I now want to say, structure — which statically captures a determinate field of potential inferences — is isomorphic to Aristotelian potentiality. These concepts are mutually illuminating.
This helps clarify how Aristotelian potentiality differs from the Platonic power referenced by the same Greek word, as well shedding light on the association I have made between potentiality and counterfactual inference.
From the other direction, the thing to notice is that for Aristotle, potentiality exists only in a pair with actuality or at-work-ness. Similarly, synchronic structure exists only in a pair with diachronic process. I always read the conspicuous lack of definition of the synchronic/diachronic interface as reflecting something like Aristotle’s principled use of underdetermination in order to focus on what is most essential and clearly justifiable.
A lot of people seem to have been very confused about this latter point during the drama over 1960s French structuralism. What passed for dialogue was often a complete disconnect. “Look at how much can be explained synchronically!” “Oh no, you’re abolishing history, free will, personality, and identity!” If the new viewpoint was forgivably one-sided in its enthusiasm, some of the reaction verged on hysteria. (See also The Dreaded Humanist Debate.)
Another source of confusion seems to be that many people apparently thought of structural causality in terms of a monolithic, complete determination. I think instead that structural causality comes in many separate blocks, in an overall context of less-than-complete determination. (See also Structural Causality, Choice; Values, Causality; The Importance of Potentiality.)