Substantiality. The material universe contains substances, fragments (proper parts) of substances, and heaps of substances and fragments. Substances are more fundamental than fragments and heaps in three respects: (i) identity, (ii) existence, and (iii) nature.
This rules out what I have called “faint-hearted hylomorphism,” along with any kind of microphysicalism. Hylomorphic composition goes all the way down. It is a universal of the material world, not something found only in special cases.
Distinct Indiscernibles. It is naturally possible for two or more substances to be intrinsically and extrinsically indiscernible (with respect to all natural properties).
This rules out Scotus’s haecceities and Leibniz’s principle of the identity of indiscernibles.
Ante Rem Realism. When distinct substances belong to the same genus or species, this common membership is explained by the operation of one or more forms.
This rules out the notion that forms are merely intentional objects or post rem universals, as in the views of van Inwagend, Jaworski, or Marmodoro.
Intrinsic change. There are instances of fundamentally intrinsic change in the features of substances.
This rules out four-dimensionalism, perdurantism, super-substantivalism about space, the at-at theory and the relation-to-time theory of change.
Generation and Corruption. There are instances of both generation and corruption of substances. In each case, a substance is generated out of other substances and corrupts into other substances.
This rules out both Democritean atomism and Empedoclean elementalism.
Continuity. Each bit of matter, space, and time has (at least potential) proper parts, and each is continuous (i.e., any bounded infinite chain of proper-part relations composes something).
This is perhaps not a core commitment, but it is one that fits well with the others.
Finitude. At every moment, every bounded region of space contains only finitely many substances and finitely many actual fragments (integral parts) of substances.
We will call an actual proper part of a substance an integral part. A fragment can be an actual part of a substance even if the substance itself is not actual. These can be called remnants. (See R. Koons, “Remnants of Substances: A Neo-Aristotelian Resolution of the Puzzles,” (2020) Quaestiones Disputatae 10(2):53-68.)
The Analytic Thomist 