But the idea that science has nothing at all to tell us about souls seems to me clearly wrong. It can tell us a lot about what they are not. For one thing it seems clear that souls are not things on which arithmetic can be performed. Science can tell us that the soul can't be found by scientific inquiry. It can't by definition say that only what can be found by scientific enquiry actually exists.
Science, or at least empirical inquiry, can tell us that there is no reason to believe in an afterlife. There is an important distinction here between an afterlife, which is something prolonged in time, and eternal life, or an experience of eternity, to which time is irrelevant.
Science tends to strengthen the argument of Aristotle that the soul is the form of a living thing – this is also the position of Thomas Aquinas, and so of classical Christian theology. I don't think McGilchrist is a Christian – he calls himself a panentheist – but it is certainly his position, too. He compared the soul to a wave – something that is composed of water, but at the same time distinguishable from it. In that sense, he was talking about souls as time-bound entities. Waves end. Perhaps there are several kinds of soul we can talk about.
Science, it seems to me, gives us reasons for supposing that nothing can go on for ever. You don't need science to believe that. But at the very least the discovery of the big bang shows that the universe had a beginning and will have an end. This shows that while something might be eternal, it cannot be immortal, and that must go for souls too.
McGilchrist's big book The Master and his Emissary has been criticised by Raymond Tallis among others for using science wrongly in the service of philosophy: not that the science is wrong, but that it is only a backdrop yet is treated as if it were a load-bearing part of the scenery. This seems to be exactly the mistake that he criticises so fiercely in others – the leap from scientific result to metaphysical significance. But science and philosophy are like the two sides of an arch – they can only reinforce each other indirectly. That still doesn't mean that science can say nothing about the soul. If you build an arch with only one side it will tumble into a silly heap.
The entire post can be read here.