Back in the 1970s, Phillip Sherrard published an essay on Logic and the Holy Trinity in a journal called Studies in Comparative Religion.

Sherrard hit upon something that I think hasn’t been fully explored by philosophers and theologians in western Analytical philosophy in their critiques the Holy Trinity.

What Sherrard touches on is what has come to be known these days as Paraconsistent Logic. Essentially, Sherrard argues that the Trinity just is an antinomy and aporia. However, this needn’t implode all logic. I highly recommend reading his entire essay, but I will share some of the more salient points he makes:

Logic may be defined as the capacity to draw conclusions from a given starting-point or from a series of given starting-points. In principle, there are no grounds for affirming that this starting-point or these starting-points must be logical in form. The logical capacity can make deductions from a starting-point that is illogical in form just as well as it can from one that is logical in form: Platonists and Christian theologians alike agree on this. Platonists and theologians also agree that logical analysis is governed by certain laws, of which the most basic is that of non-contradiction, expressed in its simplest form in the proposition that a thing cannot simultaneously be and not be.

The question at issue between Platonists and theologians does not therefore concern the nature of logic itself or how it must be used when it is used. It concerns only the relationship between the logical order and the metaphysical order. The arguments of the Platonists, we have seen, depend upon accepting as true the idea that there is an adequation of the two orders. This does not mean that for the Platonists the order of logic coincides with the metaphysical order. But it does mean that the order of logic on its own level mirrors the structure of the metaphysical order, so that the laws of logic not only derive from but also analogically may be applied to the metaphysical order. In other words, when metaphysical Reality is reflected on the logical plane of the human mind, the concepts it forms of itself will be, or at least in principle should be, logically consistent and non-contradictory because, the Platonists affirm, ultimately nothing in the nature of this Reality is opposed to the principle of logical consistency and non-contradiction. It is for this reason that the Platonists feel quite justified in applying the laws of logic to their representations of the metaphysical realm, and why they claim that there can in the nature of things be no doctrine that is beyond logical explanation.

This Platonic line of reasoning is of course a circulatory one. It presupposes that the structure of metaphysical Reality is graded in a manner that is reflected in the order of logic, and it then proceeds to apply the gradations of the logical order to metaphysical Reality and to assert that the pattern which emerges represents the nature of this Reality more adequately than any pattern which ignores these gradations. But unless he is to admit that the presupposition underlying his line of reasoning either is a matter of faith or is arbitrary, then the Platonist must be able to point to the objective grounds on which he accepts it as true. He must, that is to say, be able to show why he presupposes that ultimately nothing in the nature of metaphysical Reality is opposed to the principle of non-contradiction and so why he is entitled to predicate a direct correlation between this Reality and the order of logic. Logic itself cannot demonstrate the validity of this presupposition. Indeed, there is no way in which it is possible to demonstrate it. All that one can do is to assume that it is valid and then go on to apply the laws of logic to formulations of divine Truth as if it actually were valid. But the validity or otherwise of the presupposition itself is beyond either proof or disproof.

This is a perspective that I think has been taken up outside of Philosophy of Religion by philosophers such as Graham Priest and other theorists of what is known as Paraconsistent Logic. The Stanford Encyclopedia of Philosophy writes:

“Contemporary logical orthodoxy has it that, from contradictory premises, anything follows. A logical consequence relation is explosive if according to it any arbitrary conclusion BB is entailed by any arbitrary contradiction AA, ¬A¬A (ex contradictione quodlibet (ECQ)). Classical logic, and most standard ‘non-classical’ logics too such as intuitionist logic, are explosive. Inconsistency, according to received wisdom, cannot be coherently reasoned about.

Paraconsistent logic challenges this orthodoxy. A logical consequence relation is said to be paraconsistent if it is not explosive. Thus, if a consequence relation is paraconsistent, then even in circumstances where the available information is inconsistent, the consequence relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a controlled way that treats inconsistent information as potentially informative.”

Now, to be clear, I am not 100% committed to this idea, but I simply wish to throw it out there as a way of shedding light on some of our (possibly unwarranted) presuppositions when discussing the Trinity. Why should we assume, as Sherrard notes, that the internal life of a Divine, Uncreated, Infinite, Non-Contingent Being conforms to the traditional Laws of Logic as the Platonists have assumed?

Speaking of presuppositions, Fr. Aiden Kimel over on his blog has struck at a few more:

The first presupposition is univocity of being (see also the Wiki entry). Far too many Analytic types go into their analyses of the Trinity thinking of God as something like a “big self.” This is basically a retrojection of late-modern psychologistic views of what a “person” and a “self” are back onto ancient creeds that may have meant something else by those words. (The word “hypostasis”, by the way, is a bit finnickier than what we mean by “Person” when we use it in modern English. I fear that some nuance may have been lost in translation. But that’s a topic for another post).

Another presupposition is this idea that finite, created, contingent minds could ever even comprehend an infinite, uncreated, non-contingent mind. As theologian James N. Anderson writes:

If God is necessarily beyond human comprehension, we shouldn’t be all that surprised to encounter elements of paradox in our thinking and speaking about God. Why should we take for granted that our limited conceptual apparatus is sufficiently refined to allow us to grasp and articulate the metaphysics of the Trinity without any residue of paradox? Christians have commonly viewed the doctrines of the Trinity and the Incarnation as “mysteries”. If the notion of doctrinal mystery is grounded in divine incomprehensibility, it can serve as a defeater-defeater with respect to theological paradox by giving the Christian adequate reason to think that any apparent contradictions in divinely revealed doctrines are merely apparent.

The third presupposition is that, most Analytical arguments seem to be foisting upon the doctrine of the Trinity a Theistic Personalist view of what we mean by the word “God.” Modern Western philosophers would do well to familiarize themselves with Classical Theism, since that is the millieu that gave birth to this idea and the backdrop against which it would be best understood.

The fourth and final presupposition is that of preference towards the Kataphatic method over the Apophatic method. As Fr. Kimel writes, “[I]f apophaticism is the proper way to grasp the divine transcendence, then the analytic theological project would appear to be undermined at the root. At the very least, it would have to assume a more modest posture. “

Now, in closing, I don’t want to say that I am completely committed to the Paraconsistent Antinomic view of God that these ideas seem to be leading to. I am still undecided on the matter, but it does look like a promising avenue of thought. I merely list these presuppositions because I, for one, had never really given much thought to these things and kind of took them for granted. When I see internet “debunkers” of the Trinity, it seems as though they, like me, also had not given much thought to these issues.

In the meantime, Christians who worship the Triune God can defend their rationality against interlocutors by appealing to Positive Mysterianism, which seems to be a fine epistemological view to take. I conclude with a quote from the Internet Encyclopedia of Philosophy:

The moral of this story should perhaps be that “identity,” as Frege famously remarked, “gives rise to challenging questions which are not altogether easy to answer” (Gottlob Frege, “On Sense and Reference”). For all that critics have ridiculed the doctrine of the Trinity as a prime example of the absurdity of Christian doctrine—as the late Bishop Pike did when he suggested that the Trinity was “a sort of committee god”—Trinity talk is no worse off than much non-theological talk about the identities of non-divine persons and ordinary material objects.