In the fourth lecture of his Metaphysics class Dallas revisits his “non-circular” definition of identity but gets into the question of whether there could be two things which completely resemble. Dallas speaks on “the identity of indiscernables” and “the indiscernability of identicals,” also known as Leibniz’s law (for Gottfried Leibniz) and questions whether it is better described as a criterion than a law. What he will drill down to is the idea that there might be more to any object than its properties (possibly its substance?).
He speaks of a handout “Summary Notes on Identity Lecture” which temporarily can be found here and the “Johnson selection” Dallas speaks of is “The Relation of Identity” by W.E. Johnson which can be found here in chapter twelve of Logic, Vol. 1.