In particular Campbell explored the nature of 'control variables'. The idea here is that we can rightly claim to have identified the cause of something (e.g. what causes the volume of a radio to increase is the volume knob being turned) when the explanans stands in the relationship of a 'control variable' to the explanandum. I don't recall all of the characteristics of these 'variables', but they include the notion that there should be no gratutitous redundancy, a total mapping of causes onto effects, a dose response, and a ready computability of the cause, etc., in bona fide causal explanations.
Upshots of Campbell's view include the idea that there can, even in a 'deterministic physical universe' be non-physical (i.e. psychological) causation (since the best explanation of most human behaviour is psychological rather than physical: psychological factors behave more like control variables for behaviour than do microphysical brain states). This, to say the least, challenges in a very interesting way some of the presuppositions of mainstream physicalist philosophy.
An obvious worry - that was reflected in at least two of the questions (I had to leave after a few of these) - with Campbell's position is its apparent 'anthropocentrism'. One way to put this worry is to say: Campbell seems to be trying to derive a metaphysical conclusion about the nature of causation itself from explanatory considerations - about what we (humans) find explanatorily satisfying. This is a move which many hard-nosed metaphysically-minded sorts will want to resist.
Despite the worry, I find myself attracted to Campbell's position - mainly because of the easygoing, unpretentious way it pricks the side of the 'oh-we're-so-hard-nosed-and-scientific' contemporary physicalist philosopher of mind. And so I naturally wonder what a good defense of what may appear to be its anthropocentric bias might be.
I found myself thinking of the ways in which Wittgensteinian conceptions of the relation of meaning to use, or of the nature of the will, or of the relation of perception to its objects, have been defended against the objections to them lodged by Grice et al. The Wittgensteinian attempts to draw conclusions about what is intelligible - conclusions about meaning, what it makes sense to say - from premises about what people would say in various situations. For example, they would say that there are many situations in which we would not describe someone as trying to perform some action (because it's so easy and they just succeed straight off 'without having to try'). This then is used to count against theories of action which suggest that intentional action just is, at a minimum, action which we are trying to do.
The Gricean says: 'Well, just because we wouldn't
Just as the Gricean seems to want to extend talk of (say) 'trying' to a whole gamut of cases - regardless of whether we would normally find it helpful to locate trying there - to the end of providing us with an objective account of what makes for intentional action, so too the metaphysician seems to want to extend talk of 'causation' to a whole gamut of cases regardless of whether we would normally find it helpful to cite the cited events in explanations, all to the end of providing an account of what makes for the happening of happenings. In both cases they find themselves tempted to say "In restricting your talk of 'trying' or 'cause' to those cases in which talk of causes or of trying is genuinely informative, you are merely demonstrating your anthropocentric bias."
By contrast the Wittgensteinian could reply: "The burden of proof lies not with I but with you. You are assuming that I am being anthropocentric (letting my sense of what counts as a good explanation get in the way of my ontology), but I am claiming that the concept just is like that. You are trying to remove it from the context which gives it its life in the first place. It's not that I'm giving a biased account of what a cause can be. It's that you are giving a misleadingly broad account of causation. A cause isn't to be defined as that which features in a satisfying causal explanation (that would just be circular), but we can look at which explanations are and are not successful in specifying causes to give us a good sense of what a cause is. (After all, as I seem to remember Campbell saying, causes just are that which are cited in causal explanations.) In your desire to secure the objectivity of genuine causality you try to distance it from human concerns, but unwittingly thereby also uproot it from its sense-conferring context of application."
Campbell's homely account of causation, to the extent that I understood it, brought that concept nicely back down to earth for me. That process was also helped by Wittgensteinians such as Anscombe - who talk of the ways in which pushing and pulling and cutting and startling are causal notions which jointly determine what is meant by causality (rather than instantiating some further hidden connecting phenomenon called 'causation'). As a result I find myself less inclined to turn to some special discipline called 'metaphysics' to help me work out what that mysterious causal relationship 'really' consists in. Causation is now even more than ever just one of hundreds or thousands of (albeit abstracted) concepts jostling around our richly elaborated form of life.