This book is not like other academic works in theology. This book is not even much like other works in analytic theology. This book is its own thing – a short, tightly argued provocation, unlike anything else I have read.

In The Contradictory Christ, Beall argues that the classical Christian understanding of the incarnation leads inexorably to the conclusion that Jesus Christ, both God and human, is the bearer of contradictory properties. Jesus Christ, qua God, is impeccable, he cannot sin. Jesus Christ, qua human, is peccable, he can sin (or at least, could have sinned). But these ‘qua’ clauses do not help us avoid the contradiction. Rather, since Jesus is human, Jesus can sin. Since Jesus is divine, Jesus cannot sin. For Beall, we need not balk at such a blunt contradiction, or attempt to wiggle our way out of the jaws of inconsistency, since the way is open for us to face the contradiction head on and accept both horns of this seeming dilemma. The correct view of logic, for Beall, tells us that these contradictory properties are indeed contradictory, but this does not mean that they can never hold true together. Some contradictions are nonetheless true. Clarifying our understanding of the logic of everyday concepts like conjunction, negation, and entailment will show (so the argument in The Contradictory Christ goes) that we need not reject or reconceive these contradictions. Rather, we can embrace them as the conceptual price we must pay to take seriously the doctrinal commitments of orthodox credal Christianity.

As I said at the outset, this book is unlike other recent books in analytic theology, and this overview of its scope should give you a sense of why this has to be the case. To make his argument, Beall has to introduce the reader to some tools of contemporary formal logic. It is not the usual sort of monograph in theology that contains an elaboration of the truth-conditional semantics for first-degree entailment, so some of the text will look foreign to those not familiar with this kind of technicality. However, these technical interludes are there for a reason, not only to help the reader who might have already learned some formal logic to see where this new ‘subclassical’ kind of logic differs from the logic they might have learned, but to show anyone what the rules of this game are. Yes, finding pages of formal logic in your theology monograph is jarring, but it should be no more so than when a monograph veers into extended discussions of Latin (or Greek or Hebrew) grammar, or dives into the minutiae of Aristotelian metaphysics, or meanders into extended reflection on Dasein. Theology can be an interdisciplinary affair. According to Beall, we need to reconsider the notion of contradiction, and to do that, the contemporary techniques of formal logic provide some of the necessary correctives.

Such an interplay between contemporary technical work in logic and considerations in theology is rare, but Beall is not without precedent. Discussions of divine foreknowledge and human freedom intersect with recent work on the meaning of counterfactual conditional statements (for one example, see Ken Perszyk (ed.), Molinism: The Contemporary Debate), and Alvin Plantinga's treatment of the ontological argument and the problem of evil (see his God, Freedom, and Evil) is well known for making use of the twentieth-century understanding of the relationship between possibility and necessity and possible worlds semantics. The nearest recent parallel for the breadth and depth of Beall's appeal to distinctive methods in logic in tackling a theological question is the application of Peter Geach's work on relative identity to the formulation of Trinitarian theology by A. P. Martinich and Peter van Inwagen. This work, just like Beall's use of first-degree entailment, puts contemporary logic to use to clarify theological questions, and to provide new options for the theologian.

In the rest of this review, I will give a brief summary of exactly how Beall argues for his case, and I will then close by offering some brief appreciative and critical comments.

There are six compact chapters. In the first, Beall gives an outline of his approach, aimed towards giving a coherent, systematic, and comprehensive account of what can be truly said of Christ. In this chapter, he sketches out some key terminology, distinguishing contradictory claims (pairs of sentences that contradict each other, which are rather everyday items – if I say ‘it's raining’ and you say ‘it's not raining’, and you and I are talking about the same time and place and using our words in the same senses, then our two claims are contradictory) and contradictory beings (a being is contradictory when contradictory claims are true of it). The aim is to show that the person of Christ is contradictory in just this second sense.

The second chapter (‘Logic and its possibilities’) is the toughest, technically, for a reader new to logic. Here Beall introduces a number of key concepts from contemporary formal logic, all by way of introducing First-Degree Entailment and its attendant theoretical apparatus. The key ideas here are that sentences are evaluated as true and as false (as you might expect), but that truth and falsity are independent of one another. Logic (for Beall) leaves open the possibility of a sentence being neither true nor false (a so-called ‘gap’) and likewise it leaves open the possibility of it being both true and false (a so-called ‘glut’). This liberal account of truth and falsity is put to use to define the notion of a logical possibility – a distribution of truth and falsity to sentences in the language that at least respects the meanings of logical vocabulary like ‘and’, ‘not’, ‘if’, ‘all’, and ‘some’ – and the allied notion of theory-relative possibility, which imposes further constraints, salient to the theory in question. For Beall, theological possibility is central (we are doing theology, after all) and for a logical possibility to count as theological the further constraints to be satisfied are those appropriate to properly theological vocabulary. Although it is consistent, in the widest possible sense, to deny that God is good, in doing so, you take up a position that goes against the meaning connections between ‘God’ and ‘good’ in theological discourse, in just the same way that someone who denies that 1 + 1 = 2 shows that they are not using these terms as they are used in arithmetic.

With this under our belts, Beall leads us, in chapter 3, to present the theory according to which contradictions are true of Christ, and presents seven virtues of that theory: chiefly its simplicity, the way it fits the ‘data’ of accepted theological discourse, and the way in which it does not shift meanings or find ambiguities or distinctions where none seem to be present. In the remaining chapters, Beall defends his view against a broad sweep of objections (chapter 4) and then shows how it fares in comparison to alternative views of the incarnation (chapter 5). Then, in a suggestive final chapter, Beall gestures at the wider question of the Trinity, and makes some remarks concerning how this work can be extended to give an account of the coherent (but inconsistent!) account of the identity and non-identity claims in Trinitarian theology.

In the remaining space, I will pay Beall the compliment of a friendly request for elaboration on what I think is an as yet unexplored tension in the view. Beall argues that one virtue of his approach is that it does not revise the meanings of terms. We need not say that Jesus can sin-qua-human and that Jesus cannot sin-qua-divine, we can simply use the everyday predicates ‘sins’ and ‘can sin’ without introducing qua-qualifications or other technicalities, because we can bear the cost of endorsing a contradiction. Yes, Beall's account avoids changing those meanings, but the price is varying meanings elsewhere. Our everyday understanding of the meaning of ‘not’ is that each claim excludes its negation – there is no possibility in which a sentence and its negation are both true. Paraconsistent logics are revisionary accounts of how we should understand negation: they are proposals to shift our understanding of the logical vocabulary to allow for a wider space of possibility. There are good reasons to make this shift, but we shouldn't deny that it is a revisionary account of the meaning of logical vocabulary.

If it were just a matter of accounting which meanings have shifted, we could agree that it is worth shifting our understanding of negation (and consistency and consequence), since theology and logic both benefit. However, there is also a sense in which, for Beall's view, everyday meanings of other terms (such as human and divine) also shift in the face of reflection on the incarnation. The Christian theologian learns that – contrary to pre-incarnational thinking – divinity does not exclude humanity, since they are compatible. We can say that one predicate excludes another when there is no possibility where both apply to the same subject. For a paraconsistent logician, exclusion comes apart from contradictoriness.

Now we can restate the tension in incarnational theorizing in different terms. For Beall, Jesus is peccable (all humans are) and impeccable (God is impeccable): these are contradictory, but compatible, predicates. Now let's jettison talk of negative predicates and consider exclusion instead. (Recall that, for the paraconsistent theologian, exclusion and negation come apart, so these are different issues.) On the traditional view, humanity entails peccability, but divinity excludes peccability, in that there is no theological possibility in which any One who is divine is nonetheless peccable. If Jesus is both human and divine, then either the entailment or the exclusion must be jettisoned, since He is either a human who fails to be peccable (and is a counterexample to the entailment) or he is God and is peccable, and is thereby a counterexample to the exclusion. Neither horn of this dilemma is appealing for the orthodox theologian, so one option is to recapitulate the disambiguation strategies according to which Jesus is peccable in one sense, or in one aspect, and fails to be peccable in another.

The wiggle-room opened up in the move to a paraconsistent logic does not help us much when it comes to compatibility and exclusion, which can be stated in negation-free terms. It is an open question whether ‘inconsistent theology’ can avoid recapitulating another attempt to articulate a consistent theology of the incarnation in its account of compatibility and exclusion between predicates.

As I hope you can see, there are many different questions to be answered in the conceptual territory Beall has mapped in this insightful, provocative, and revolutionary monograph. While it hasn't answered all my questions concerning how to spell out the consequences of Christian commitments concerning the incarnation, it has broken significant new ground, and covered a great deal of territory.

So much is covered that you might think this was a hefty tome, but it is short. The book is all the better for it, even at the cost of being dense, with many ideas per page. It is an exciting and interesting intervention, and one that is a necessary read for anyone interested in the different ways in which we have attempted to make sense of theological language. As a logician interested in theology, I am delighted to see work in logic and work in theology intersect in this way. Long may this discussion and the interaction between different disciplines continue!