Saint Thomas' Three Levels of Speculative Knowledge

Saint Thomas says there are three and only three types of speculative science (speculative meaning that which has the knowledge of the truth as its proper end, as opposed to practical science which has action as its proper end -23): three areas of orthodoxy (as opposed to orthopraxy).

1. fisica = scientia naturalis (natural philosophy)
2. mathematica
3. metaphysica = first philosophy = scientia divina = theologia -268

These different types of speculative knowledge are defined regarding their relation to motion and mutability, viz. regarding the lesser or greater mutability of their proper objects, i.e. the lesser or greater proximity of those objects to matter and movement.

1. The proper objects of natural philosophy are those objects which are inseparable from matter and movement both according to their being and according to the consideration of them (their intelligibility or definition), sensible matter is part of their definition.
2. The proper objects of mathematics are those objects which depend on matter and movement for their being but not for the consideration of them, sensible matter is not part of their definition.
3. The proper objects of metaphysics are those objects which do not depend on matter or movement for their being nor for the consideration of them. -24, -268

All of the references are from Tommaso, Commenti a Boezio, ed. Pasquale Porro, Milano: Bompiani, 2007. (Q. V, art. 1, resp.)

Thomas makes the same division in his Commentary on Artistotle's Physics.

2. ...[T]here are...things which do not depend upon matter either according to their existence or according to their definitions. And this is either because they never exist in matter, such as God and the other separated substances [angels], or because they do not universally exist in matter, such as substance, potency and act , and being itself.

3. Now metaphysics deals with things of this latter sort. Whereas mathematics deals with those things which depend upon sensible matter for their existence but not for their definitions. And natural science, which is called physics, deals with those things which depend upon matter not only for their existence, but also for their definition.

And because everything which has matter is mobile, it follows that mobile being is the subject of natural philosophy. For natural philosophy is about natural things, and natural things are those whose principle is nature. but nature is a principle of motion and rest in that in which it is. Therefore natural science deals with those things which have in them a principle of motion.

Saint Thomas Aquinas, Commentary on Aristotle's Physics, Notre Dame: Dumb Ox, 1961, 2.