In his latest, inspiring, and challenging book, Beall (Reference Beall2023) makes substantive claims both about the nature of reality and about the nature of God. I'd like to raise some questions on both scores.

A key metaphysical assumption Beall makes is that most of reality has no gaps or gluts: we can make claims about it that are either true or false. There are nevertheless what he calls ‘recalcitrant data’: parts of reality that are ‘gappy’, namely such that what we can say about them is neither true nor false; and even more surprisingly perhaps, parts of reality that are ‘glutty’, of which what we can say is both true and false. In other words, reality harbours some contradictions. In this book Beall considers ‘trinitarian reality . . . a rare fragment of reality’ (p. 74) which has glutty status.

The emerging view is very intriguing for the reader, who would want to hear more about the overall metaphysical theory Beall endorses. He holds that reality as a whole has fragments of special status (gappy or glutty). If the Trinity is a rare but not unique fragment of this kind, what other suchlike fragments are there? And if there are others, do they all pertain to the realm of the divine, or are some of them natural phenomena? Either way, what does this entail about the Trinity? In other words, is the Trinity an ordinary or extra-ordinary fragment of reality? If it is an ordinary albeit ‘recalcitrant’ fragment of reality, does this diminish in any sense what's extra-ordinary about the divine? If on the other hand it is an extra-ordinary fragment, why take it to reveal what reality in general is like? My point is that it would be good to know more about how the author's understanding of the divine sits within his understanding of reality as a whole. Further, what is the significance of thinking of some gappy or glutty aspects of reality specifically as fragments of it? What is the relation between these parts and the whole of which they are parts? Is the implicit idea that if we exclude such fragments from what we take reality to be, we are left with an incomplete jigsaw? What would make such an idea compelling? Is there anything other than faith – are there philosophical reasons? – that justify this assumption, for Beall?

To assess how potentially ad hoc Beall's advocacy of glut theory is, for the sake of making room for the Trinity within the domain of what's real, it would be interesting to know more about how Beall would position himself in relation to a fellow supporter of the denial of the principle of non-contradiction: Graham Priest, who makes his case in favour of dialetheism on the basis, not of ‘recalcitrant data’, but of a core problem concerning ordinary objects. Priest (Reference Priest2014, see also Marmodoro Reference Marmodoro2020) considers us in the predicament of either embracing dialetheism, or being bereft of a metaphysics that can account for the unity of objects. He holds that objects are unified by unifiers; ‘gluons’, as he calls them, which have glutty status. Hence, Priest's stance: a metaphysics without gluons cannot account for the unity of objects; on the other hand, a metaphysics that admits of gluons thereby embraces dialetheism. As I understand the difference in approach between Priest and Beall, the former makes the case that ordinary objects could not be fully accounted for, metaphysically, unless we endorse dialetheism, while for Beall some (extra-ordinary?) fragments of reality have special glutty status and require a gluttist approach to be understood. Vis-à-vis Priest's, Beall's advocacy of glut theory seems to the philosophers without confessional commitments to be less motivated. To put the point starkly: if there were not a trinitarian and incarnate God, would there still be compelling reasons to endorse glut theory, according to Beall? He may pledge that his goal in the book under discussion is merely to provide an account of the Trinity based on a ‘simple, flat-footed – and charitable – reading of the [Athanasian] creed’ (p. 9); but he is not in fact doing just this, when making claims about reality as a whole. I believe it is fair for his fellow metaphysicians to ask for further explication of the overall philosophical framework within which Beall's account of the Trinity is embedded, because he mentions the framework.

Beall treats as a datum that the Trinity is a glutty fragment of reality, as revealed by the incarnation of God in Jesus, and aims to respond ‘to the so-called logical problem of trinitarian reality’ (p. 1) by cutting the Gordian knot: there is no problem; it is misguided to attempt to describe the Trinity both consistently and fully – consistency comes at the cost of incompleteness, namely a partial consideration of what the Trinity is. Beall writes that ‘The contradictory axiomatic claims of the Trinity do not ‘compete’ for the truth about God; they are the truth about God – the full and radical truth about God’ (p. 42), which is that,

To put the point explicitly: ‘God is contradictory precisely because God is identical to three divine beings who are not likewise identical to each other’ (p. 56). (As it is immediately clear to the reader, the transitivity of identity is thus negated.)

Within the limit of this brief discussion, it is impossible to pay justice to all the interesting ideas and arguments Beall makes concerning God thus understood. I want to engage here specifically with what the author presents as one of the significant virtues of his theory, simplicity: ‘By my lights, the contradictory account – of God incarnate and God in Trinity – has no competitors with respect to simplicity’ (p. 70). What is meant here by ‘simplicity’? The pages that follow reveal an ambiguity. On the one hand, the author means that his approach to the Trinity is methodologically the simplest, where ‘simple’ is explained by contrast with ‘elaborate’: the contrast between elaborate ways of ‘consistentizing’ divine reality within the confines of the classical-logic approach, versus ‘a simpler direction . . . namely, accept[ing] the contradictions’ (p. 70). Here Beall's stance seems to be that accepting contradictions is explanatorily parsimonious; but even if so, it isn't ontologically parsimonious, because it achieves its target explanation by positing that bits of reality have a special status. So the methodological simplicity comes at a cost.

On the other hand, it is the resulting glutty account of God that is presented as best capturing His ‘simplicity’ (pp. 70ff., and 84ff.). This comes as a surprise to the reader. For a glutty God does not seem simple at all; the Persons are identical to God, but they are not pair-wise identical to each other. This account of God makes Him be a set of relations, of identity and non-identity; but relations undermine simplicity.

Beall does explain the sense in which his Trinitarian God is simple thus:

The reader would benefit from further explication by the author here. On a classical conception of identity, God, being identical to Himself, is simple; however, God for Beall is dialetheically identical to Himself: each Person is identical to God, but not (pairwise) identical to the other Persons. The challenge is to understand how trinitarian identity, so explained, impacts on the simplicity of God. Beall elsewhere talks about the trinitarian identity relation, as follows: ‘What, if any, salient entailment patterns figure in trinitarian reality and its central identity relation?’ (p. 52). Note that he refers to such logical entailments as patterns (pp. 52–53); and of them he also says that they ‘reflect some of the central structure and fundamental patterns of the trinitarian identity relation in divine reality’ (p. 53). So for Beall as I read him the identity and non-identity relations making up trinitarian identity give God structure and patterns. But if so, God is not simple. Beall claims that from a mereological perspective, there are no parts to God (p. 74); however, he still commits to a trinitarian divinity that is structured into patterns. So, even if not mereologically complex, divine reality is complex, qua structured into patterns of identity. Logical structure undermines metaphysical simplicity, and gives rise to complexity.

In response, Beall might want to distinguish metaphysical from theological complexity, as Leftow reports about some salient medieval thinkers did:

Is the Trinity only theologically complex, but metaphysically simple? Would such a distinction help Beall's (unqualified) claim that his glutty trinitarian God is simple? I believe not, because independently of the discipline within which they are made, claims about God are either about ‘how God is’, or about how ‘He appears to be’. Claims about ‘how God is’ concern the nature of God, whether they are stated in the discipline of philosophy or of theology. So, I do not subscribe to the medieval distinction that Leftow reports above, and, in consequence, I do not believe that this distinction would aid Beall's explanation of the simplicity of God.

So by my lights, the court is still out regarding the nature of reality and the glutty nature of some regions of it. Beall focused on the most challenging metaphysical problems about the nature of God and put forward an original account to help us understand it.