I have continued to read, despite the lack of evidence by way of reviews posted here. The following is but a brief summary, but I hope a helpful one.
I have been recently reading several Gordon Clark books (The Trinity, The Doctrine of Man, Faith and Saving Faith) and in two of those books he addresses an issue of terminology that he finds to be confusing and unclear.
With regard to the Trinity it is the issue of the use of the terms "ousia" and "hypostasis," which came to represent different meanings in the Western and Eastern Church.
Clark in several places recommends a better term to denote the "essence" (the singular aspect) and "personhood" (the triune aspect) of the Trinity. In his analysis of Augustine he recommends he term "definition" to replace Augustine's "substance" or "essence." Thus, the definition of God is singular, whereas his personhood is triune. He makes the same recommendation in responding to Berkhof, noting that the attributes predicated of God constitute the definition of God--i.e. the attributes are identical in the Being named by the term God. To quote: "If now the attributes are identical in God, and if that unity may be designated by the name sovereignty or omnipotence, and if therefore the terms love, justice, grace, and whatever, are used to designate the various effects God produces in the world, the whole confused discussion of the classification of attributes may be dropped."
What of Personhood then? Taken as attributes of God (or distinctions within the definition) the persons of God (Father, Son, Spirit) are not co-extensive: the attribute of Fatherhood does not extend to the Son or Spirit, nor the attribute of Sonship extend to the Spirit or Father, and so forth. The particular predicates attached to one cannot be attached to the other, yet certain predicates belong to all three (e.g. omnipotence). For defining Personhood, Clark mentions three possible choices regarding individuation and discards two because they are inimical to the other conclusions concerning the Trinity. The one open to him is the Platonic/Leibnitzian theory of individuation, which states in brief that man is a collection of his thoughts concerning himself. So too the Trinity is the collection of God's thoughts concerning Himself, with each person thinking particular thoughts of himself that are not coextensive with the other persons (Clark's example is when Christ thinks "I or my thoughts will assume or have assumed a human nature,"). Because God's thoughts are eternal, the collection of propositions that define His persons are immutable and remain unconfused (however much our thoughts concerning Him languish in confusion).
Thus, Clark's emendations to the doctrine of the Trinity are to remove the term substance and replace it with the term "definition," which is more easily recognized in its immaterial unity; and to define the individual persons according to the qualitative theory of individuation, which considers an individual as the collection of thoughts one predicates of oneself. Thus, God is defined by his attributes, with each of the Persons retaining certain predicates coextensively as well as retaining certain predicates individually that cannot be appended to the other persons.
To those who would reject a theory that "reduced" God or any other person to a system of propositions, the task is open to provide a more coherent and understandable theory to which we may assent.