This lecture is part of Dallas’s general introduction to relations. He works to describe a view (seen in A.E. Taylor and F.H. Bradley) in which the relation “makes a different in the term” (8:00). So the relation of the book being next to the apple makes a difference in the terms, book and apple – indeed a difference in the object itself other than the relation. This is what, as Willard says, “the doctrine of internality of relations” (11:00).
Another point that Willard will make is that any relation presupposes certain qualities in its terms (17:00). So a piece of chalk and a book can’t get married.
What Dallas concludes with is that one must distinguish between the essential and accidental properties of a thing in order to account for the externality of relations. Dallas prefers to say about the externality of relations that the difference produced by the relation consists in the relation alone.
Later in the lecture (27:45) Dallas turns to discuss Russell’s essay “A Proof that Relations Exists” which attempts to refute the position of Taylor and Bradley.