A little bit of metaphysics can go a long way. I've decided to do a series of posts on this point. Here's the first helping.
We find ourselves in a world full of regular causal events. Suppose that, on the basis of this, someone were to propose the following two-part position, which I will call (following Galen Strawson) the Realist Regularity Theory of Causation (RRTC):
(1) External World Realism. There is an external world of mind-independent objects.
(2) Causation in the mind-independent world is simply regularity of succession (insofar as it is anything).
RRTC recognizes an external world, and it recognizes that this world is regular; but it insists that this regularity of succession is not explained by any feature of this world, whether we take the relevant explanation to be an explanation of why there is any regularity at all, or whether we take it to be an explanation of why there is such-and-such regularity rather than some other kind of regularity.
We might argue for such a position in this way. In order to form any reality-relevant concept of causation other than regularity of succession, i.e., in order to get beyond regularity in our account of causation, we must be able to identify some feature (or features) of our experience that is both causal and exhibits more than a regularity. Such a feature cannot be found; therefore causation in the world is simply regularity.
That such a feature cannot be found might be established by an eliminative argument. [Astute and informed observers will recognize that the following argument is influenced by Hume's discussion of necessary connection in ECHU, Section VII, Part I.] If such a feature exists, it must be found in our experience either of bodies or of minds. When we look at the bodies that we experience, this additional feature would have to be available to our senses. However, when we examine the qualities we sense, we find no such feature. A billiard ball hits another billiard ball, causing it to move. All we see in this scenario is one thing following another: this three-dimensional bit of color against this colored background, moving up to and touching (with a sound) this other three-dimensional bit of color, which then moves. All our sensory experiences can be handled in this way; so this supposed feature is not available to the senses. Therefore nothing in our experience of bodies shows there to be more to causation than mere regularity of succession.
This naturally brings us to minds, which we can divide into our own mind and the minds of others. When I contemplate my own mind, there are only two possible cases in which this feature could show up: either in my mind's causal power over my body, or in my mind's causal power over itself. Let us take my mind's causal power over my body first. Inquiry into this possibility seems very clearly to show that no causal feature beyond regularity is found in our experience of our power over our own bodies. Two signs of this emerge immediately. The first is that we find the question of mind-body union so perplexing. How is the mind related to the body (and vice versa)? It is a highly controverted issue. If, however, we were able to identify a causal feature beyong regularity in the experience of the mind's control over the body, this question would not be so mysterious. The second sign is that there is nothing in our experience of the mind that gives us any indication of why we can move our arms at will and but cannot move our liver at will. If we suddenly became paralyzed, we would find nothing different in our experience of the mind; it just would now be the case that what happens in our mind is no longer followed by the moving of the arm. Thus the only causal feature we experience in our experience of the mind's control over its body is regularity of succession.
What, then, of our experience of the mind's control over itself, e.g., in the formation and examination of ideas? But here, as with the body, we do not have unlimited control. There are things about our minds we do not control. Yet we have no more knowledge here of why we control some things and not others. We can only learn by experience that the mind's internal attempt to do X is followed by a doing of X (or not followed by it). Likewise, this self-control is very different at different times; but we cannot identify any feature in our experience that explains this difference.
This only leaves other minds. But it seems manifestly false to say that we have direct experience of the causal features (beyond regularity) of other minds, particularly when we cannot find any such features in our own minds, which we know much more intimately and directly. Even if we were to say that we do have direct experience of other minds, we still cannot identify any aspect of this experience that fits the description of what we are looking for; because the motions and changes due to things other than ourselves are not more clear and less mysterious to us than those due to ourselves.
Thus we do not find such a feature in bodies or in minds; and it seems reasonable to say that there is no third thing falling within our direct experience. Therefore, one might say, the argument holds: we must accept that everything we call 'causation' in the mind-independent world is merely regularity of succession.
It seems clear, however, that RRTC is not a tenable position. I will discuss the reasons why in a post to follow.