I’ve explained each of the four classic Aristotelian “causes” as playing what Brandom would call an expressive role, helping to explain other meaning, and pointed out how different this is from standard modern notions of what I’ve been calling univocal causality. An Aristotelian cause (aitia) is much more like a nonexclusive reason than it is like anything expressed by mechanical metaphors.
There is another very important modern way of thinking about these matters, inspired by Hume’s critique of realism about causes in the modern sense. Hume pointed out that modern-style talk about cause and effect involves a kind of inferential extrapolation from observed regular patterns of succession. Implicitly influenced by this, much work in the sciences relies directly on statistical correlations observed in data from controlled experiments. What particular causes are said to be at work then becomes a matter of optional statistical inference, subject to possible debate.
Then, too, from the side of subject matter, in fields concerned with complex dynamical systems that can only be modeled in a very tentative way — like ecology, economics, and medicine — it has come to be widely recognized that many causes combine to produce the results we see.
Both the statistical approach and what I’m gesturing at as a “complex systems” approach to causality avoid reliance on mechanical metaphors. Neither of these perspectives rules out underdetermination or overdetermination, or the simultaneous presence of both.
Aristotelian “causality” is simultaneously underdetermining and overdetermining. That is to say, in advance it leaves room for varying outcomes, but in hindsight it provides multiple rationales for a given outcome. Its purpose is to provide not certain prediction, but intelligibility and reasonableness.
In principle, nothing would stop us from combining this with statistical or complex-systems views, but these are still very different approaches. The statistical approach is quantitative and relies on counting minimally interpreted facts, where the Aristotelian approach is qualitative and puts the whole emphasis on rational interpretation. The complex-systems view relativizes causes in the modern event-based sense, without making them like any of the Aristotelian ones, none of which corresponds to an event. It is also not interpretive in the sense developed here.
One might consider mathematical-physical law as a kind of formal cause. Statistics and things like dynamic models could be taken as modern, quantitatively oriented descriptions of what I have called material tendencies. (See also Secondary Causes; Form; Aristotelian Matter; Efficient Cause; Ends; Natural Ends; Aristotelian Identity; Aristotelian Demonstration.)