Heisenberg offered an interpretation of the quantum state which made use of a quantitative version of an earlier notion, <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="RSTA20160390IM1"/>, of Aristotle by both referring to it using its Latin name, potentia, and identifying its qualitative aspect with <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="RSTA20160390IM2"/>. The relationship between this use and Aristotle's notion was not made by Heisenberg in full detail, beyond noting their common character: that of signifying the system's objective capacity to be found later to possess a property in actuality. For such actualization, Heisenberg required measurement to have taken place, an interaction with external systems that disrupts the otherwise independent, natural evolution of the quantum system. The notion of state actualization was later taken up by others, including Shimony, in the search for a law-like measurement process. Yet, the relation of quantum potentiality to Aristotle's original notion has been viewed as mainly terminological, even by those who used it thus. Here, I reconsider the relation of Heisenberg's notion to Aristotle's and show that it can be explicated in greater specificity than Heisenberg did. This is accomplished through the careful consideration of the role of potentia in physical causation and explanation, and done in order to provide a fuller understanding of this aspect of Heisenberg's approach to quantum mechanics. Most importantly, it is pointed out that Heisenberg's requirement of an external intervention during measurement that disrupts the otherwise independent, natural evolution of the quantum system is in accord with Aristotle's characterization of spontaneous causation. Thus, the need for a teleological understanding of the actualization of potentia, an often assumed requirement that has left this fundamental notion neglected, is seen to be spurious.This article is part of the themed issue `Second quantum revolution: foundational questions'.