Dallas begins this lecture moving through the four arguments for universals. These are 1) the argument from predication, 2) the argument from similarity, 3) the argument from mental acts (which is unique to Husserl) and finally 4) the argument from the unity of classes or extensions of concepts (36:47).
The nature of universals is a topic of great familiarity to Dallas, having written his doctoral dissertation on it. You may notice that we are missing a few lectures in which Dallas finishes on substance and introduces universals.
The last part of the lectures is an introduction to the last big topic of the course: relations (49:00). They fall for him with qualities under the category of predicates.
The difference between qualities and relations is that qualities are predicates which are true of things taken one at a time. Relations are predicates which are true of things taken two or more at a time.
This is a rather important metaphysical topic for our day because many more recent philosophies and religions have tried to argue that relations are “a fundamental part of the furniture of the world” (1:01:00). This can be seen in so-called “Eastern” religion, in metaphysical idealism and even in Christian accounts of God which see the relations of “trinitarianism” as the indicative of all of reality. All of these groups denounce “dualism” which is another way to say that relations are metaphysically fundamental. What this amounts to, as Dallas says, is that no substances are independent. Which would mean that God is not independent of the world he created.
Needless to say, Dallas disagrees. And this is a place where Dallas’s phrases like “the substantiality of the spiritual” and “the sufficiency of God” derive their meaning.