Potentiality (dynamis) is yet another great Aristotelian expressive metaconcept. Plato had the intriguing idea of explaining things and states of affairs in terms of power (also dynamis), but left power as an unexplained explainer, and required it to be postulated as pre-existent. Aristotle thoroughly reconceptualized the term to eliminate these weaknesses. Every Aristotelian potentiality begins from actuality or at-work-ness.
Instead of referring to postulated powers behind things or abstract logical possibility, Aristotelian potentiality is a way of talking about the aspects of a conceptual content captured by what Brandom would call modally robust counterfactual inference. Such robustness of inference across counterfactual cases is implicitly central to the most elementary meaning of Aristotelian substance or “what it was to have been” a thing (ousia), as what grounds the weak unity that allows us to talk about the same “thing” persisting through time even though something about it changed.
The semantic importance of counterfactual inference in determining the sense of what things are is a thesis shared by Aristotle, Hegel, and Brandom. It is explicit in Brandom and Brandom’s Hegel, and implicit in Aristotle. We cannot even really form a view of any thing as a thing of a certain kind unless we at least implicitly consider its potentiality.
Aristotle was clear that potentiality is an irreducible ingredient in things, and potentiality clearly captures counterfactuals. Brandom has made the role of counterfactuals in the development of universality more explicit. Facts alone give us at best a very brittle structure of assertions with no real conceptual articulation or interpretation, so perspectives that try to ground things on facts alone are doomed to ultimate failure. (In this light, Nietzsche‘s elimination of potentiality also turns out to have been a very serious error.) Overly strong, question-begging notions of the Identity of things have helped obscure the vital role of counterfactual inference in stabilizing our experience of the world. (See also Modality and Variation.)
Tentatively mapping this to Brandom’s Fregean terminology, I think Aristotle would intend the relation of potentiality to actuality to be one of reciprocal sense dependence paired with asymmetrical reference dependence. That is to say, at a level of determination of meaning, potentiality and actuality are interdependent and equally important, but in the order of logical truth about representations, actuality or the concrete is the starting point in terms of which potentiality is evaluated. Potentialities are potentialities of some actuality.