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.
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.)