Two in one: contradictory Christology without gluts?

Abstract

The central thesis of JC Beall’s paraconsistent Christology is that Christ, being human and divine, is a contradictory being, and a rational Christology can accept it, since logic nowadays does not exclude the possibility of true contradictions. In this paper, I move from Beall’s theory and I present an alternative view. I quote seven statements of the so-called ‘Athanasian Creed’ which synthesizes the results of conciliar Christology. The aim of the Creed is to combat monophysitism by stressing the duplicity and unity of Christ: two (incompatible) natures inseparably joined in only one person. I note that the two-in-one principle, so intended, may be seen as an ancestor of what has been called ‘conjunctive paraconsistency’, whereby there could be true contradictions but contradictories cannot be separately true. I specifically oppose this view to Beall’s idea of Christ’s human divinity (or divine humanity) as a glut, showing that in the conjunctive account, true contradictions do not require any overlapping or joint ascription of truth and falsity.

1 Introduction

This paper examines JC Beall’s contradictory Christology (Beall 2019 and 2021a¹) and suggests an alternative view. The capital thesis of Christology is that Christ, the Son of God, is both human and divine, and, as noted in the first centuries of Christianity, his double nature implies a long series of contradictions: as human, Christ is mutable, mortal, peccable; as God, he is immutable, eternal, impeccable, etc.² Should we accept this ‘explosion’ of sub-properties? Is really Christ a contradictory being, with all the contradictory consequences?

JC Beall has tackled the problem, noting that if we look at Christology with the secularized lens of sub-classical logics, there is no problem in accepting that the Christological contradiction and all its contradictory consequences are true. Christ is (has been) a contradictory being, and it is rational (at least logically grounded) to believe he is (has been).

I do not enter the debate on whether the Christological contradiction is acceptable as such (and whether it is rational to believe it or is not). My aim is to look at Christology as a case study for supporting a non-standard conception of ‘true contradiction’ which has been labelled conjunctive paraconsistency (Ripley 2015; Barrio & Da Ré, 2018; d’Agostini 2021). The basic idea is that non-explosive conjunctions of contradictories are not simplifiable: from ‘p and not p’ we are not entitled to infer ‘p’ or ‘not p’ separately.³ There is a clear similarity with what orthodox Christology has opposed to any form of monophysitism: that Christ is two in one; he is both divine and human, but not one thing without the other, the two conjuncts are inseparable.

Conjunctivism in paraconsistency is not so much frequented nowadays, but it has been variously defended in the philosophical tradition.⁴ Now I suggest that Christology could be one of its ancestors. So I present seven statements of the so-called Athanasian Creed, in which the ‘two in one’ principle is fixed in the clearest terms. This text is one of the most ancient documents presenting the results of Conciliar Christology. What it states corresponds to the orthodox acquisition, whereby Christ is the case of two (ideally opposed) natures inseparably joined in only one person. In it, the author does not seem to reject the idea of ‘contradictory Christ’ in some respect, since he assumes that Christ has the two natures, no heretical ‘mixture’ is plausible; he is perfectly human and perfectly divine, homo et Deus. But the author also states that the two properties are inseparable: Christ is not ‘only man’, nor is he ‘only God’.

In this line, I propose an alternative view to Beall’s glutty Christology, and I note that the conjunctive approach (as clarified in the Creed) can easily avoid three objections to the idea of contradictory Christ.⁵ First, for Beall (as well as for standard dialetheists and glut-theorists), a true contradiction is an excess (glut) of truth values, a sentence which is true and false, and so is the Christological contradiction. This depends on Beall’s conception of a true ‘p and not p’ as a simplifiable conjunction, so that ‘p’ is true and ‘not p’ is true too (which means: ‘p’ is false). So accepting a true contradiction means to accept falsehoods, and Beall’s Christology has been criticized in this regard (see Sect. 3.1). Instead, in the version of conjunctivism here presented, there is no overlapping or coincidence of truth and falsity, so no glut. That contradictions of the form ‘p and not p’ are not simplifiable means that each contradictory, separately taken, is untrue, so there is no falsity, since ‘not p’ as such, not unlike ‘p’, is untrue.

A second problem is that, in admitting the distinct truth of both ‘p’ and ‘not p’, a contradictory Christology is not able to disprove the reasons of the two main forms of heresy, whereby Christ is ‘(only) human’ (Arianism) or ‘(only) divine’ (Eutychianism). This objection has been advanced as well (Sect. 3.2), and we see that the conjunctive view avoids the allegation, since it stresses (with the orthodoxy) the inseparable unity of the two properties.

Third, Beall mentions ‘metaphysical neutrality’ as one of the virtues of his Christology (CC: 62–63). Here, he defends a version of what Wyatt (2021) has labelled ‘pure’, i.e. anti-metaphysical, deflationism.⁶ It has been objected that such a view does not seem adaptable to the Christological concern, since the doctrinal truth of Christ’s divine humanity implies the effective, real existence of a certain fact which makes the conjunction true. On the other hand, Beall’s view does not seem so perfectly ‘neutral’ as it pretends to be. Many ‘metaphysical’ postulates seem sparsely active in the theory (Sect. 3.3). And finally, that a theory of ‘true contradictions’ could really exempt itself from any metaphysical commitment (in grounding-explanatory sense) is arguable. I will show that the notion of truth presupposed by conjunctivism, as presented in the Athanasian Creed, could take charge of these concerns, since it postulates the occurring of only one truthmaker (Christ) which grounds the unity of the two properties, humanity and divinity (Sects. 2.3 and 4.3).

In Sect. 2, I present the seven Christological statements of the Creed, and then (Sect. 3) I move to Beall’s Christology, advancing the three objections. Section 4 presents a version of conjunctivism as an idea of true contradictions without gluts (without overlapping of truth and falsity) and shows how it can avoid the three objections. In the last section, I summarize the main points (and justify the question mark of the title).

Before proceeding, some specifications about notational conventions might be useful. In general, I use the familiar symbols for ‘and’ and ‘not’, ‘∧’ and ‘¬’, respectively (even if there could be doubts about expressing a non-simplifiable conjunction by classical extensional ‘∧’). When I speak of facts (truthmakers), I use the propositional names p, q, etc. without quotation marks; when I mention sentences (or propositions), I use inverted commas: ‘p’, ‘q’, etc.; when I speak of truthbearers, I use angle brackets: ‘〈p⟩ is true’. Similarly, for properties, I use capital letters without quotation marks: P; mentioned predicates are with inverted commas: ‘P’; objects are expressed, as usual, by small letters such as a, b, etc. (but for Christ: see fn. 12 below), when I mention truthmakers (object + property) no quotation marks: Pa; and predicative sentences are mentioned with inverted commas: ‘Pa’. For propositional (or sentential) variables, I use Greek letters: φ, ψ, etc.

2 The Athanasian Creed

The idea that the contradiction of the Incarnation is ‘conjunctive’, so contradictories are not only joint but inseparable, is in the line of the canonical rejection of monophysitism (the thesis that Christ has only one nature), as it is paradigmatically expressed by the Athanasian Creed.⁷

In a general and very simplified account, ‘monophysitism’ may have three versions (‘H’ and ‘D’ stand for the properties—and related predicates—humanity and divinity, respectively):

• (I) Christ has only one, hybrid HD nature

• (II) Christ is only H

• (III) Christ is only D

They all can be seen as trying to ‘consistentize’ the human divinity or divine humanity of Christ, by forgetting or overshadowing the weird combination of H and D. The orthodox view, instead, is firmly based on admitting the two natures (physeis), so it rejects (I), the first form of monophysitism. But, at the same time, it stresses the inseparable unity of H and D in Christ. So also (II) and (III) are rejected, Christ is two in one, two natures for only one person.

Altogether, the thesis is that H and D are both perfectly instantiated in Christ (there is no diminishing of one or the other property, and no mixture or confusion), but they are joint in only one entity-person. Accordingly, canonical Christology consists of two basic theses:

• o Ch1: Christ is H and D

and:

• o Ch2: Christ is not H or D separately.

The combination of Ch1 + Ch2 tells us that in the peculiar being we call ‘Christ’, we discover a true conjunction of putatively incompatible properties, and hence a true conjunction of contradictories (or contraries), but the conjunction is such, that the two conjuncts, separately taken, are unacceptable—untrue. This is namely what the ‘conjunctive’ view (in the version I favour) states: in a true contradiction, the conjuncts are not separately true (see hereafter, Sect. 4).

In what follows, I isolate seven propositions of the Creed: the first three insist on the former, the duality of the natures (against (I)), and the other four establish (and justify) the latter, i.e. their inseparable unity in Christ (against (II) and (III)). This is why I think that if we re-read the Creed from the perspective of logic, we can find some insights about the special conjunction of contradictories in case of true contradictions, and about inconsistencies in general.⁸

2.1 Seven propositions

The Athanasian Creed is a clear synthesis of conciliar theology. The first part develops the trinitarian doctrine. The second part focuses on the Christological problem. We are interested in the second part, in which the author grounds (explains and justifies) how it is that .

Dominus noster Iesus Christus, Dei Filius, Deus [pariter] et homo est.

Our Lord Jesus Christ, the Son of God, is [equally] divine and human.⁹

The author presents the seven statements I mentioned, specifying first the perfect duality of the natures, and then explaining how the unity of D and H is to be intended (and how is realized). The first three claims are the following:

(1) Deus [est] ex substantia Patris ante saecula genitus: et homo est ex substantia matris in saeculo natus.

Christ is God, generated before history from the substance of the Father, and he is human, born in history, from mother’s substance.

(2) Perfectus Deus, perfectus homo: ex anima rationali et humana carne subsistens.

He is perfect God, perfect human, made of rational soul and human flesh body.

(3) Aequalis Patri secundum divinitatem: minor Patre secundum humanitatem.

He is equal to the Father in virtue of divinity: minor to the Father in virtue of humanity.

These first three statements justify the duality and mutual irreducibility of the natures against those forms of monophysitism whereby there is a sort of mixture or hybrid HD in Christ, so are against (I).

Then we have the critical statement (4), which works as a hinge point, launching the idea of the unity:

(4) Deus [est] et homo, non duo tamen, sed unus est Christus.

Christ is divine and human; but one is Christ, not two.

So (4) introduces the disproval of (II) and (III): Christ is one, and no separate ascription is acceptable. The subsequent part gives us some suggestions about the kind of unity we have between contradictory properties, so about the truthmaker we postulate when we say that ‘Christ is both H and D’ is true, and we intend it in terms of Ch1 and Ch2.

Here are the other claims:

(5) Unus autem non assumptio divinitatis in carnem, sed assumptio humanitatis in Deum.

However, he is one [unus autem] not in virtue of divinity turning into carnality, but for the assumption of humanity in God.

(6) Unus omnino, non confusione substantiae, sed unitate personae.

He is completely one, not for the confusion of substances, but for the unity of the person.

(7) Sicut anima rationalis et caro unus est homo: ita Deus et homo unus est Christus.

Just like a human being is one [unus est homo], made of rational soul and flesh, in the same way Christ is one, both God and man.

These claims can be seen as specifically addressed against the two main heresies: that Christ is only H (Arianism) and that Christ is only D (Eutychianism).¹⁰ Now, I will very briefly consider and comment on the seven statements.

2.2 Two properties

(1) Christ is God, generated before history from the substance of the Father, and he is human, born in history, from mother’s substance.

The Biblical narration says that Jesus Christ was the Son of God and the son of a carnal mother. So there is a duality of germinal substances.¹¹ There is no contradiction, at first: the author underlies that eternity and temporality come from different substances, and the language reveals that the causal mechanisms are different. Christ as historical entity is natus (born), as pre-historical is genitus (generated).

The locutions ante saecula – in saeculo, meaning ‘before history’—‘in history’, imply the explosive series of ‘compatible incompatibilities’. Expressing ‘Christ’ by λ¹²:

• o Dλ → λ is eternal, immutable, impeccable.

• o Hλ → λ is temporal, mutable, peccable.

As Beall notes, Ch1, i.e.

$$\mathrm{H\lambda }\wedge \mathrm{ D\lambda }$$

Is ‘contradiction entailing’ (Beall, 2021a, 2021b, 25); accepting Ch1, it is inevitable to accept the consequences. Adopting a simple graph:

The perfect duality of the natures is what conveys all the conflicting consequences, so making the conjunction contradictory in itself: the two properties are mutually exclusive, in virtue of their intrinsic nature (and the related consequences).

Now genitus (generated) involves an action, the action of God; natus (born) is a state, the historical fact of Jesus’ birth. The distinction can support ‘qua-theories’; Beall notes they ultimately try to ‘consistentize’ Christology (since contradictory properties belong to two diverse ways of considering the phenomenon). In this, they are similar to positions that in paraconsistent literature are called ‘non-adjunctive’: two contradictory accounts of a certain fact are accepted, but under the condition that there is no real conjunction of contradictories, the two terms belong to (are true in) different views, or worlds, or systems.¹³ As Beall contends, qua-solutions, if they do not change ‘ad hoc’ the meaning of H or D, come at great expense of the real subject of Christology, i.e. the unity of Christ’s person: ‘do not keep the principal subject of Christology where it should be: namely, on Christ’ (Beall, CC: 62). Accordingly, we may say that non-adjunctive contradictions are not contradictions anymore, just because there is no real unity or jointness of the incompatibles.

However, as far as we can see here, the author of the Creed is mainly concerned with establishing the duality. The second statement further clarifies the double nature of Christ, hence the exactness and ‘perfection’ of the properties. (It also gives us, in passing, a first hint about how the jointness of D and H is justified, a justification later specified by the last statement.)

(2) He is perfect God, perfect human, made of rational soul and human flesh body.

Christ is not ‘incomplete’ or ‘diminished’ God, nor is he incomplete human. Since the two properties are perfect, entirely instantiated in Jesus, they are correctly described by the two predicates ‘D’ and ‘H’. The state description in terms of Ch1 is correct (true), because Jesus is both and completely D and H.

The third statement introduces a new contradiction: Christ is both equal and minor to the Father:

(3) He is equal to the Father in virtue of divinity: minor to the Father in virtue of humanity.

The contrariety aequalis / minor recalls the dualisms genitus / natus, ante saecula / in saeculo, and suggests new ideas about the special ‘fact’ which makes ‘Dλ ∧ Hλ’ true. It clarifies that Jesus’ life manifests or exhibits, unequivocally, the (putative) incompatibility as well as the contact between H and D. The special consequences (his being equal to- and different from- the Father, his temporality and eternity, mutability and immutability, etc.) can be seen as the natural effect of Jesus’ location at the border of the two properties, and so at the border of time, where eternity encounters history, spirit encounters carnal body (see Sects. 2.3 and 4.4).

The fourth claim, as mentioned, plays a critical role: it introduces the unity, by declaring that yes, Christ is ‘Deus et homo’, but one, not two.

(4) Christ is divine and human: but one is Christ, not two.

The perfection of the properties stated in (2) clearly opposes (I), the hybrid, so we may say it tells us that the contradiction is effective, and irreducible are all its double contradictory consequences (as in Beall’s hypothesis), but now their joined ascription to one and the same person opposes (II) and (III), as it implies the impossibility of eliminating, omitting, or reducing, one or the other term: Jesus is both D and H but he is not only D nor is he only H.

The idea of one person endowed with opposite properties is not implausible for ancient as well as modern anthropological theories. In psychoanalysis and in other psycho-philosophical conceptions of mind, it is quite usual to think that, for instance, people can be lovers and haters of the same object, so they can love what they despise. But it is hard to apply these considerations when constitutive properties of the kind of D and H are involved. In the following statements, we see that the Creed has a solution, a metaphysically grounded ‘conjunctive’ solution.

2.3 The unity of the truthmaker

While in the first group of three theses, the author wants to stress the perfect occurrence of D and H (neither diminished nor confused), the focus of the second group is the jointness of the properties, and here, the Creed also specifies how the mechanism whereby D and H are inseparably joined in one person works, and how this jointness is justified.

In (5), the author advances an enlightening distinction between assumptio (assumption) and conversio (transformation).

(5) However, he is not one in virtue of divinity turning into carnality, but for the assumption of humanity in God.

The statement is clearly against Arianism, i.e. the second form of monophysitism, since Arius’ idea was that with the Incarnation Jesus loses his divinity. Now the text says that the generation of Christ is due to a process consisting of the assumptio humanitatis: God assumes (perfect) humanity without losing (perfect) divinity. Here ‘to assume’ means ‘to include’, ‘to take on’: D and H are perfect and perfectly joined, thanks to this inclusion-embracement of humanity within divinity.

The passage presents a clear metaphysical concern (see details hereafter: Sect. 3.3). The author of the Creed does not only assert the jointness of the properties, but also feels committed to explain the process by which the weird connection has been generated. And in virtue of the assumptio, there is an operative (practical) dominance of God. This was already suggested in (1) by the dualism genitus/natus. There is a positive action of God, which brings about the extraordinary unity of D and H, and it is thanks to this positive action that Jesus, the divine limit of humanity, appears in history.

The further statement specifies Christ’s perfect (inseparable) unity, by recalling and developing what suggested in (5):

(6) He is completely [omnino = entirely, absolutely] one, not for the confusion of substances [confusione substantiae], but for the unity of the person [unitate personae]

Note the two relevant aspects: the Christological contradiction does not imply any change or diminishing of the properties but requires their joint occurrence in only one person. D and H are not confused or mixed but are simply inextricably joined, in one life, one person. The generating action is divine (as established by the assumptio), but there is no mutual annihilation of each perfectly instantiated property. The mutability of Christ is joint to, not confused with, his immutability; his eternity survives the contact with temporality, and vice versa.

The attempt to give an ontological explanation of the jointness is definitely clarified in the last statement, which justifies the two-in-one principle by an analogy to the dualistic conception of human beings as made of opposed, putatively incompatible, properties:

(7) Just like a human being is one, made of rational soul and flesh, in the same way Christ is one, while being both God and man.

The Christological dualisms are grounded anthropologically, in the same constitution of the property H, as it is suggested by the comparison: the unity of D and H is of the same kind of the unity of body and soul, material and spiritual nature, in every human being. What the Creed tells at this point is that if you accepted this basic anthropology, then you would not be surprised by the jointness of contradictories. Christ’s ‘double’ nature is not implausible, because humanity itself instantiates a similar duality. One may say that the property ‘H’ itself is contradictory, so that any ‘Ha’ for some object a is a dispositional releaser of true contradictions. In this, Christ’s Coming confirms the ancient (Greek, Socratic) idea of humans structurally made of temporal and intemporal nature, rationality and carnality, history, and eternity. The Incarnation also gives a logic for this humanity, a human logic made of compatible incompatibilities, and, I would say, of the non-contradictory nature of true contradictions.

3 Beall’s contradictory Christology: three objections

Beall’s approach to Christology is groundbreaking. It provides innovative insights for analytic theology, but also, I would say, for the philosophy of inconsistencies in general. In Beall’s view, contemporary paraconsistency may have something to teach to Christian theology, improving the underlying conception of logic. I think the converse also holds; traditional Christology may have something to teach to contemporary glut theorists.¹⁴ In this sense, the strategy of putting Christology and paraconsistency into contact is an enlightening move in itself; we can explore what the weird coincidence of humanity and divinity in Christ (with all its consequences) may suggest to our current conception of inconsistencies.

3.1 True and false?

At first, the two-in-one principle is satisfied by Beall: the unity of the natures does not obtain ‘in a way that results in two different persons or a new hybrid “divine – human” nature, but […] into exactly 1 person, who is 1 divine person who is also 1 human person’ (CC: 59). And ‘Christ is fully divine and fully human, not mostly human and in-part divine, not mostly divine and in-part human, and not some other hybrid combination of divinity and humanity’ (CC: 146). So no hybrid, the first form of monophysitism is excluded. But if we focus on how Beall has elaborated on the hypothesis, the inseparability of the two natures, and its logical consequences, seem to be forgotten or underrated. And this is due, I believe, to his idea of ‘true contradiction’ as a glut, a true-and-false sentence.

For Beall (as well as for standard dialetheists and glut-theorists), a true contradiction is an excess of truth values, a sentence which is true and false.¹⁵ And this also holds for the Christological contradictions:

Having the two contrary natures [D and H] brings about the truths entailed by having the one nature and the falsehoods of having the other (and vice versa, the truths of the other and the falsehoods of the one) (CC: 25).

Wherefore, we have the mentioned consequences, readable as a series of true-and-false state descriptions: ‘it’s true that Christ is mutable (because Christ is human) and it’s false that Christ is mutable (because Christ is God)’, and the same for all the other properties.

One of the possible objections is that this conception implies the acceptance of falsity. In Beall’s words: ‘Your Christology […] has it that various central Christian claims are both true and false, and therefore false!’ (CC: 72). Undeniably, this conflicts with our most usual intuitions about truth, and it seems hardly plausible in case of doctrinal postulates of the kind of Ch1. As Anderson (2007: 125) notes: ‘it seems hard to reconcile this outcome with the biblical emphasis on promoting truth and eschewing untruth.’¹⁶ Beall has defended the theory by saying that yes, apparently it is a weird idea, but eventually, Christ, as well as gluts in general, are special cases: ‘for most parts of reality, there’s no persistent appearance of inconsistency or contradiction’, ‘Christ is clearly very different’ (CC: 73). If anything, Beall has, primarily, a logical concern; what counts is that logical truth does not prevent (rather implies: see Beall, 2009) the occurrence of true contradictions in the form of gluts.

However, the objection should be explored carefully, since the ‘acceptance of falsity’ is usual for standard dialetheists and glut theorists,¹⁷ while it is specifically rejected by conjunctive paraconsistency (in the version I am presenting here). Beall does not say anything about the nature of the conjunction which joins contradictories. Is the ‘and’ simplifiable? Are the contradictories separately true, so that ‘p’ is true and ‘not p’ is true too, so false? We have reasons to suppose that in this context, the conjunction is ‘normal’ and it bears Simplification (see Sect. 4.2). So if we have the truth and falsity of, say, ‘Mλ’, we have the isolate truth of ‘Mλ’: Christ is mutable, period; or the falsity of ‘Mλ’: Christ is immutable, and that is all. And the same works for all the other contradictions. Moreover, in the above quotation, we see that Beall interprets Ch1, the first statement of orthodoxy, as the joint ascription of contrary properties. Contraries are mutually exclusive (which is otherwise revealed by their contradictory consequences); the truth of Hλ implies the falsity of Dλ and vice versa. In classical logic, as a consequence of Ch1, we will have that from the joined truth of ‘Dλ’ and ‘Hλ’, we arrive at the joint truth and falsity of ascribing each property to λ. So both ‘Hλ’ and ‘Dλ’ will be false; the falsity of Ch1 will be accepted in one with accepting its truth. It is hard to think that this is what we like to believe or accept when we accept Ch1 and we rationally believe it.

Clearly, Beall’s logic is sub-classical, which does not only mean that the contradiction is acceptable; it also means that classical operators, in particular the conditional (see Sect. 4.3), do not behave in the ‘normal’ way. But the ‘conjunctive’ part of the orthodoxy, i.e. Ch2, tells another story. It tells a story in which the main change does not run over the conditional, but over the conjunction (Sect. 4.2).

3.2 Heresy?

As we have seen, while Ch1 is against the first form of monophysitism (and is interpretable in terms of a true contradiction), Ch2 blocks the other two forms. If we remember this, the non-conjunctive glut postulated by Beall may encounter another and related objection (also advanced by Anderson, 2007: 117–126; reported by Beall CC: 92–95): that contradictory Christology ‘is heretical in that the theory has heretical claims as consequences’; ‘it is (allegedly) forced to make heretical claims’ (CC: 92). Beall answers noting that ‘a familiar heresy concerning Christ’s divinity may be understood in at least two ways’, as containing ‘It’s false that Christ is divine’ and as failing to contain ‘It is true that Christ is divine’, since the theory contains the latter; it is not strictly heretical in this respect (CC: 92). Beall’s explanation does not seem totally convincing here; it seems to underrate the three aspects of heresy mentioned at the beginning of Sect. 2.

If we focus on the role of conjunction and the separability of conjuncts, the objection seems more justified, and more worrying. Keeping to the classical meaning of ‘falsity’ as the truth of negation, the complete theory which includes the truth and falsity of each, Hλ and Dλ, will be pictured as including the truth of all possible conjuncts, so something like:

• o (!) T〈Hλ⟩ ∧ T〈¬Hλ⟩ ∧ T〈Dλ⟩ ∧ T〈¬Dλ⟩

Each statement and its negation will be true. The combination Ch1 + Ch2 does not imply this multiple truth. On the contrary, Ch2, the inseparable unity of H and D (which the author of the Creed mentions six times in the last three statements), typically resists against the acceptance of ‘Hλ’ or ‘Dλ’ as true-and-false; because if their negations are true too, then their negations are logically separable; they can be asserted or assumed as such.

If it is so, we would say that Beall’s theory avoids the first form of monophysitism, the hybrid, but it does not seem able to reject the other two forms:

• o (II) T〈Hλ ∧ F〈Dλ Arianism

• o (III) T〈Dλ ∧ F〈Hλ Eutychianism¹⁸

They actually are the true conjuncts of (!). As Anderson notes, by recalling a classical objection, ‘advocating dialetheism [glut theory] in order to preserve orthodoxy ironically ends up making its preservation irrelevant, since it involves the joint affirmation of both orthodox and heterodox theological claims’ (Anderson, 2007: 126). Accordingly, Pawl, 2019 speaks of ‘explosive theology’.

A similar objection has been often addressed to standard dialetheic theories: there is a risk of implicit trivialism pending over the idea of dialetheia, intended as a true sentence whose negation is true.¹⁹ The question whether dialetheic or glut-theoretic views can avoid this uncomfortable result is on debate. What I can only note here is that in a contradictory Christology with standard (non-conjunctive) gluts, Ch2 seems to be forgotten; Arianism and Eutychianism (largely intended) are both acceptable, just because all the statements involved in the theory, as well as their negations, are true. In this sense, the theory would not have dialectical means to disprove monophysitism in the two forms (II) and (III); rather, in this picture, they are both acceptable, since (and on condition that) all the conjuncts are simplifiable (separable), being singularly true.

3.3 Metaphysics?

A third (and possibly more relevant) objection is that Beall’s Christology is and intends to be ‘metaphysically neutral’, but one may advance two objections: first, the doctrinal truth of Ch1 would require the effective, real existence of a certain fact which makes the conjunction true, and second, Beall’s theory is not ‘neutral’ as it pretends to be. Beall mentions ‘metaphysical neutrality’ as one of the virtues of his Christology (CC: 62–63) and is quite detailed in defending the effectiveness and opportunity of his non-metaphysical approach (CC: 118–126). But I think both objections are justified. That metaphysic neutrality is to be ‘a virtue’ is controversial, and that a theory of ‘true contradictions’ could really exempt itself from any metaphysical commitment is arguable.

Much depends on how we intend ‘metaphysics’, and it is clear that Beall conceives it as a count noun, denoting ‘a specific metaphysical theory’, ‘a particular metaphysics’.²⁰ For Beall, a non-metaphysical view is preferable in clarifying the logic of Christology basically for three reasons: because ‘there is no revealed metaphysics’ to provide the necessary explanations (CC: 61); because metaphysical explanations are generally aimed to ‘consistentize’ the contradiction (as it happens in Pawl’s explanatory engagement²¹); and third, because metaphysical neutrality is able to preserve ‘the mystery of the hypostatic union’. The ‘mechanism’ whereby H and D are joined is mysterious and should remain such; more in general ‘[h]ow a contradiction is truly realized in a world that in most other respects is truly described by consistent theories remains mysterious at its core’ (CC: 67).

We may note that the author of the Creed instead feels committed to explain the two-in-one ‘mechanism’, first by giving reasons for the duality (natus/genitus, ante saeculum in saeculo, equal/minor), and later, explaining the unity, specifically by mentioning the assumptio humanitatis, stressing the unitas personae, and finally appealing to the contradictory (dualistic) nature of humanity (made of anima rationalis et caro). All these explanatory moves do not seem to reduce or ‘consistentize’ the contradiction, nor seem they aimed at softening the contrariety of H and D (and its consequences). So the author’s metaphysical explanation satisfies the first two reasons advanced by Beall: he does not reduce the contradiction; he appeals to a very ‘light’ and not idiosyncratic or esoteric ontology (the combination of soul and body mentioned in (7) was an uncontroversial anthropology, at that time, in that context). Maybe the ‘mystery’ of faith (at least in Beall’s sense of the term) is not saved, but the role of the metaphysical concern to support the plausibility of Ch1 + Ch2 is preserved.

As to the second objection, it is that ‘Contradictory Christology is hardly metaphysically neutral; it requires the truth of contradictions, beings who are contradictory’ (CC: 124). In answering the objection, Beall presents some elements of his ‘pure’ (non-metaphysical) deflationism. Mathematical models ‘don’t provide an explanation of how the actual contradiction was realized’ (CC: 67); ‘Logical vocabulary is not in the business of making robust or substantive semantic claims; its vocabulary is topic-neutral, and in many ways non-explanatory’ (CC: 82). Besides that, the logical approach can dispense from the reference to truthmakers, the ‘bits and bobs in the world that “make true” and “make false”’ (CC: 124). ‘It’s false that Christ is mutable and it’s true that Christ is mutable requires nothing more nor less than what is required for the truth of the respective conjuncts’ (CC: 82). All these deflationary statements intend to justify the idea that ‘Contradictory Christology is metaphysically neutral in significant ways’ (CC: 125). But can a logic defending the possibility of true contradictions really ‘fly over’ any metaphysical justification-explanation of this choice? At least the minimal commitment of truthmaker theory cannot be avoided. Ultimately, it does not require any strictly ‘realist’ or ‘thick’ conception of ‘facts’ (as specified by Jago, 2023).

If we intend ‘metaphysics’ as an ontologically sensitive approach to philosophical problems so that ‘truth’ involves truthmakers (and a problem of predicates is read as a problem of properties), we can see that many ‘metaphysical’ assumptions can be found in Beall’s Christology: first, the idea of Christ as a ‘contradictory being’ (CC: 20, 24, 84, 132), and second, the idea that there is a contradictory ‘account of reality’ (‘Given that reality itself is contradictory […] the true account of reality is itself contradictory, and thereby false in addition to being true’ CC: 73). Besides that, in Beall’s world, there are ‘natures’ and ‘properties’ (CC: 68), even if they are not primary with respect to the objects which instantiate them (CC: 64), and evidently, there are ‘strange phenomena’, such as Christ, or the Liar paradox (CC: 55, 26). Finally, there is also a four-dimentionalist ontology of human beings as ‘spacetime “worms” made up, at least in significant part, by “time slices” of our ourselves’ (CC: 118).²²

For Beall, all these ‘there is’ and especially the most controversial among them (the subsistence of ‘strange phenomena’) can remain unjustified and unexplained. Once we accept, with the authority of logic, that the divine humanity of Christ is a case of true contradiction, we do not need anything else. ‘The bar of truth does not discriminate among candidates: for a sentence – no matter what it is – to be true is, well, for it to be true’ (CC: 87). ‘The truth is what it is, and the truth can speak for itself’ (CC. 129).

But is this conception of truth adaptable to the proposal of ‘defending’ a contradictory Christology? I think it is not.²³ What is distinctive of truthmaker theory is the assumption of an explanatory commitment, especially in controversial cases (Armstrong, 2010: 61–66). And it is the concern that, as we have seen, is assumed by the author of the Creed (Sect. 2.3). In fact, the ‘two in one’ formula seems to be a good synthesis to express the nature of a contradictory truthmaker.

4 True contradictions without gluts?

The conjunctivist (in principle non-glutty) position can profitably avoid the three objections: saving the idea of ‘contradictory Christology’ from the accusation of accepting falsity, removing the suspect of heresy, and substantiating the theory by an appropriate truthmaker.

Notably, some basic ideas for conjunctivism have been launched by Beall himself (with reference to Hegel’s logic: Beall & Ficara, 2014). Beall does not adapt it to his contradictory Christology, possibly because he wants to keep to a standard conception of sub-classical logic (FDE). But the accordance of the theory with the aims of orthodox Christology strikes me as evident.

The somehow ‘revolutionary’ assumption of conjunctivism is that a true contradiction is a true conjunction of (separately) untrue sentences. Given a true ‘p and not p’, we have that ‘p’ and ‘not p’, separately taken, are untrue. The affinity with Ch1 + Ch2 seems evident. And there is no glut, since we cannot speak of truth for contradictories, while we can speak of the ‘simple truth’ of their conjunction.

To understand this position, and how it can be profitably adaptable to the two-in-one principle (avoiding the mentioned objections), it is worth considering first the logical reasons of the standard glut theory here favoured by Beall.

4.1 Why gluts?

Let us assume the uncontroversial account of ‘contradiction’ in merely syntactic terms, as a conjunction of contradictories, i.e. a sentence (or proposition, or statement, or any other truthbearer) of the form

$$\mathrm{\varphi }\wedge \neg \mathrm{\varphi }$$

In a first approximation, a glut theory is the theory whereby an instance of this form is true, so:

$${\text{T}}\langle \mathrm{\varphi }\wedge \neg \mathrm{\varphi }\rangle$$

In principle, accepting gluts (or dialetheias) means to accept this case for some ‘p’, and logically speaking, this position can be labelled ‘paraconsistent’ to the extent that the acceptance is not explosive: only some φ of the kind above are (accepted as) true.

Standard glut theory rapidly interprets the case as meaning

$${\text{T}}\langle \mathrm{\varphi }\rangle\wedge \mathrm{ T}\langle \neg \mathrm{\varphi }\rangle.$$

So ‘T’ distributes over the conjunction. The distributional property of T is otherwise given by the classical definition of ‘and’ given by the Conjunction Thesis:

$${\text{CT}}:\mathrm{ T}\langle \mathrm{\varphi }\wedge \mathrm{ \psi \rangle \ iff\ T}\langle \mathrm{\varphi }\rangle,\mathrm{ T}\langle\uppsi\rangle.$$

Hence, if the conjunction behaves normally, in accepting the conjunctive formula, we also have the distributed one. And, if we also accept the classical meaning of falsity, we have the glut:

$${\text{T}}\langle \mathrm{\varphi }\rangle\wedge \mathrm{ F}\langle \mathrm{\varphi }\rangle.$$

Accepting the possibility of true contradictions means to accept the double ascription of truth and falsity to the same sentence.

But this is not the only possible account. In particular, we should consider the two alternative options: non-adjunctivism and conjunctivism (d’Agostini 2021). Non-adjunctive theories of inconsistencies admit of simultaneous truth of some ‘φ’ and ‘¬φ’, but without admitting their conjunction; so, as mentioned in Sect. 2.2, they are similar to those qua-theories that, as Beall notes, dodge the unity (the conjunction of H and D) of Christ’s person.²⁴ The conjunctivist perspective is dual to non-adjunctivism, since it rejects the move from the non-distributed acceptance of contradictions to the distributed one, so it avoids the interpretation of T〈φ ∧ ¬φ⟩ as T〈φ⟩ ∧ T〈¬φ⟩, and as T〈φ⟩ ∧ F〈φ⟩. In this sense, we have true contradictions without gluts. The left-to-right direction of CT is restricted to non-contradictory cases. The ‘and’ joining contradictories is not the normal, reducible, ‘and,’ whereby ‘p and q’ entails ‘p’, or ‘q’.

Conjunctive paraconsistency is an anti-explosionist strategy. Given the Pseudo-Scotus argument (aka Lewis’ rule, or in other ways):

• 1 φ ∧ ¬φ

• 2 φ            ∧E 1 (Simpl)

• 3 φ ∨ ψ     ∨I 2

• 4 ¬φ          ∧E 1 (Simpl)

• 5 ψ            DS 3,4

As ‘ψ’ stands for any sentence, of whatever kind (true, untrue, false), a classical system which admits of contradictions trivializes; everything is proved true. And everything is contradictory, since for any true ‘p’, ‘not p’ will be true as well. The usual strategy is to discuss unrestricted Detachment (aka Disjunctive Syllogism).²⁵ For the conjunctive strategy instead, Simplification is the target rule: ‘φ ∧ ¬φ’ does not prove ‘ψ’ (whatever) just because a contradictory conjunction is not simplifiable: steps 2 and 4 do not hold. The connection with Ch2 can be easily seen by noting that when we have Simplification, we have distinct assumption (assertion), so separability of the conjuncts, which violates the inseparability of the natures.

A true contradiction without truth distribution will be the mentioned true conjunction of untrue sentences. The idea may seem weird at first but it can be supported by noting that not any propositional ‘and’ perfectly satisfies CT, and there are many cases of ‘unreducible’ conjunctions in natural language (Schein, 2017). If we look at the consequent semantics, we may recall that fusion in relevance logic is a special conjunction working as a ‘binding operator’ (Mares, 2012), so it fits the intended aim: once given ‘p and q’, neither ‘p’ nor ‘q’ are inferable. Besides that, a capital principle of truthmaker semantics (see Fine, 2017 and Jago, 2018) is that the left-to-right direction of the biconditional does not always work: a truthmaker for ‘p and q’ is not always a truthmaker for ‘p’ (or ‘q’). Finally, Nelson’s account of intensional operators (Nelson, 1930: 444) offers an enlightening antecedent.²⁶ He writes: ‘I do not take pq [p and q] to mean p is true and q is true, but simply ‘p and q’, which is a unit or whole, not simply an aggregate, and expresses the joint force of p and q’. This is exactly what conjunctivism intends to stress: the inseparable unity of ‘p’ and ‘not p’, and this is exactly, I think, what Christ is intended to instantiate: the joint force of humanity and divinity.

4.2 The full truth and the acceptance of falsity

The plausibility and merits of this position have been variously presented; I do not think it is worth giving a detailed account of its benefits and logical consequences.²⁷ Our concern is only to suggest a conjunctivist interpretation of the two-in-one principle, so proposing a contradictory Christology without gluts, and maybe a generalization of the ‘two in one’ hypothesis. To this aim, it might be useful to see how a conjunctive conception of contradictions can avoid the objections addressed to Beall (and to glut theory in general). In favour of conjunctivism in general (and not only in case of Christology), there might be a series of reasons. As strategy against explosion, one might say, it does not seem to have any primacy as compared to the more usual restrictions of Detachment. For our particular concern, I would only point to the mentioned problems, and first to the idea that a conjunctive conception of true contradiction avoids the acceptance of falsity.

The acceptance of falsity is justified by Beall’s ‘insubstantial’ and ‘discorporate’ truth, but it typically conflicts with the exclusion principle, or rather alethic exclusion, whereby if we accept that ‘p’ is true, then we are committed to exclude it is false, so ‘not p’ cannot be true. The distinctive feature of conjunctivism with respect to Beall (and glut-theorists in general) is that the subsistence of contradictions is acknowledged, while preserving this basic principle, which is perfectly consistent with our most usual intuitions about falsity (that ‘false’ is what should be excluded, removed, avoided, etc.). Dialetheists and standard glut theorists may accept more or less deflationary truth theories, but they are committed to reject exclusion: ‘the exclusion constraint […] is (of course) dropped, since some sentences may be gluts’ (Beall, 2009: 18). For conjunctivists instead, the constraint holds for any possible true ‘φ’, even for a true case of ‘φ and not φ’. I will note later that preserving exclusion might be profitable for some two-in-one explanation of contradictory truthmakers; for now, we can see that the separate ascription of truth to ‘p’ and ‘not p’ in case of true ‘p and not p’ will be incomplete. The ultimate reason for alethic exclusion is namely that when we speak or think of truth (we believe, assume or assert something), we cannot be satisfied by the incompleteness of only one ‘part’ of the story, especially when the other part disproves what we say or think.

Beall justifies his glutty Christology by saying that ‘true falsehoods are strange – surprising’ pieces of evidence, but we should not reject them, since ‘a false theory should be rejected unless doing so precludes accepting the full truth’ (CC: 73), and unquestionably, for Beall, ‘the full truth of Christ involves falsehoods’ (CC: 100). So for Beall, the acceptance of falsehoods (false truthbearers) is justified, somehow required, when we deal with ‘the full truth’ of strange phenomena, like the Liar paradox, or the case of a human-divine being. Now I oppose that namely the ‘full truth’ of these contradictions would require the rejection of separate ascriptions.

Consider for instance one of the typical cases of (putatively) ‘true contradictions’, the case of borderline predication.²⁸ We have a borderline tall man: we see he can be said tall, but also non-tall. So the idea of the tall-non-tall man as a contradictory case seems appropriate (Priest, 2019). Then, consider two persons, one asserts ‘he’s tall’, the other ‘he’s not tall’. They have justifying reasons, but we cannot strictly say that they ‘tell the truth’, because what they say is incomplete, and as such potentially misleading: it is not ‘the full truth’. To have the ‘full truth’ of the borderline man, we must have both, but both together. Those who assert only one part of the story do not tell the exact complete truth, and what is worse: they present their thesis as it were the whole truth.

The full truth of Christ might be so saved without conceding the problematic acceptance of falsity. As in the case of the tall-non-tall man, we would accept ‘Hλ and Dλ’, but without admitting the separate truth of the conjuncts. Altogether, conjunctive paraconsistency is based on two simple statements of the kind of Ch1 and Ch2: first, that there might be true conjunctions of contradictories, and second, that contradictories, separately taken, are untrue. While the first statement might be seen as introducing a standard glut-theoretic conception, the second, pointing to the inseparability of contradictories, parts company with it.

4.3 Trivialism and heresy

As we have seen in Sect. 3.2, Beall’s theory may be pictured as not rejecting but ‘including’ one-nature heresies, just in virtue of its assumption of ‘true falsehoods’. In fact, glutty positions in this respect seem to be too liberal. If we want to be said Christian (quicumque vult), in accepting Ch1 as expressing a contradiction, we must be ready to reject cases of ‘only Hλ’ or ‘only Dλ’. And this is obtained by the ‘non-glutty paraconsistency’ I am sketching here.

As we have seen, the move from the conjunctive to the distributed version of true contradiction is closed under CT. Now the question is: is this classical rule undisputable? In other terms: should we maintain the usual meaning of conjunction, if we accept instances of ‘φ and not φ’? Possibly, the most relevant perplexity is that if we accept true inconsistencies of conjunctive form by maintaining the usual behaviour of conjunction we obtain a proliferation of gluts. This is a well-known effect of the dialetheic perspective. As Priest himself explains (2002: 654), if ‘A is both true and false at a world […] given that the conjunction behaves normally, it follows that A ∧ ¬A is false; and so ¬(A ∧ ¬A) is true at the world as well’ (the emphasis is Priest’s). In practice, if we accept that ‘p’ is true and ‘not p’ is true too, then we have that each is true-and-false (as we have seen in Sect. 3.2), so for any glut we have a super-glut doomed to multiply the process.²⁹

In practice, if we accept the standard picture, a glut-theoretical (unamended) view consists of three statements:

• o GT1: there are some true contradictions

• o GT2: there are some true and false sentences

• o GT3: a true contradiction is also false

Assuming GT1 as primary, the other two statements require CT + FA, classical conjunction, and negation-falsity. And GT3 is a clear consequence of GT2. But GT3 risks plunging contradictory theories into trivialism. As it has been frequently noted, in accepting GT3, dialetheists are faced with some ‘expressive’ problems. The implicit acceptance-rejection of the Law of Non-Contradiction seems to be self-defeating: if I want to defend the idea that ‘p and not p’ is true, I cannot succeed, since I am also forced to accept that any opponent who asserts it is not true will be right.³⁰ In the same way, Beall’s theory does not contain any positive rejection of the heresy (in (II) and (III) form). But do we really need to move from GT1 to GT2?

Maybe no, we do not. Beall has colourfully noted that in case of true contradiction, negation is ‘on holiday’ (Beall, 2006b). We can interpret it as meaning that ‘not’ loses its exclusionary properties: it is not able to exclude the opposite. This is what happens in ‘φ and not φ’ true cases, but when our conjunction works in the non-normal way, the conjunction is true and its negation false. GT3 is avoided, and ‘truth’ works in the traditional way: it is still able to exclude falsity. Neither conjunct, neither ‘φ’ nor ‘not φ’, can be said true, as such, while their conjunction ‘φ and not φ’ is true and its negation is false. In the same way, we can say that while ‘Hλ and not Hλ’ is true, its negation (in any form) is heresy. Christ is a true case of divine humanity, or human divinity, without any diminishing or confusion of one or the other property, and without any possibility of eluding or omitting one or the other.

4.4 Two in one

The third objection regards the ‘metaphysical neutrality’ of Beall’s contradictory Christology. The metaphysical reasons of conjunctivism cannot be detailed here. But it is interesting to note that the idea of ‘two in one’ may offer an unusual and promising line of research for contradictory truthmakers. When we want to defend the idea that a contradiction is true, we have the two problems tackled and indicatively solved by the Creed. First, we should specify that the two contradictories are really what they are supposed to be, and so can be correctly pictured by ‘p’ and ‘not p’, or, in predicative terms, the two properties we ascribe to the same object are really ‘P’ and ‘not P’—which is what the first three statements of the Creed do. Then, we should explain how it happens that despite their incompatibility in principle, they are joined—and this is what the last four sentences specify.

Traditional ‘Christological logic’ is not afraid of metaphysical explanations, while contemporary logic (or rather a significant part of it) resists against them. As we have seen, Beall says that the ‘mechanism’ whereby putatively incompatible properties, such as humanity and divinity, are joined is, and should remain, ‘mysterious’ in itself, while the author of the Creed explains the two-in-one mechanism, and his explanatory moves do not reduce the contrariety between H and D but give us some ideas about the nature of the truthmaker postulated by Ch1. Now I think this program can offer useful insights for the metaphysics of contradictions, typically in the line of the conjunctive hypothesis.

If we ask about what kind of truthmaker may make Ch1 or other assertions of joint incompatibles true, the answer involves a problem originally advanced by Armstrong (2004), and generally overshadowed by dialetheists and glut theorists. He asks: if we want to accept the idea of truthmakers for gluts, and we postulate there is some fact which makes ‘p and not p’ true, ‘should it be said that the two truthmakers [for ‘p’ and for ‘not p’] are identical, or merely overlap, or are disjoint?’ (Armstrong, 2004: 108). Graham Priest has not directly answered Armstrong’s question (which was openly addressed to him), but he thinks the two facts hypothesis is the right one. Both dialetheists and glut-theorists agree that there are two (non-identical) truthmakers, so a contradictory state or situation is made of two facts, the positive and the negative, the former working as truthmaker, and (possibly) the latter as falsemaker. The duality of the truthmaker is paralleled by logic: as Priest writes: ‘being true and false is not a third truth value. It is the possession of two truth values’ (Priest 2019: 140).

The two-fact account is problematic in various respects. Typically, it implies the existence of ‘negative facts’ (the ‘bad boys of metaphysics’, Jago, 2018: 11), and someone believes that the acceptance of negatives is the most serious challenge for truthmaker maximalism and truthmaker in general (see Tallant, 2018). There are ways of sorting out the difficulty. (For instance, Jago, 2018: 149–154 notes that we perceive negatives by perceiving ‘edges’, so they can work for truthmakers of ‘not p.’³¹) But if we keep to the idea that truth ascriptions postulate the ‘subsistence’ or ‘there being’ of a certain fact, then T〈p⟩ means that there is a fact p in the world, and T〈¬p⟩ means there is not. A contradictory (glutty) fact will be a fact that there is and there is not, subsists and does not subsist at the same time, is and is not what it is. So we see that in a truthmaker conception, the idea of two ‘overlapping’ facts, meaning two distinct ‘p’, one of which to be described in negative form, is implausible.³²

Christ’s being two in one suggests an alternative view. It tells that in case of contradiction (joint subsistence of incompatible properties), the truthmaker is only one. So at least in this case, a true contradiction will be only one fact, able to make the conjunction of contradictories true; there is only one person, Christ, simultaneously having the two (inseparable) natures of divinity and humanity (see Sect. 2.3). The interesting consequence is that accepting the one-fact hypothesis, there is no need to postulate negative facts; no need for subsistent/present and non-subsistent/absent facts. Because ‘Hλ and Dλ’, as well as ‘Mλ and not Mλ’ and all the related contradictions will work each as only one, entirely positive, state of affairs.³³

Can we generalize the hypothesis? St. Athanasius could appeal to a well-consolidated anthropology, and to the authority of revelation. But how can we find, in a secularized metaphysics, this weird single fact whose true description is ‘Pa and not Pa’, or ‘p and not p’?

The dialetheic metaphysics proposed by Priest, 1995, and later by Priest, 2014, may give us a first answer, also clarifying the role of negation. The example of the tall-non-tall man is paradigmatic, I believe (see also d’Agostini 2023b). Typically ‘real’ contradictions are (instantiations of) limits, edges, or borders: limits of thought, of being, of language, of objects, of properties, of worlds, of facts. The idea of expressing them by contradictory state descriptions is in order, because in our common language and thought, we mark the limits of properties by negation, and if we acknowledge this, we endorse the idea of contradictory situations as borderline cases, deserving borderline predication. When we have some ‘Pa and not Pa’ for some object a, and property P, this happens because the object is located at the border or limit between the extension and the anti-extension of P. ‘Not’ so works as a border operator, and in this respect, paradigmatic contradictions are cases of vagueness: the borderline tall man is to be said both tall and not tall; the borderline bald man is bald and he is not.³⁴ Such a condition can be generalized (Priest, 2003 and 2019; Varzi, 2003), because, for any property we encounter in our empirical life, we cannot a priori exclude borderline cases. But in the same way, we can accept that Jesus’ life, instantiating the relationship between H and D in the form of their unity, descriptively exhibits the contact between H and D: he made the divine limits of humanity visible.

The consequences for the meaning-use of ‘not’ are clear. In case of true ‘Pa and not Pa’, ‘not’ still marks the anti-extension of the property P but it does not mark the mutual exclusion of P and not P any longer. The ‘holiday of negation’ (Beall, 2006b) can be better explained now. In true contradictions, negation is ‘on holiday’ since ‘not’ loses the property of excluding the opposite, and we see now that the ‘holiday’ is metaphysically justified, because we have only one truthmaker; only one fact (one person) able to ground ‘Pa and not Pa’. What is mostly interesting is that in having GT1 (T〈Pa and not Pa⟩) while rejecting GT2 (T〈Pa⟩ and T〈not Pa⟩), the exclusionary features of negation are preserved, but only for falsity, i.e. negation accompanied by truth: ‘not Pa’ as such does not exclude ‘Pa’ (the contradiction is true), but still, if ‘not Pa’ is true, then ‘Pa’ must be untrue.

5 Summary and concluding remarks

The Athanasian Creed tells us that whoever wants to be Christian, they must believe that Christ is (has been) perfectly divine and human, with all the contradictory consequences, but the two natures are inseparably joint in only one person. It is a clear defence of the two canonical statements of orthodox Christology: Ch1: Christ is both divine and human and Ch2: the two properties are inseparable. The combination of Ch1 + Ch2 implies that the conjunction ‘Jesus is God and man’ is true, but its conjuncts, separately taken, are unacceptable/untrue.

The two statements, Ch1 and Ch2, are fixed in seven theses of the Creed: the first three stating the duality and perfection of the two natures, and the other four grounding (justifying, explaining) their inextricable unity. The first three are intended to counter those forms of monophysitism whereby Christ has not two natures but a specific mixture of humanity and divinity (I), and the others disavow those forms which state he is only human (II) or only divine (III).

I have tried to show that this account can be interpreted, in the line of Beall, as implying the acceptance of Ch1 as a true contradiction. But, in my diagnosis, it would require a significant change in the logic inspiring Beall’s Christology. I have suggested that the combination of Ch1 and Ch2 is in the line of the position in paraconsistency called ‘conjunctive’, distinctively informed by two basic assumptions: there might be some true-acceptable contradictions of conjunctive form (paralleled by Ch1), but the two contradictories are not true as such, they cannot be assumed-asserted separately (Ch2).³⁵ In Sect. 4, I have briefly presented a version of conjunctivism in which the ‘inseparability’ of contradictories (the failure of Simplification) is justified by assuming that a true contradiction is a true conjunction of untrue sentences. It is an unusual and promising philosophy of paraconsistency, sparsely present in contemporary literature, launched and endorsed by Beall himself (Beall & Ficara, 2014 and 2023). In my judgement, the focal point (and greatest benefit) of the theory is the idea of contradiction without truth value gluts. In this line, we can accept the subsistence of true contradictions while preserving a capital feature of classical truth: the exclusion principle, whereby if ‘p’ is true ‘not p’ must be false, so no joint ascription of truth and falsity is possible.

While Beall interprets Ch1 as a glut, so that the truth of Christ ‘involves falsehoods’, I suggest assuming, in the line of the two-in-one principle, it is a conjunctive contradiction whose terms are not singularly true. I have tried to show that such a position can avoid some objections to Beall’s Christology (and to standard glut theories in general). Beall does not say anything about the ‘and’ joining contradictories, but it is clear that his glutty interpretation of Ch1 involves a normal conjunction, so entails the separate assertion-assumption of each contradictory, which implies the acceptance of falsity. The idea of true contradictions without gluts avoids this uncomfortable condition. Beall says that if we want to save ‘the full truth’ in case of contradictions, we should admit the weird but possible occurrence of ‘true falsehoods’; I have argued there is no need: rather, to preserve the ‘full truth’ of contradictory cases, we should simply reject the separability of contradictories (Sect. 4.2).

The aim of this article is not to defend the preferability of non-glutty paraconsistency over standard glut-theoretic conceptions, in Christology or in other contexts.³⁶ Maybe it is not ‘absolutely’ preferable. This explains the question mark in the title. Actually, one may contend that the resulting ‘true contradiction’ is not a contradiction anymore, as the state description ‘Hλ and not Hλ’ behaves as an atomic sentence, made true by only one fact. Such a position may seem closer to Pawl’s idea of the compatibility of purported incompatibles (‘the conciliar Fathers did not see these predicates as incompatible’, Pawl, 2014: 63) than to Beall’s idea of contradictory Christ.

My program here was not to arrive at a decision in this regard. What I can say, for now, is that a conjunctive account of the Christological contradiction and of inconsistencies in general has the merit of preserving alethic exclusion, a typical feature of traditional truth (Sect. 4.3), and seems to be compatible with a metaphysic-sensitive logic and truth theory (Sect. 4.4). The ‘transparent truth’ presented by Beall, 2009, confirmed in Beall, 2021a, coherently applied and firmly defended in CC, renounces these two features. Beall’s theory (here and elsewhere) is ‘purely’ deflationary, which means (as Wyatt, 2021 clarifies) it is non-metaphysical in principle; his glutty truth requires dropping the ‘exclusion constraint’ (Beall, 2009: 18). But both traditional features of truth (exclusion and metaphysical commitment) seem required when dealing with Christological themes or other controversial issues: in our most usual truth-talk, we need to reject ‘falsity’, in any sense and respect; and if we believe that there are contradictions, we need to explain the plausibility of a contradictory world. I have simply mentioned a possible explanation, the one (advanced by Priest, 1995 and 2014) of contradictory facts as borders or limits of properties. This hypothesis (here simply hinted) seems to me in the line of the idea of Christ as the divine limit of humanity realized in history.