Science deals with what can be observed, directly or indirectly. So in one sense, you could say that science is simply not providing any answers to the question about the existence of a soul or spirit component of a human being.
That, of course, keeps science polite to religious ideas.
What science knows about the human body and the evolution of humanity does have some consequences for a soul-belief, however. This question is more philosophical than really science, but the two are not separated, and they shouldn't be.
First, the idea of a human spirit -- a ghost in the machine -- was developed when primitive people had an animistic view of life. Life was, they thought, a magic component that kept living beings alive. It was considered as real a thing as any other. Various religious people had different beliefs about how you could observe this spirit, and how it behaved.
Religions also needed a belief in a spirit/soul to postulate life after death. The soul-belief has remained a common (but by no means universal) part of human religions all over the world. At this time people had no idea how the human body worked. They knew about various organs -- like the heart or kidneys -- but really didn't have a clue what they were for. As we can see in the Bible, they often postulated various mental/psychological/moral functions for these organs.
Fast forward: We know how the body operates: we are essentially a machine. We also know that human thought is developed through electro-chemical processes in our brain, not very unlike a computer. We know basically how it works on a micro-level; the mystery that remains is to really understand how all these small thought processes build up a single self-aware consciousness. But we know that who "we" are -- our thoughts, feelings, memory -- are directly related to physical and chemical components in our brain. Sometimes disease or an accident damages small parts of the brain. People then have parts of their memory disappear, or being altered, or they lose motoric control over different parts of their body. We know how different chemical stimuli can create visions and change how the brain perceives reality. Many well-known and often-used substances can seriously change even a person's emotions.
What room, here, for a non-body component called a "soul" or "spirit"? If our personality was in a mystical spirit, why does it change corresponding to a body change? When a part of the brain is damaged, how come the personality supposedly in this spirit changes too? When we die, parts of our brain usually collapses and takes its thought patterns with it. Eventually, so much of the brain is gone that we are proclaimed dead, and the rest of the body is buried or burned; considered useless. Since a small brain damage does small damage to the personality in the supposed "soul", how can anyone believe the same "soul" suddenly is alive and well, with all memory, feelings and personality traits intact, when the brain is totally destroyed? What transfers this memory or whatever from the brain stem to this mystical soul?
In fact, the idea of a soul or spirit is ludicruous. To say that science has not disproved the idea for all intents and purposes is fooling oneself. In all other ways of life, the logical absurdities of postulating a "spirit being" would lead all sane people to reject it. We would assume that the idea was rejected. But out of respect (mistaken IMO) for religious emotions people still pretend that science has not disproved the idea of a spirit. For all intents and purposes, it has.
Let me illustrate with an example: say I postulated an idea that cars really had a car-spirit. The reason a car stopped when the gan run out was not, I claimed, the gas per se, but that the car-spirit had been depleted. When the car ran, it was driven by the car-spirit force, not by any combustion engine, even though I acknowledged the existence of such an engine. Would anyone seriously think this even made sense? That I had explained anything? That this actually merited any serious considerations, given that nobody had ever disproved the "car-spirit"? Of course not.
The existence of the human spirit has exactly as much merit as the car-spirit.
- Jan