Duns Scotus and Thomas Aquinas: Notes on Divine Infinity

John Duns Scotus imputes the following line of reasoning to Thomas Aquinas:

1) If form is limited by matter, then form is finite (if p, then q--mp)
2) God, being simple, is not limited by matter (deny the antecedent, ~p)
3) So God is not finite (true conclusion, but invalid argument, ~q)

See https://plato.stanford.edu/entries/duns-scotus/

Scotus thereby indicates that Aquinas reasons fallaciously which naturally leads to an invalid argument. By "invalid," I mean that the conclusion does not follow deductively from the premises (3 cannot be deduced from 1, 2). In other words, 1) and 2) do not entail 3).

The argument would be deductively valid if someone reasoned:

1) If form is limited by matter, then form is finite.
2) God is not finite (deny the consequent, ~q).
3) So God is not limited by matter (~p).

I am using the ~ (tilde) for negation.

Now Scotus appears to posit that something is finite or infinite by reason of "its own intrinsic degree of finite or infinite perfection." He argues that simplicity (non-compoundedness) or the state of being non-mereological will not necessarily produce infinity; on the other hand, Scotus asserts that finitude "is not a result of composition." For Scotus, infinity is potentially a positive, intrinsic property--"an intrinsic degree of perfection." But Aquinas clearly believes that infinity is a negative property: it tells us what something is not, namely, not finite or limited.

This technical debates makes us wonder, Is infinite being a measure of intrinsic and unbounded excellence? Imagine an actual qualitative infinity filled with various degrees of perfection. We would normally call such an infinity, "God." So Scotus thinks God is filled with maximal degrees of perfection; hence, Scotus reckons it's possible to deduce other perfections from the attribute of divine infinity.