Mr. Alan Aversa has attempted twice to write a comment for the post "Reductionism in Contemporary Science" but it has not shown up, so I am posting it here:

St. Thomas's commentary on Aristotle's Metaphysics really helps clear this up: Are All the Classes of Causes Studied by One Science or by Many?. Mathematics, e.g., does not treat of final causes, and modern physics (mathematical physics) is a combination of physica and mathematics; it is a scientia media (See Replies to 6 and 7 of his Division and methods of the sciences; also In II Phys. lect. 3, n. 8; Summa Theol. 2-2.9.2, ad 3@m (3rd reply); In I Post Anal. lect. 25, n. 2.). Mathematical physics is "formally mathematical and materially physical." 

I suspect that it has been eaten up by Blogger as spam because of the embedded links.

Edit. He also added this comment, which is also not being published for whatever reason, to my second post on Stephen Barr:

Read St. Thomas Aquinas's De Mixtione Elementorum and the Thomist article on it: "Elemental Virtual Presence in St. Thomas" by Christopher Decaen. 

Thanks!