Physics is particle physics. The physical world consists of atoms that consist of particles (electrons, protons, neutrons). This was discovered not so long ago, though it was conjectured by the ancient Greeks. It is not part of common sense and is not suggested by perceptual appearance. If anything, physical objects look continuous not granular. We have empirically discovered, as a result of arduous experimentation, that big objects are made of invisible small objects, and that these small objects have a characteristic structure consisting of a nucleus surrounded by orbiting particles. This is one of the greatest scientific discoveries of all time, on a par with the discovery of the heliocentric theory; it is something to emulate, envy, and aspire to. It sets an example to all other sciences. But is it an example that has been followed? Have the other sciences discovered anything analogous to the atomic theory of particle physics? In particular, are there psychological particles analogous to physical particles? Is psychology particle psychology?
Do the other sciences speak explicitly of particles and atoms? We might cite the doctrine of logical atomism: language consists of atomic sentences compounded into molecular sentences, where the atomic sentences contain subatomic parts, viz. words. The picture is that elementary semantic particles (words) combine to form atomic wholes that can then combine to form molecular compounds (conjunctions, negations, etc.). These molecular compounds can then form larger semantic entities such as paragraphs or speeches or books. The semantic universe is thus a universe of elementary semantic particles that join with other such articles to form larger units—ultimately the whole of semantic reality. We could even go cosmological: there are semantic planets and solar systems and galaxies (e.g. the works of Shakespeare). Language has infinite potential, so we can envisage an enormous proliferation of semantic entities existing alongside the physical galaxies described by cosmology. Maybe there are just a few primitive semantic particles, analogous to the physical particles, which generate this whole hierarchy of existence. Logicians talk about the “logical particles” and we might seek to model logic on particle physics (including cosmology). We have found higher-order uniformity in nature: nature is organized atomically, with elementary particles lying at the bottom, physical or semantic. It is particulate, corpuscular, and combinatorial. Similarly, linguists speak of grammatical particles, defined by the OED as follows: “a minor function word that has comparatively little meaning and does not inflect, e.g. in, up, off, or over used with verbs to make phrasal verbs”. Admittedly, this restricts grammatical particles to a small subclass of semantic units, but we can envisage a more generalized notion of grammatical particle that takes in verbs and nouns. Isn’t linguistics really about the constituent structure of language, and hence a theory of linguistic atoms and their combinations? And what about biology—aren’t cells the analogue of the particles of physics? A whole organism is like a medium sized physical object: it contains organs as parts (physical and mental) and these organs are made of cells, the atoms of the body. The cells in turn have subatomic constituents (e.g. mitochondria) and even a nucleus. So biology looks like an atomic theory too: it follows the pattern of particle physics—an encouraging emulation. Biology is particle biology. The cells are invisible to the naked eye and took some discovering; their discovery was a major piece of scientific progress. Again, a high level uniformity in nature is revealed: things turn out to be collections of invisible units not continuous substances. Reality is particulate, discrete, and reticulated, though it could have been continuous, smooth, and unbroken. Geometrically, it is like a matrix not a continuous solid. We could say that science is particle science. 
But what about psychology—is it too an atomic theory? Superficially, it may appear so: it deals in such units as concepts, phenomenal points, and combinations thereof. We look at a train of thought and discern constituent structure: the train consists of carriages, the individual thoughts, and these are made of simpler elements, usually designated as concepts. The concepts are like the subatomic particles of logical atomism, with thoughts as the atoms. In vision, likewise, we have an array of components corresponding to points in the visual field: here green, there red, with an impression of square woven in. The brain is certainly a particulate entity, with its neurons and their simpler parts, reaching down to the level of chemicals. But in the case of psychology the analogy starts to creak (maybe it should have started to creak earlier): the whiff of metaphor starts to permeate the proceedings. It is true enough that mental processes such as reasoning consist of simpler cognitive elements, and it is true that thoughts are made up of concepts: but are concepts really like subatomic particles? Here an uncomfortable dilemma presents itself: concepts are either the end of the line, or they are not. If they are, then our atomic theory peters out disappointingly early—there are no deeper psychological particles to be discovered. But then we don’t have the kind of empirical discovery that characterizes atomic theory in physics, since we know a priori that thoughts are composed of concepts. But if concepts are not the end of the mereological line, and there are more basic psychological particles to be discovered, then we have hitherto failed to identify what the basic particles of the mind are. This means that psychology has not made the kinds of empirical discoveries that physics so spectacularly and arduously made. It is merely reporting a boring fact of common sense, namely that we have concepts and they compose our thoughts. This is like “discovering” that animal bodies have limbs or that trees have leaves. The mere existence of parts does not an atomic theory make. Physicists knew that physical objects have parts long before they established the atomic theory we now justly celebrate; parts are not atoms. Likewise, parts of thoughts are not atoms in the epistemologically significant sense exemplified by physics. Concepts are not like electrons and protons, but more like limbs and leaves.
The thing about atoms is that they have a specific structure that has an explanatory aspect. They are not merely very small parts but articulated structures: they have a distinctive architecture. Thus they have a discrete nucleus made up of protons and neutrons surrounded by a shell consisting of orbiting electrons of varying numbers. The constituent particles have various properties, notably electric charge, positive or negative. All this explains the behavior of the matter composed of these particles, thus allowing for the reduction of chemistry to physics. It is not just a matter of conjoined chunks, mere aggregation. Atoms and their constituent particles are organized in a certain way, not anticipated by common sense or contained in the very concept of matter. That is why atomic theory ranks as a momentous scientific discovery; it is not the mere the assertion of invisible granular parts. It is the analogue of the discovery of the solar system as a system of interrelated parts orbiting a sun under the force of gravity. This is not merely the claim that the planets and the sun are parts of a larger whole; it is a theory of how the parts hang together. The atom is often compared to the solar system in its internal structure, but we could equally compare the solar system to the atom (and might have done so if we had revealed the structure of the atom first): both are tightly organized complex wholes held together by forces and laws, the nature of which we have managed to articulate (if not finally explain). But nothing like this is true in psychology: the mere observation of constituent structure is a far cry from the kind of explanatory atomic theory supplied by physics. Where is the nucleus of the concept, where the conceptual electrons, and where the law-governed orbits? At least in the case of the biological cell we have something approximating to this, but in the case of concepts (or points in the visual field) nothing comparable suggests itself: we just have the banal observation that thoughts are made up of concepts. In order for psychology to become particle psychology it needs to do a lot more than that. I don’t say it cannot do this more, but in its current state it does not. It is an entirely open question whether psychology can mimic the model of particle physics; certainly nothing in it now deserves to be compared to that model. And nothing we now know of the mind suggests a research program capable of development into a full-blooded particle psychology (the same is true of linguistics once we take the measure of genuine particle physics). So nothing in our current psychological knowledge warrants any claim of prestige deriving from a supposed analogy with particle physics. Not that this is a common claim—but it is worth making explicit how feeble the analogy to physics actually is. Physics is particle physics, but psychology isn’t particle psychology. The gulf is wide and deep. One might well suppose that a quite different paradigm would be appropriate for psychology—though what this might be remains to be determined. At any rate, we should not tacitly assume any reassuring analogy to physics based on the idea of atomic composition. The “corpuscular theory”, so beloved by Locke and Boyle, primitive though it was, finds no counterpart in psychology (with “ideas” as the mental corpuscles). By all means let us continue to stress the combinatorial nature of the mind–its generative, recursive, discretely digital character—but let us not interpret this as a vindication of a hankering for the glories of modern physics. We have not discovered the hidden particles of the mind, along with their architectural features, in anything like the sense in which physicists have unveiled the hidden particles of the physical world.  Whether this shows that psychology is still in its infancy, or that its maturity is the same as its infancy, remains moot.
 It is an interesting question whether there could be a general particle theory not just a variety of special particle theories. Are there any abstract properties shared by all particle theories (beyond truisms)? Is the concept of a nucleus essential? Does the idea of an orbit find a place in all atomic theories? Is there always some sort of glue holding the atom together? It seems unlikely that such concepts generalize in the way required, in which case the idea of a general theory of particles seems infeasible. Still, the question is worth pursuing.
 Much the same can be said of mathematics: composition without atomicity. We certainly have the idea of elements that combine according to fixed rules, addition being the obvious example, and maybe we can make sense of numbers as parts of other numbers; but it would be stretching a point to claim a significant analogy with particle physics. Again, where is the idea of a laboriously discovered structure with the abstract architecture of a physical atom? Are there nuclear numbers and orbital numbers? Are there mathematical forces that hold numbers together? The idea seems metaphorical at best. Mathematics is not particle mathematics, though it is a generative system with divisions and discontinuities (as well as continuous quantities). Physics really is special in that it reveals a hidden layer of reality that is not anticipated by our ordinary perceptions and conceptions, and is in many ways alien to them. The physical atom is a universe apart (so to speak), and this is before we get to the peculiarities of quantum theory. Psychology has yet to encounter its subversive quantum theory—particles as anti-particles, in effect. It is conservatively Newtonian, steeped in common sense.
I am probably missing the point, but theoretical physics is far from being particle physics. In mainstream engineering practice it makes sense to say that for most intents and purposes applied physics deals with particles. But this is definitely not the case in fundamental physics itself (quantum mechanics with all its conflicting interpretations, string theory etc.). The controversies about wave-particle duality and conceptual disagreements on this subject just illustrate how outdated and misleading the “planetary” atomic model discussed in the article is. And I am sure Colin you know all that, so it is not clear why you chose this particular metaphor to compare physics and psychology. Why cognitive neuroscience would not count as psychology’s “subversive quantum theory”? Why is it difficult to imagine that the former could develop an alternative vocabulary and, if empirically adequate, it would just replace or supplement the current psychological vocabulary? Whether it will use particles or waves or some other basic concepts in its theorizing is not that important.
Yes, you’re right, you are missing the point. Even if there are no classic nuggety particles, physics postulates invisible tiny realities called electrons, protons, etc. These constitute visible objects. This is just a version of corpuscular atomic theory. All my points can be run using this alternative framework. As to neuroscience, it would need to do more than provide a new vocabulary; it would need to show that commonsense psychology is actually false. Nothing suggests this.
The requirement to show that commonsense psychology is actually false is very strong and seems excessive. I mentioned empirical adequacy as a better criterion for rating competing theories than truth for a reason. The more useful, in terms of predictions and practical utility, theory is definitely pragmatically more valuable than the competing theory, isn’t it? I don’t see why a less empirically adequate theory should be preferred. Thinking in terms of a current medical analogy, if there is solid evidence that vaccine A works better than B for you (with usual disclaimers), you would take A. The same goes for theories if we count commonsense psychology and neuroscience as such. And just like a better working vaccine A does not make B “actually false”, but just less efficient — why this approach is not extendable to the context of competing psychological theories? For all we know, there could be many theories and, unless we assume there must be only one which is true. Why would we assume that? Of course at present common sense psychology is way better than neuroscience in the business of everyday behavioural predictions, but it looks way worse in handling psychological and psychiatric issues than most of the contemporary scientific alternatives. I do agree with you that neuroscience has a long way to go and it even may be a dead end as a replacement for common sense psychology. If the latter would be the case, it would happen because neuroscience will not become more empirically adequate that common sense psychology. But both have utility today and both can co-exist – it is a perfectly reasonable scenario.
This would require going into many familiar questions in epistemology and philosophy of science. The question at issue is whether the (alleged) contradiction between quantum theory and commonsense physics has any analogue in the relation between neuroscience and commonsense psychology. I know of no reason to believe this.
Yes I agree that continuing to push the counter-argument (or side-argument) won’t be the best use of our time. A side note in case it is not clear, I find your thinking simulating, intellectually honest and open minded even when I am not convinced, like in this case. So I won’t distract you further on this.
That is a prudent response. There is far too much argy-bargy out there and not enough real thinking.