One of the assumptions of materialism is that the physical world is completely causally closed. Even though this proposition is well supported by evidence some would doubt it (perhaps reasoning that causal closure is broken only in rare cases, and thus explaining why it hasn’t been revealed by our scientific investigations). What is impossible to doubt, however, is that the universe of observable phenomena is casually closed. And if we define as physical that which is observable, which not a radical suggestion, this in turn implies that the physical world is completely casually closed.
If it is indeed the case that the observable world is causally closed it must be the case the all the causes of something observable are themselves observable. This should seem intuitively plausible, since if we observe effects it seems reasonable to suppose that we can deduce information about the causes, making the causes observable. This is, of course, not to say that the causes are necessarily observable with our current level of technology, simply that they are observable in principle. For example, we can observe atoms through a scanning tunneling microscope by observing their effects on a stream of electrons; atoms did not suddenly become observable when the scanning tunneling microscope was invented, rather it was the case that they were observable but we simply lacked the tools to directly investigate them.
Let’s say for example that some observable phenomena, X, can be caused by two factors, A an B, either independently or in combination. If we observe X then we can only deduce that A or B (or both) are the cause, and this is not enough to consider A and B observable. However, if A and B are observably different they must differ in some observable property. And if they differ in some observable property that must mean that they can cause different observable effects, and thus we could set up additional tests to determine which of the factors is a cause of X, making them observable. Given this there are only two possibilities if the observable world is not to be completely causally closed. One is that X is caused by two different factors, A and B, which differ only unobservably. This claim, however, is essentially saying that only the observable properties that A and B have in common are responsible for X, and thus the observable phenomena are still causally closed. (A possible rejoinder to this case is to suppose that there is some third factor, C, that shares the same observable properties as A and B, but differs in an unobservable property, and isn’t a cause of X. However, this is a contradiction, because by observing X we would know that A and B didn’t have the unobservable property that differentiate them from C, and thus the property isn’t unobservable after all.) The other possibility is that there are two factors that can cause X, A and B, and that while A is observable B is unobservable. However, to avoid the pitfalls outlined above, we further stipulate that whenever B is the cause of X A is as well (perhaps because of some other factor). If this was a possible situation then X would indeed have an unobservable cause, but this situation too hides a contradiction. The contradiction is made evident when we consider what reasons we have to say that one thing is the cause of another. In either the senses of a sufficient or necessary cause we say something is a cause of some state, Q, when the absence of that thing would have prevented Q from occurring, or if that thing by itself could have brought about Q. B can play neither of these roles, since we stipulated that it is necessarily accompanied by A, and thus it can’t be the case that it brings about X by itself, nor can it be the case that its absence prevents X from being brought about, since A is a cause, and thus B isn’t really a cause at all. Again, the observable phenomena are completely causally closed.
From this reasoning we conclude that, by our notions of observable and cause, the observable world must be completely causally closed. And if we define as material that which is observable then the material world is also completely causally closed. Some may object, saying that there are no material causes for observable conscious states, and hence that we can’t claim the observable is identical with material. This would be a problem if we allowed all conscious experience to count as observable, however, as presented here, we can take as observable to mean only those phenomena observed with our outward-directed senses, and the causal closure holds just as well. And from that we could deduce by observing other people that our conscious states really do have a basis in the material / observable, or that they are unobservable by our outward-directed senses but have no causal powers (they are epiphenomenal). And if we reject epiphenomenalism (see here) then we can conclude that the mind really is identical with some material phenomena.