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Interesting. Seems Aquinas was getting himself an additional layer of analogical thinking beyond Aristotle. Thanks for notice of Aquinas’ prime/functional distinction. I do not buy that potentiality can be a substratum of change. (And down from Galileo-Descartes and Newton [and Einstein’s version], I take inertial motion as brute, requiring no cause nor substrate, only matter [non-zero mass], actual matter, and spacetime.) Potentials belong to and are followers on actualities, and they are delimitations on alterations of actualities. The notion of form that I find useful from philosophy (mine—the paper coming in July) for most promising account of distinction between and relations of science, mathematics, and logic is not complement of actualities (as potentialities are complements to actualities). Let me put my hand on the table. The spaces between the fingers of my left hand are less than the number of fingers. That is a formality belonging to a concrete actuality, but it is not complement to actuality, rather to concreteness. That feature of multiple fingers or of musical staffs is a formality in the empirical world. They follow on concretes. Like potentials, they cause nothing (they're followers, not drivers.) Concrete actuals have the causal powers. We have other mathematical formalities not in the world independently of intelligence in the world, but as our toolkit improving our facility with the formalities belonging to the world, and these stand as analytic geometry to synthetic geometry. This is a big paradigm shift from Aristotle (or Kant). Alien to be sure outside my longtime shop. I’ll be studying much further the next couple of years the matter-form scheme of Aristotle, the descendant Arab and Scholastic schemes, and the matter-form scheme of Kant and how they treat science, mathematics, and logic within those schemes (within their complete theoretical philosophy schemes). I aim find out (follow-on paper) if better and how is mine for comprehensive frame for the modern age of the hard sciences, mathematics, and logic. ~~~~~~~~~~~~~~~~ I leave in this post for future handiness a taxonomy of interpretations of the Aristotle texts pertaining to matter and substantial change, gotten from the 2018 dissertation by Ryan Miller (a taxonomy originated in a paper by others). (α) The persisting substratum of substantial change is something which has the nature of pure potency. This is ‘the standard prime matter reading,’ commonly associated with Aquinas. (β) The persisting substratum of substantial change is something which is not pure potency. (i) If the something is featureless and omni-potent, this is the ‘prime matter’ position of most late Scholastics, including Ockham, Scotus, and Suarez (with variations), now defended by Christopher Byrne. It is closely related to the Averroistic solution to the Problem of the Mixt, because it presumes that there can be sub-substantial subjects. (ii) If the something has no actual features, but a somehow specified potency, this is the position of Richard Rorty (1974) and (tentatively) John MacFarlane. (iii) If the something is what is actually generically true of the elements, which are not themselves composed, then this is the anti-prime-matter position of Hugh King and Robert Sokolowski. (iv) If the something is a relatively simple homoeomerous substance with normal properties or an assemblage thereof, this is the anti-prime-matter position of Daniel Graham and Christopher Shields. (v) If the something is a property, then this is the ‘Weak Revisionary Interpretation’ of Mary Louise Gill and Montgomery Furth. It is closely related to the Avicennian solution to the Problem of the Mixt, because it presumes that properties can transfer between substances. (γ) The persisting substratum of substantial change is pure potency, not something. This is the position suggested by Aquinas in De Principiis Naturae and defended by Dermot O’Donoghue, Friedrich Solmsen, Joseph Owens, Patrick Suppes, Patrick Toner, and Anna Marmodoro. It is also the position taken by Richard Rorty in his dissertation, Christine Korsgaard in an unpublished paper, and with somewhat different auxiliary assumptions by Mary Krizan. (δ) The substratum of substantial change does not persist through that change. This is the ‘Strong Revisionary Interpretation’ of Barrington Jones, William Charlton, Sarah Broadie, and Michael Rea. (ε) Substantial change occurs without a substratum. This is the position that both Aristotle and the Eleatics regard as unintelligible. (ζ) Substantial change does not occur. This is the Eleatic position in its Empedoclean guise.