In the history of philosophy materialism and idealism are regularly opposed to each other: they are conceived as rival metaphysical systems. Each is thought to have its appeal, with oscillation between them, but it is assumed that you cannot be both. They are logically incompatible doctrines. The world is either completely material or it is completely mental—it cannot be completely both. But on reflection things are not so simple; it is possible to combine materialism and idealism. There can be a coherent materialist idealism and also coherent idealist materialism. You can be a materialist and an idealist. How is this possible?
Suppose you are attracted to an identity theory of mind and body: you think that mental states are identical to brain states. You think this for the usual reasons (parsimony, causation, anti-dualism, etc.) and you subscribe to the view that reality is generally material (consisting of atoms in the void, say). What is to stop you conjoining this materialist viewpoint with the proposition that so-called material nature is really mental? Suppose you agree with Berkeley about material objects—they are really ideas in the mind of God with counterpart ideas in human minds. Then you accept that brains and their states are mental objects too, along with other material objects. So you hold that the brain states with which mental states are identical are themselves mental entities, ultimately ideas in God’s mind. Thus mental states are identical with ideas in the mind of God (ideas of brain states). Ideas are identical with other ideas. Pain, for example, is identical to an idea in God’s mind, since C-fiber firing is an idea in God’s mind. You reduce the mental to the physical and then you reduce the physical to the mental. You are a global idealist who is a materialist about the mind. Or you might hold, with Eddington and Russell, that the world of physics is ultimately a world of conscious experience (“neutral monism”) while at the same time believing that minds reduce to brains (which themselves reduce to ripples in the mental substratum). You are a materialist about the mind but an idealist about reality in general—an idealist materialist. You are certainly more of a materialist than someone who holds that the mind is quite independent of the brain and also that reality is generally mental. You hold that everything mental is physical (atoms in the void) but that everything physical is ultimately mental (those atoms are really mental in nature).
Now suppose that you attracted to the doctrine that material objects are bundles of dispositions to appear a certain way—you would call yourself a phenomenalist. Perhaps you think this is a good way to avoid skepticism, or that it is the only hope of preserving naïve realism. Objects have no being independent of the mind: idealism is true of them. What is to stop you conjoining this belief with the claim that experiences are really material processes occurring in brains? You are a materialist about sense experience and all other mental phenomena. Your position is like that of someone who believes that colors are dispositions to produce color experiences but also believes that color experiences are brain processes. This seems like a perfectly consistent position: colors could be dispositions to elicit brain processes, these being what color experiences are. And the same is true for a general idealism about the objects of perception: this doctrine might be combined with a materialist view of experience. The brain itself is a bundle of dispositions to produce sense experiences, but sense experiences are states of the brain (and hence themselves dispositions to produce experiences). You are an idealist about material objects (so-called) but a materialist generally: you think objects depend on minds for their existence, but you also think that minds are physical things. You are a materialist idealist. You are certainly much more of an idealist than someone who holds that objects are mind-independent: for you hold to a central tenet of traditional idealism while rejecting the claim that reality is ultimately mental.
We might describe the first sort of metaphysician as a global idealist who holds to a local materialism and the second as a global materialist who holds to a local idealism. It would be misleading to label either an idealist or a materialist tout court, since they differ from a theorist who rejects those local claims. We need to make room for these mixed positions, since they exist in logical space and have their own attractions. We thus require an expanded terminology. But now I want to complicate matters further by introducing an additional ontological layer. Suppose you hold that reality consists of ideas in God’s mind in the style of Berkeley, while also accepting the mind-brain identity theory: you are a global idealist and a local materialist, as described above. But suppose also that you believe that God is a corporeal being (as Hobbes apparently did)—you are a materialist about God. So you believe that the world consists of ideas in God’s mind but also that God’s mind is material. Then you are a global materialist global idealist local materialist (because you accept the identity theory of human and animal minds). You think that everything is ultimately material because God is material and God’s ideas form the basis of all reality—while also accepting that mortal minds are reducible to brains. Are you a materialist or an idealist? There is no answer to that question, because your position combines elements from each doctrine—you believe a mishmash of idealist and materialist elements. Likewise, you might hold that materialism is generally true in the sense that everything reduces to physics while also holding that physics is ultimately about a world of conscious experience (following Eddington and Russell). Thus you might hold that objects reduce to dispositions to produce experiences, experiences reduce to brain states, and brain states reduce to the conscious stuff that makes up the world in general. You think that everything is material but that the material is ultimately mental. Are you a materialist or an idealist? Again there is no answer to that dichotomous question: you are a global idealist global materialist local idealist. You think that everything is ultimately mental but that everything reduces to physics and that objects are mind-dependent. You simply don’t fit into the traditional dichotomy of materialism versus idealism.
If that sounds complicated, consider what happens if we add a further wrinkle: suppose we introduce the idea of a neutral substance that is neither mental nor physical, as in neutral monism. Now we can say things like, “God is neither mental nor material but something in between” or, “Mind and matter are the result of a neutral substance that is neither”. This produces a further range of possible positions that refuse to fall into the usual categories. I won’t elaborate further, but it is clear that the metaphysical landscape is now populated with a startlingly large array of options. The traditional dichotomy is woefully inadequate to capture this range. But even without adding the notion of a neutral stuff we can generate positions that can’t be slotted into the usual two categories. And this is not just a logical nicety but corresponds to positions with intrinsic appeal—positions someone might conceivably adopt. Hobbes might agree with Berkeley’s critique of traditional theories of perception but still insist that everything is material because God is; or an idealist might wish to maintain that mind and brain are identical as a way to avoid epiphenomenalism. Couldn’t Eddington believe that everything is ultimately mental in nature while maintaining that all the sciences reduce to physics? What about the idea that mental states reduce to brain states but brain states are constituted by an alien type of experiential state? That would give us an identity theory between one kind of mental state and another, mediated by a physical state of the brain. Pain is identical to C-fiber firing; C-fiber firing is identical to alien experiential state E: so pain is identical with E, whatever E is. Is this a materialist theory of pain or an idealist theory? Both and neither: it contains elements of both. Being red is a disposition to produce experiences of red, but experiences of red are states of the brain, but states of the brain are really experiential in nature, but these experiences are ultimately grounded in an unknown type of physical property–what kind of theory is that? It is a complicated combination of materialist and idealist elements. Metaphysics is not as simple as we have been led to believe by the old division between materialism and idealism. In principle, nothing prevents us from contemplating indefinitely many layers of mental and physical reality, each giving way to the other: a mental layer rests on a physical layer, which rests on a further mental layer, which rests on yet another physical layer, and so on. Would someone who thinks this layering can go on infinitely many times be a materialist or an idealist? Neither: they would be a materialist idealist and an idealist materialist.
 I won’t consider the question of whether the terms “mental” and “material” (or “physical”) can bear the weight placed on them in these metaphysical controversies, assuming that they have enough content to form coherent theories. My question is whether a simple dichotomy is adequate to the philosophical landscape. Of course, there is also metaphysical dualism, which holds that there are both mental and material facts at the basic level; I am only considering the monistic theories of materialism and idealism.
 Compare particles: it has turned out that there are far more layers of particles than we first thought—from molecules to atoms to electrons and protons to quarks, etc. And it may be that we are not yet at the end of the line—or maybe there is no end of line and there exists an infinitely descending series of particles. Similarly, it might be supposed that mental and physical layers alternate multiple times before bedrock is reached—or maybe it is never reached and we have infinite alternation. Nature is not generally averse to infinity.