I’ll have to go back and reread the chapter you mention—Philip Sherrard’s “Metaphysics of Logic” in his Christianity: Lineaments of a Sacred Tradition (Holy Cross, 1998)—before I can offer anything close to a solid response.
What I can certainly say, however, is that I’m always more than a little dubious when someone tells me there are some things to which logic can’t be applied, even at the level of the Trinity, since of course this very claim, insofar as it negates the proposition “there is nothing to which logic can’t be applied”, depends for its truth on the logical law of the excluded middle! Is that really what Sherrard wants to claim?
While I’m reviewing this chapter—and don’t hold your breath!—perhaps you and other readers might wish to make a corresponding study of a little book called Christianity and the Doctrine of Non-Dualism (Sophia Perennis, 2004) by “A Monk of the West”. (We learn from the translator’s preface that the author was a lay brother of the Cistercian Order, one Alphonse Levée in the world; the book was first published in French in 1982.) The contrast between these authors’ positions is stark. Sherrard writes:
“The Christian doctrine of an Absolute that is triune and personal, and its idea that what is created and relative may have an eternal destiny within the Absolute itself, without on that account ceasing to be created and relative, conflicts with [the] extreme non-dual form of metaphysical doctrine” (105).
It appears clear from the context, as I glance back at this passage, that the “extreme form” he’s talking about is simply Shankarian Advaita Vedānta, in which, quoting Sherrard again, “the creature qua creature represents a state of bondage, mental or physical, in unreality, total deliverance from which is possible only on condition that it ceases to exist as a creature”.
Contrast this with the following in Christianity and the Doctrine of Non-Dualism:
“The ‘person’, however we conceive it, cannot be the last word concerning the Real…. There is no ‘person’ where there is no relation and otherness. The idea of a unique person who could be identified with the totality of the Real, and that of a personal Infinite, are thus equally illusory…. ‘As Creator, God is both Trinity and Unity. As Infinite, He is neither Trinity nor Unity, nor anything that can be enunciated’ [quoting Nicholas of Cusa]” (107).
“We will say unequivocally that after more than forty years of intellectual reflection on [advaitic] doctrine … we have found nothing that has seemed incompatible with our full and complete faith in the Christian Revelation” (136).
Try as one might, it’s hard in this case not to think that, for once, the Catholic is right, and the Orthodox wrong! But I shall look again at Sherrard, time permitting.