As everyone knows, Newton abandoned the materialism of his day by introducing the “occult” force of gravity. Clerk Maxwell expanded physics further into the immaterialist camp with his theory of electromagnetic fields of force. These developments cast the whole notion of materialism (or physicalism) into doubt. But was physics before Newton and Clerk Maxwell materialist? Was mechanism a materialist doctrine? To answer that question we need to know what “materialism” means, i.e. what matter is. We need a criterion of the physical: what is it for something to be physical (or material)? What are the necessary and sufficient conditions? This question is far from easy. The OED gives this for “matter”: “physical substance or material in general; (in physics) that which occupies space and possesses mass, especially as distinct from energy”. For “material” we read “the matter from which a thing is or can be made”, contrasted with “mind or spirit”. Under “physical” we have “relating to the body as opposed to the mind” and “relating to things perceived through the senses as opposed to the mind; tangible or concrete”. These definitions only take us so far and offer little to elucidate what is meant by the metaphysical doctrine known as “materialism”. Two points stand out: first, matter is to be distinguished from energy; second, matter is perceived through the senses. Energy is not material and what is not perceived by the senses is not material (what is so perceived is). This gives the result that energy is not subject to materialism and secondary qualities are material simply because they are perceived by the senses (and atoms are not material because they are not so perceived). This is far from what philosophers have intended by using the terms “materialism” and “physicalism”. We clearly need to go back to the drawing board.
One approach, much favored, is to invoke geometrical concepts like size and shape. Thus Descartes spoke of extension and modes of extension as characteristic of physical substance. It is necessary and sufficient to be physical that something has shape, shape being a physical attribute. More generally, the physical is to be defined as what possesses primary qualities. The view goes with the idea that space and matter are intimately connected: matter is what occupies space (as the OED states). There are many problems with this approach. First, as to sufficiency: don’t persons and sentient beings generally occupy space and have shape? Is it contradictory to suppose that God is spread out through space, as in pantheism, and has a tripartite form (the holy trinity and all that)? What if thoughts and sensations have shape of some sort—does that preclude them from being immaterial? Doesn’t it depend on what kind of stuff they are made of? Is extension logically sufficient to make something materially constituted? Descartes already had a problem with space in this regard, given that space is extended (his solution was to declare space a rarified form of matter). And is shape really a physical property? What if perceived shape is actually a secondary quality (as modern physics appears to suggest)? Then reducing everything to shape is not a form of materialism at all, since shape is projected from the perceiving subject, i.e. is mental. Maybe in objective physical reality nothing has shape, or at least determinate shape: does that imply that materialism must be false? But more fundamentally, is geometry physical? Is Euclid’s Elements a work of physics? There is certainly a strong tradition stemming from Plato and going back to Pythagoras that geometry is about the world of abstract geometrical forms, loosely proximate to the realm of the gods. If we are Platonists, we don’t regard geometrical forms as physical in the sense of being made of physical substance; and we don’t suppose that they are perceivable by the senses (the intellect must be employed). We might even adopt a kind of idealism about geometry, holding shapes to be ideas in the mind of God. In that context reducing everything to geometry is the furthest thing from materialism as traditionally conceived. So the prospects for a form of materialism based on primary qualities like shape depends upon your metaphysics of geometry: you have to think that geometry is about physical substances–whatever your account of that concept is going to be. Second, in regard to necessity: is it really a necessary condition of being physical that a thing has shape? Do electrons have shape just by being physical? What about fields? Could there be a physical universe with no shaped objects? So long as there is physical stuff we have a physical world; possessing shape is an added ingredient. The connection between matter and shape looks to be contingent and adventitious, not a matter of strict definition. The same goes for size and number: are these necessary and sufficient for being material? If size is relative, then nothing has size in a universe containing a single object; but surely there could be a physical universe with just one object. And how can number confer materiality on a thing, given the ontological standing of numbers? The basic point is just that these qualities are not intrinsically physical (whatever that means): they are, if anything, abstract, or possibly psychological. That is why Berkeley has no trouble including primary qualities like shape in his idealist universe. We still have no criterion of the physical that will confer content on the doctrine known as “materialism”.
You might think we could resort to the doctrine of mechanism: materialism is defined as the thesis that everything is subject to mechanism. This is certainly the form that materialism took before Newton and later Clerk Maxwell. The problem here is that mechanism is neither necessary nor sufficient for materialism. The OED defines mechanism as “the doctrine that all natural phenomena allow mechanical explanation by physics and chemistry”. Correct: but what is “mechanical explanation”? It is explanation by deterministic contact causation—the kind that is found in typical machines. But this is not a necessary condition of being material, since we can conceive of physical systems that don’t work by such causation: they are made of material particulars but their behavior is not to be explained in terms of deterministic proximate causes—maybe the entities concerned never actually touch each other, or act probabilistically. The nature of an object’s composition is not the same as the nature of the explanations that apply to it. And the applicability of mechanical explanation is not sufficient for materiality either, because non-physical things might interact by means of contact causation: immaterial minds might make contact and thereby influence each other, or a part of an immaterial mind might affect another part by immediate contact. The mode of interaction between things is not determinative of what composes them. So mechanism is not a good way to define materialism, conceptually speaking, though it was the form that materialism took in earlier times. Mechanism is a view of what constitutes an adequate scientific explanation not a view of the composition of basic reality: these are orthogonal questions. It isn’t as if planets ceased to be material once Newton’s non-mechanistic physics became established! So we still don’t know what it is for something to be material.
Is it the possession of mass? If we define mass as “quantity of matter”, we invoke the concept of matter in defining what matter is, which makes the definition circular. If instead we define mass as resistance to motion (inertia), then it doesn’t follow that the object in question is material: couldn’t immaterial entities vary in their degree of resistance to motion? And what about massless particles? Likewise, being subject to gravitational force (weight) is not logically sufficient for being material, since immaterial things might be subject to gravity too—this could be a basic law of a conceivable universe. What about limiting the concept of the material to the brain, which would still enable us to define a workable materialism for mental states? That is, we define “material” as “neural”, thus enabling us to claim that the mental is reducible to the neural—no need to attempt a general definition of the material. But are neurons material things? This takes us back to where we started: in virtue of what are they declared to be material or physical? Is it because they are objects of sense perception, or is it because they occupy space, or is it because they have shape? What if electricity is non-physical (as was once thought)? What if shape properties are non-physical in the manner of Plato? What if perceived shape is a mental projection, so that the shape of neurons is as subjective as their color?  What if in objective reality nothing really has determinate shape? We can certainly define a doctrine of “neuralism” that maintains that everything mental reduces to neural properties, but it doesn’t follow that materialistic metaphysics has been thereby vindicated. For that we would need a proper notion of what it is to be material; but the concept of materiality remains elusive. It is true that there is the popular sense of the word in which it connotes undue concern with worldly values (money, real estate, etc.), but that has nothing to do with materialism as a metaphysical thesis—though this thesis might derive spurious content by association with materialism understood as a life-style. Maybe the word “materialism” has always connoted that which is to be contrasted with the divine or supernatural, but clearly this notion is not specific enough to define the intended metaphysical doctrine (human and animal minds are not divine or supernatural). The notion is irredeemably hand waving and honorific, more a device of rhetoric than strict ontological taxonomy. It operates to define what side you are on in the wars of religion.
Is time material? Is space? What about numbers? And values? Are the four fundamental forces of nature material, or electric charge, or motion? We have the idea of chunks of stuff like rocks and furniture and bits of food, but this is not enough to give us a perfectly general notion of matter capable of making useful ontological divisions. This is why there have been such controversies, even within physics, about whether this or that qualifies as “physical” (gravity, light, fields of force, the ether, etc.). The concept of shape has been the last redoubt of the would-be materialist, but as indicated above that proves a frail reed too. Geometric form is really not a promising basis on which to define the putative concept of the material, because geometry itself is not a physical science in any intuitive sense; someone who believes that the world is a pure mathematical structure of abstract geometric forms is hardly a materialist. And space, the concrete reality in which geometry manifests itself, is a poor candidate for erecting a viable notion of the material, even if it is not defined by reference to human perception. We need some idea of space-occupying physical stuff, but what exactly is this elusive stuff supposed to be? It is no wonder that theorists, sensing the difficulty, have proposed that material stuff is really mental stuff: but then materialism turns out to be a form of idealism, i.e. the view that reality is ultimately mental. The panpsychist is no materialist.
We can imagine intelligent beings that revere matter for its supernatural associations, while finding mind quite far removed from the divine. They suppose that God miraculously created matter in the initial act of creation, while minds arose by mundane natural processes. These beings worship matter and extol its remarkable properties (they are very taken with light and love rainbows): they display big chunks of it in their temples and teach physics as a holy science. The soul excites them not at all—any more than the stomach does: for these happy beings are not much concerned with matters of moral conduct. For them there is nothing bravely hardheaded or thrillingly anti-religious about regarding matter as the basis of everything real (God, for them, is the Matter of all matters); for them it would be heretical to be an idealist, proclaiming the unreality of matter and asserting the sole dominion of the mind (that animalistic thing!). For us, however, materialism sounds anti-religious and we devoutly wish to distance ourselves from religious conceptions; while for them dwelling on the soul exclusively and repudiating matter is what excites religious opposition. Could it be that the historical enthusiasm among human freethinkers for something called “materialism” has its psychological roots in opposition to religion (no doubt well-founded opposition)? But once religion loses its cultural hold on us the rhetoric surrounding the term becomes obsolete: we no longer have any use for the concept of the material (beyond its quotidian practical uses). We can go on talking about the mind and the brain and wondering whether neurons are the ground of all mentality, but we can dispense with the general notion of the material. We need not concern ourselves with the pseudo-question of whether or not neurons are material things. We can ask whether they are mechanical things and expect to be talking sense (they are probably not), but insisting on an answer to the question of whether they are material or immaterial is outmoded gibberish—rather like forcing an answer to the question of whether gravity is material or immaterial, or energy, or radiation. We no longer think there is anything to the ancient contrast between the sublunary and the superlunary—this is a pointless bifurcation from a scientific point of view—so why cling to the obsolete and unhelpful contrast between the material and immaterial? Both belong to a worldview built around religion, but that worldview no longer commands scientific or philosophical interest. Materialism is accordingly an empty doctrine. 
 According to old-style biology, organic structures are imbued with vital spirits, and hence are not reducible to the inorganic materials dealt with by physics and chemistry. That would make neurons likewise imbued with vital spirits, this disqualifying them from being purely physical. So identifying mental phenomena with neurons would not vindicate materialism. And can such vitalism be ruled out a priori?