In The Self and Its Brain, written with John Eccles, Karl Popper takes on the mind-brain problem. In chapter 19 (they’re short chapters; it begins on page 67) he takes on panpsychism. It’s a disaster. I’ll try to summarize his arguments and then deflate them quickly here.
Of relatively little interest, he acknowledges that panpsychism has been around for a long time - Thales (“everything is full of gods”), Aristotle (“soul is mingled with everything in the whole universe”), Plato (the universe is “a living body endowed with a soul”), Spinoza (“all things are animate in various degrees” and of course the famous apostasy “Nature, which is the same as God”), Leibniz (with his idea that bodies are spirits seen from without), Schopenhaur (who thought that Kant’s noumenon was will).
He then goes on to say that panpsychists are dualists, which is a particular (and basically wrong) interpretation interpretation of panpsychism, as it mistakes the epistemology of the panpsychist – who thinks he cannot, in principle, determine the causal link between mind and brain because there is none – for his ontology. The whole point of panpsychism is to disbelieve in dualism. Nevertheless this is what Popper thinks.
They [panpsychists] believe… that psychological or mental processes and physical or material processes run parallel, without interaction; that mental (World 2) processes can act only upon other mental processes, and that physical (World 1) processes can act only upon other physical processes, so that World 1 is closed, self contained.
So, that’s disapointing given what a hero he is of mine. He then presents three criticisms of panpsychism, and for anyone tempted to go around thinking “Popper disbelieved in panpsychism” it’s useful to see they’re all severely confused and glib. It’s worrisome.
1. His first critique is by analogy. To say that mind is pre-existing in the world, and brought out of it by elaboration of the physical world (eg, that a grain of sand is a simple subjectivity, and a brain is a complex one, but they are on a continuum), is like saying that the solidity of a crystal is inherent in the liquid that precipitates into it. To which I say, what? The solidity of a crystal exists in the mind of someone observing it. Solidity is a human concept – it is not a natural kind! But subjectivity is, by definition, not in the mind of someone observing in it. Subjectivity is in its own mind. One can describe a crystal just fine at the atomic level. I took organic chemistry – I spent hours doing so, with math and geometrical diagrams. The concept of solidity never entered into it. It’s a heuristic convenience, to refer to a crystal as being solid – not an ontological claim. So – that was a bummer.
2. He says that panpsychism tries to avoid the concept of emergence. But that’s not true. It doesn’t have a problem with the concept of emergence per se. It has a problem with the concept that the mind – in particular, and without concerning any other phenomenon in nature – emerges from the material world.
He goes on to imply that panpsychics are trying to cynically win a war without caring about truth. “The main motive of post-Darwinian panpsychism was to avoid the need to admit the emergence of something totally novel.” To which I say: the need? The need? It sounds like you think that I am somehow lazy – that I want to avoid work of some sort. But this is tantamount of an ad hominem attack. But we don’t believe this is a competition to see who can do the least work. We’re trying to understand the best way to model the world. What if we regard emergence as a fluffy, incoherent, vague, hand-wavy affair that – just like dualism – is avoiding the need to get rid of all the confusion about the mind-brain problem up front in order to proceed with (trivial) explanations of how the brain works?
3. Finally, his real argument. Popper uses the concept of memory to disprove (in his view) panpsychism. He proposes a thought experiment that the brain is constructed in such a way that it takes some amount of time, call it 1 second, to construct a memory. If you zap a brain more than once a second, you will prevent it from ever forming a memory – by definition. But he then goes on to conflate memory with consciousness. Listen carefully:
After every memory loss… it takes some little time before we can, as it were, re-assembled ourselves and become fully conscious. 
Ay-yay-yay. What a doozy of a bad argument! There are two sneaky things going on here. The first is the word “fully.”
Of course, “fully” is a panpsychic concept, so it’s gratifying to see Popper using it. But it is annoying that he doesn’t catch himself in his own contradiction. For the word implies that there is something, in his mind, less than full consciousness. What is that less-than-full state? Where is it? Who has it? Because the panpsychics think that that brain had it. It has degrees of consciousness. One wishes to tell Popper how to listen to his own intuitions: When memory is functioning wonderfully, it becomes, as you say, fully conscious. When memory is not, it is conscious only in the moment, and has no continuity of consciousness. But continuity is not consciousness. When I forget a phone number that I have been mumbling beneath my breath for the past ten seconds I do not say I have lost consciousness. I have just lost continuity of consciousness – I can no longer reproduce, now, the consciousness that I just had, then.
But the second and worse thought-error Popper makes is that he conflates memory with consciousness. It’s all there in that sentence. He just effortlessly glides from describing how you prevent a brain from forming memories to asserting that such a brain is unconscious. I won’t bother going into all the reasons why this is wrong neurobiologically and medically, or pointing out that our society does not believe he is correct. For example, H.M. was kept alive for decades despite being unable, due to his lack of hippocampi, to remember his doctors for more than a handful of minutes. I’ll just point out it’s bad philosophy – his forte. Memory has never been understood as being equivalent to consciousness, and so to treat it as such is simply a fudge.
Sadly, because I was not around to correct him, Popper proceeds towards his conclusion. Along the way he throws in a bunch of wild assertions – “it is well known that, as a consequence of an injury, or an electric shock, or a drug, a person may lose consciousness” (um, that’s a turn of phrase we use in the Emergency Room and on the football pitch – that’s not a philosophical claim) – “consciousness, and every kind of awareness, relates certain of its constituents to earlier constituents” (um, no, that’s exactly what panpsychics dispute; we think that what makes the low-level consciousness of a grain of sand so low-level is that it has no such capacity) – but finally comes around to delivering what he thinks is a devastating blow to the panpsychic cause.
This thought experiment [about memory = consciousness] speaks strongly against the theory of panpsychism according to which atoms, or elementary particles, have something like an inside view; an inside view that constitutes the unit, as it were, out of which the consciousness of animals and men is formed. For according to modern physics, atoms or elementary particles have emphatically no memory: two atoms of the same isotope are physically completely identical whatever their past history. 
Readers of this blog who know that I think the electromagnetic field keeps getting overlooked as a candidate for consciousness will see the kind of thing I am talking about; he acts as though materialism requires us to locate consciousness in particles, which is to say, fermions. Fields – and in fields, bosons - appear not to be good candidates for him. To which I ask (again): why not?
Second of all he seems to be building his triumphant point on his conflation of memory and consciousness. But if subjective experience does not require memory, then even atoms would go back on the table – even for Popper – as candidates for consciousness.
Finally, he triumphantly concludes, in italics
Thus we should not assign inside states, or mental states, or conscious states to atoms: the emergence of consciousness is a problem that cannot be avoided, or mitigated, by a panpsychist theory. Panpsychism is baseless, and Leibniz’s monadology must be rejected. 
I suppose Popper has done us a favor here: he has combined bad thinking about memory, emergence, and materialism with sweeping arrogance. It’s a kind of apotheosis of bad anti-psychism. It should lead any curious person to ask whether something isn’t rather amiss in modern materialism.
For of course if you are open to my conjecture (conjecture! not theory!) that matter is a measure of uncertainty (aka a prediction), and that light is a mechanism for updating that uncertainty (aka learning), and that movement is a revision of the prediction (aka control), and that the electromagnetic field is the medium in which this informational process unfolds, and that therefore that the universe is at every level of organization and every point of space “thinking,” with the most complex and interesting thoughts occurring in brains that – as Popper intuits – can sustain complex conformations of the electromagnetic field that model and summarize activity in other areas of the field in the past (aka memory), and then execute hypothesis testing about those other areas (aka intentional action), one can see how intentionality (aka will) could be much more than a property of the human mind or even brain. Intentionality would become a property of the universe per se.
Obviously this conjecture – which is panpsychic through and through, but certainly not dependent on psychological constructs or particles (fermions) – needs a good deal of space to be developed. But it would be sad if limited and sloppy critiques of panpsychism like Popper’s were allowed to block this kind of inquiry simply out of tradition, convenience, or respect for his remarkable achievements in other areas of the philosophy of science.