Can science tell us anything about the soul? A lovely clear answer came from Iain McGilchrist, talking at the RSA this week. "No," he said, and the room filled with laughter, not entirely kindly. He had been responding to a questioner who wanted to know whether the increasing sophistication of brain imaging would not reveal the soul to be an illusion, an unnecessary imprecision.

"To expect that we will find something in the brain that corresponds with the soul is just crass," he said. The moderator, Jonathan Rowson, pressed him: "Is it the case that science can help us understand better what the soul is?"

"No," said McGilchrist.

But was he right?

I think he was importantly right about the question that wasn't quite asked, and which was hovering over the audience then as it hovers over any discussion of these matters: can science tell us whether the soul is? Can science decide whether souls exist at all? This is, I think, like asking whether brain imaging can tell us whether love exists. It's just a category mistake. There are things going on in the brain of a lover which would not be there but for love, but to discover that they are concerned with love requires an analysis from the top down, in terms of other thoughts and emotions. You can't know that they mean love without talking to the person whose brain you examine.

Generally, and like most of the RSA audience, I am wholly on the side of McGilchrist when he argues against scientism, as in his wonderful squelching of Steven Pinker:

"There is more truth about the human predicament in King Lear than in a thousand textbooks of genetics, irrespective of whether the play is a faithful account of the historical Lear or not, and indeed of whether there was ever a King Lear at all. And on whether there is a God or not, true science can have precisely nothing to say."

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.