Augustine on the Trinity: Potential Objections

For a paper, I'm trying to anticipate and respond to objections to Augustine's psychological analogy for understanding the Trinity. For the sake of argument, since not everyone accepts it, I'm temporarily waiving the requirement that God is perfectly simply in the sense that God has no proper parts. With this in mind, the objection is this. Augustine thinks that their are three features of the human mind that are such that they express a created model of the Trinity insofar as they are three numerically distinct "somethings" that exist in a single substance. The expression "the same substance" is equivocal, so the objection might go, between the three persons of the Trinity, on the one hand, and the three features of the soul, on the other hand, in the sense that the latter substance uses "same substance" in the sense of something with three *parts* and the former does not use the expression in this sense. Or, a little more rigorously: first, assume that there exists something k such that k is composed of proper parts a and b; assume, also, that there are three things x, y, and z such that x, y, and z are one k iff they are the same k. Now,

(1) If k is composed of proper parts a, b, and c then a, b, and c are the same k in the sense of meaning A(k).

(2) If there are three individuals x, y, and z that are one k iff they are the same k, then x, y, and z are the same k in the sense of meaning B(k).

(3) Necessarily, it is not the case that anything is possibly A(k) and B(k) in its sense of meaning.

(4) If two sentences, expressions, or words do not have the same sense of meaning or a logically equivalent sense of meaning, then they are equivocal in their sense of meaning.

(5) Therefore, the sentence "a, b, and c are the same k" and "x, y, and z are the same k" are equivocal in meaning. 

Obviously, (1) will have to be modified if it is to capture Augustine's analogy in a sufficient manner, but I'll worry about that later.