Nope, the natural sciences can never prove nor disprove the existence of souls.
It is a purely philosophical issue, relating to our most intimate and impenetrable (except by God) consciousness of our Self.
That I have a soul is self-evident to me. It should be to all souls. BUT the fact that anyone or anything else has a soul, is not as easy to believe if you take time to think about it. They could all just be like robots, or computers, or figments in a dream.
It is only on Faith in God’s Revelation and sound theology that I can believe that all humans have souls, and that no other corporeal creature has a [spiritual] soul.
The soul is what ultimately makes us “conscious” of our self. I don’t just see something. Photons don’t just enter my eyes and affect a neurochemical or bio-electrical effect in my brain. I actually “see” what I see. It is not just a decentralized affecting of circuitry, there is some centralized and ultimately simple principle that makes me conscious of my consciousness, and conscious of my consciousness of my consciousness ad infinitam. It allows me, beyond all capacity of the brain or individual components thereof, to identify as “I”, as my “self”.
A soul is what allows us to infinitely self-reference.
This would be impossible materially, as it would require an infinite amount of matter…which clearly our brains do not have…or else an infinite continuity of division of matter without losing detail…something that, with discreet particles, we know cannot happen.
A good symbol of the soul is a fractal. A fractal keeps self-referencing itself…and within the fractal, is an image of itself. BUT in order to be a true image of itself, the image must contain the image of the self. And in order for THAT image to be true, it must contain the image of the image of the image of the self, ad infinitam.
And yet, while we can draw fractals down to a certain size, and can make formulas for them…no fractal in the material world can ever have an actual existance…because it would either require infinite matter…or matter that can be shaped and subdivided without losing any detail down and down forever…but again, with discreet particles, we know this cannot happen.
And yet the soul allows the Self to know itself fully, including its knowledge of itself, and that knowledge of itself knowing its knowledge of itself…forever and ever.
This cannot be explained with mere matter. It can only be explained with an irreducible spiritual principal, which we call the soul…which is made in God’s image and so can self-reference…(as well as freely will, deciding niether through arbitrary chance, nor a deterministic chain of rules playing out…but a true and culpable choice)
And yet, even our brains cannot know our souls as only they can know themselves. We can concieve of the concept of “soul” in our brain by analogy…such as a fractal or a self-seeing eye…but ultimately it is like the notion of “infinity”…in our brains, it is only a notion…we get the “idea” of it, but never truly picture it. It cannot be imagined.
The only way science might be able to lend support to the existence of the soul, is to show that in a free choice…the brain follows an absolutely free decision…niether as the result of the deterministic outplay of physical laws, or of any sort of seething quantum randomness. But I’m not sure that it can in fact demonstrate that the latter isn’t true…because it might appear that way, and they might assume it was the cause when really it was an effect.
The fact that people say they are self-conscious is really the best empirical evidence. The fact that when presented with the question of its own existence by the brain, the soul answers in the affirmative. But you could get a computer to say that too…or even recreate a circuit system that would mimic the neurons of “knowing about souls analogically” exactly. And yet, this computer would not truly have a soul or really be conscious.
Ultimately, you can only believe other people have souls if you have trust in a logical Reality, and Faith in Divine Revelation.
And you can only truly know your soul, not even in the brain, but in your soul itself, the Sanctuary of your own Consciousness, where none but God may enter.