism includes the qualitative as well as the quantitative. Well, not as I have defined it, a definition that is held by most scientists if not philosophers. But, of course, if materialism is defined differently then my specific arguments above do not apply. For example, there is the various varieties of non-reductive materialism. Also, there is the materialism endorsed by both Galen Strawson and Bertrand Russell who hold/held that material stuff is by no means exhausted by what physics tells us about it (see this essay by Strawson. Also a response by Danial Dennett and a reply by Strawson might be of interest. Go here). I should add, though, that this does not mean that alternative definitions of materialism are necessarily tenable. For example, non-reductive materialism seems to entail that consciousness is causally inert, but I regard this as being untenable (see my blog post A Causal Consciousness, Free Will, and Dualism ).
But the more basic point is that if it is agreed that modern reductive materialism is untenable then the consequences of accepting this materialism also don't apply. A type of materialism might be still true, but not the type of materialism that the birth of modern science seemed to suggest. And modern science doesn't appear to add support for these other types of materialism. Hence, it still remains the case that we have little more reason to reject the existence of souls and the like now, than we did prior to the birth of modern science in the 17th Century.