Among the greatest of the Latin scholastics, Francisco Suárez (1548-1617) was a profoundly original and highly sophisticated theologian-philosopher who significantly influenced early modern thought, and also produced monumental summaries of several centuries of Latin scholastic argument. A full third of his gigantic Metaphysical Disputations was devoted to an extremely detailed and systematic discussion of causality. A large volume entirely dedicated to efficient causes has been translated to English, and a web search popped up several secondary discussions. My comments here will be very high-level, mostly based on those.
In this scholastic context, traditional Aristotelian terms like cause, being, and substance are all given very different explanations from the nonstandard but hopefully both more historical and more useful ones I have been giving them. Latin scholastics tended to have a somewhat neoplatonizing, substantialized notion of Aristotelian causes. A common view was that any cause must be a substantial entity of some sort, whereas causes in the common modern sense are events, and I read Aristotle himself as identifying causes with “reasons why”.
Suárez held to the view of causes as substantial entities, and apparently went on to argue that all causes give Thomistic being (esse) either to a substance or to an accident in a substance. This influx or “influence” is described as a kind of immaterial flowing of being that makes or produces, without diminishing the agent. In the case of an efficient cause, this influence occurs through action, and the substantial efficient cause is called an agent. (By contrast, in the above-linked article, which has brief additional remarks on Suárez, I quoted Aristotle saying in effect that an agent’s action is more properly an efficient cause than the agent, and that something like a technique used in an action is more properly an efficient cause than the action.)
Suárez’s metaphysical emphasis on actions producing being in things has been characterized as transitional to a modern, event-based view of causality. While Suárez himself held to the idea that causes were substantial agents, early modern mechanism indeed seems to have kept his emphasis on action but moved to an event-based view.
It seems to me to have been a historical accident that mathematical natural science arose on the basis of an event-based view. While mathematics certainly can be used to develop precise descriptions of events, any mathematical analysis relevant to this can also be construed as a “reason why” rather than a mere description. On the frontier of analytic philosophy, Brandom is again suggesting that a consideration of reasons actually circumscribes — and is necessary to underwrite — consideration of events and descriptions. This suggests a new motivation for recovering Aristotle’s original reason-based view.