To Ablabius: On not three Gods, has long been held up as a distinctive and paradigmatic text for both Gregory, and for the approach of the Cappadocians. A careful reading of the text shows that to a large extent it simply doesn't do what many think it does. In this summary, I follow aspects of both Behr (427-434) and Ayres (345-364).
The confronting problem for the text is how the Cappadocians can avoid being tritheists. The argument is put in terms of speaking of a singular human nature, yet three individual persons. This is, we may recall, the grammatical distinction that Gregory employs in his Epistle to Peter. It is, also, commonly taken as a starting point for discussion of Social Trinitarianism and the Eastern tendency to start with the Persons.
Yet, in Ad Abl., Gregory's argument is that such an analogy fails at exactly this point. In defending against the charge of tritheism, Gregory advances two arguments, or in Ayres' schematic, two lines of argument with two sections (A1-B1-A2-B2).
The first of these is to exclude polytheism by definition, and to understand that to speak of a 'nature' is at once to be speaking of something singular and simple. Gregory elaborates to say that in common usage we speak of 'men', but properly speaking we should speak of 'man'. This is negligible when talking about human beings, but more particular care must be taken in speaking about God, for more is at stake.
Gregory's second line of argument is about what names describe. He is insistent, as Basil before him, that names do not define essences, and so begins with an argument for 'Godhead', θεότης, denoting the activity of God. He writes, “ nature is unnameable and unspeakable, and we say that every term either invented by the custom of men, or handed down to us by the Scriptures, is indeed explanatory of our conceptions of the Divine Nature, but does not include the signification of that nature itself”. Names signify operations.
Yet, the objection that might be raised is that common operations signify common operators co-working, as 3 farmers farming, of 3 orators orating. Gregory raises this objection to more clearly argue his case. For Gregory, the operations of the Divine Persons are not individuated, but they share the same and singular operation. He writes, “every operation which extends from God to Creation, and is named according to our variable conceptions of it, has its origin from the Father, and proceeds through the Son, and is perfected in the Holy Spirit” (notice how this echoes Basil in De Spiritu Sancto. It is right at this point we should note how divergent this is from the Social Analogy. The distinction of the divine persons is not the same as that observed in human persons.
The core elements to take away from Ad Ablabium is this: simplicity of nature, common operation and common power of the common divine essence; the incomprehensibility of 'what' God is, and 'what' a divine person is; that the persons are not psychological entities unto themselves; that persons can be distinguished causally and in relation but not in essence nor in operation.