1 The doctrine of incarnation and its fundamental problem

The so-called doctrine of incarnation lies at the very heart of Christian theology and, in particular, Conciliar Christology. This doctrine states that, more than two thousand years ago, the Virgin Mary witnessed the most incredible miracle of all. Not only was her womb filled with a life conceived by no man, but such a life was that of Jesus Christ, the God who became human. As the Nicene Creed states, Jesus Christ has a divine nature (because He is truly divine) and He has a human nature (because he is truly human). He is, thus, the ‘true God’ who ‘became a man’ (cf. Pawl 2020, 43; Tanner, 1990, 2).

Now, the very idea that God can become flesh and blood, have eyes and hands, be mortal, fallible, imperfect and capable of suffering, must appear to anyone, believers and non-believers, as baffling. While wrestling with the bewildering truth which is enunciated by the doctrine of incarnation, a great number of philosophers and theologians have identified one of the sources of such a bewilderment in what has been called the fundamental problem of Christology, that is, the doctrine of incarnation appears to affirm inconsistent predicates of Jesus Christ, for His two natures, the divine and the human, appear to be contradiction-entailing.

From the divine nature of Jesus Christ, it follows that He is, let’s say, immortal, infallible and incapable of suffering. Since God is immortal, infallible and incapable of suffering, and since Christ is God, then Christ is immortal, infallible and incapable of suffering. From the human nature of Jesus Christ, it follows that He is, let’s say, mortal, fallible and capable of suffering. Since human beings are mortal, fallible and capable of suffering, and since Christ is a human being, Christ is mortal, fallible and capable of suffering. Jesus Christ is, thus, immortal and mortal, infallible and fallible, incapable of suffering and capable of suffering. As Richard Cross writes:

[The] problem specific to the doctrine [of incarnation] is this: how is it that one and the same thing could be both divine (and thus, on the face of it, necessary, and necessarily omniscient, omnipotent, eternal, immutable, impassible, and impeccable) and human (and thus, on the face of it, have the complements of all these properties)? (Cross, 2011, 453)

In order to cast a better light on this issue, it might be beneficial to focus our attention on one of its instances. We, thus, consider the case in which Jesus Christ appears to be both mutable and immutable. With admirable clarity, Beall (2021) presents the issue in the following way:

  1. 1.

    Christ is immutable. [in virtue of His divine nature]

  2. 2.

    Christ is mutable. [in virtue of His human nature]

  3. 3.

    Christ is both immutable and mutable. [from 1, 2]

Premise 1 is grounded on the idea that, if something has a divine nature, this something is immutable. Since Christ has a divine nature and whatever has a divine nature is immutable, Christ is immutable. Premise 2 is grounded on the idea that, if something has a human nature, this something is mutable. Since Christ has a human nature and whatever has a human nature is mutable, Christ is mutable. Finally, conclusion 3 follows from premise 1 and premise 2. Given premise 1 and premise 2, Christ appears to have inconsistent properties. Christ is both mutable and immutable. And this is the bewildering truth which is forced upon us by the doctrine of incarnation. This is the fundamental problem which seems to afflict such a doctrine.

Some important specifications. Given what we will discuss in the next Sections, it is interesting to notice that, according to Beall, the above argument has three enthymematic assumptions. (1) The first enthymematic assumption is represented by the entailment from x is immutable to x is not mutable. Such an entailment guarantees that conclusion 3 is inconsistent. For ‘Christ is both mutable and immutable’ entails ‘Christ is both mutable and not mutable’. (2) The second enthymematic assumption is the so-called ‘transference principle’, that is, something that has a nature N (e.g. a divine nature) has whatever properties are entailed by having such a nature (e.g. being immutable). As we have already discussed in the previous paragraph, such a principle is used for grounding premise 1 and premise 2. (3) The third enthymematic assumption is a belief which lies at the very heart of Conciliar Christology, that is, Jesus Christ has a divine nature and independently and without diminishment also has a human nature. Such a belief is important because it allows us to reach conclusion 3 from premise 1 and premise 2.

In recent years, Jc Beall’s contradictory Christology has represented a real novelty in philosophy of religion and analytic theology (Beall, 2019, 2021): For Beall’s application of sub-classical logics to the so-called fundamental problem of Christology is, no doubt, one of the most exciting and original developments in these research areas. The present paper focuses on Beall’s The Contradictory Christ, and it has the following structure. Section 2 presents how Beall’s contradictory Christology addresses such a problem and Section 3 discusses how his contradictory Christology is compatible with the idea that the hypostatic union is fundamentally mysterious. This is not all, though. The present paper also uncovers an hidden assumption of Beall’s contradictory Christology, that is, our theological language has to be understood in a univocal way. In order to underline the role played by this assumption, we discuss James N. Anderson’s account of theological language. Anderson is, in fact, famous for overcoming the fundamental problem of Christology by endorsing the view that our theological language is equivocal. All this is discussed in Section 4. Section 5 presents a philosophical option which compromises between Beall and Anderson’s view: when our theological language is used to speak about Christ and his two double natures (his divine nature and his human nature), such a language is both literally and analogically used. We develop a formal treatment of this position as well.

Before we begin, it is important to make a brief clarification. The present paper does not deliver any knock-down argument against Beall’s and Anderson’s views. The main aim of the paper is to carve a logical space in which we can coherently develop the idea that, given some of its theological applications, our language might be taken to be both literal and analogical. We also present some rationale in its favor. We show that such an idea is logically tenable and, for this reason, it has to be taken seriously by both philosophers of religion and analytic theologians.

2 Beall’s contradictory Christ

Given the fundamental problem which seems to afflict the doctrine of incarnation, a great number of theologians and philosophers have tried to alleviate such an issue. Regardless of their specificities and differences, it is fair to say that all these attempts are fueled by the same presupposition – the doctrine of incarnation stands in need of a proper understanding, and a proper understanding is an understanding which commits the doctrine of incarnation to the truth of no contradictory claims, for no claim can be contradictory and, at the same time, true. As Beall writes, “what immediately removes this option from the theological table [e.g. the option according to which it is true that Christ is immutable and mutable, and thus, it is true that Christ is mutable and not mutable] is the view that logic itself rules out the possibility of such true but logically inconsistent claims” (Beall, 2019, 402).

In recent years, Beall has challenged this presupposition, and he has argued that logic itself does not rule out the possibility of such true but inconsistent claims. It is only a specific breed of logics, that is, classical logics, which takes such claims to be prohibited. Beall, then, nudges us to consider all the possibilities which are available in logical space, and he encourages us to explore other kinds of logics as well. According to Beall, we have no reason to restrict ourselves to the idea that propositions must be either true or false, for some propositions can be neither true nor false, and some others can be both true and false. The recent development of sub-classical logics and, in particular, what is called ‘first degree entailment’ has clearly shown that we can accommodate all these possibilities in a logically tenable way.

At this point, the application of the ‘first degree entailment’ to the fundamental problem of Christology should appear to be natural. Given a logical framework in which contradictory claims can be true, the contradictory claims which are forced upon us by Conciliar Christology do not represent a problem anymore. Consider the argument presented in Section 1. Since Christ has a divine nature and whatever has a divine nature is immutable, Christ is immutable. Since Christ has a human nature and whatever has a human nature is mutable, Christ is mutable. Christ is, thus, immutable and mutable. Against all those approaches that try to show that the conclusion of this argument is only an apparent contradiction, Beall takes such a conclusion to be genuinely true. In Beall’s contradictory Christology, a Christology which abandons classical logic and employs first degree entailment, it is true that Christ is immutable and mutable. This idea is summarized by Beall as follows:

Contradictory Christology responds to the fundamental problem by accepting the apparent contradictions as genuine contradictions. This is not simply ‘because we can’ (given the correct account of logic); the view is motivated by the screamingly apparent contradiction at the heart of Christ’s role – perfect God but also as human in imperfection and limitation as you and me. On a mistaken view of logic the proposed solution to the fundamental problem would be off the table. But we need not carry a mistaken view of logic. And once dropped we may fully explore the logical possibility of embracing the contradiction of Christ at face value (Beall, 2019, 416).

Having grasped the core ideas of Beall’s contradictory Christology, someone might think that such a Christology commits us to some form of irrationalism about Christ and His two natures. Someone might argue that, since rationality demands non-contradictory theories and Beall’s contradictory Christology is contradictory, Beall’s contradictory Christology is not rational. It is, thus, irrational. Now, given the topic of our paper, it is interesting to note that this objection has been raised by Anderson (2007). Beall addresses this worry by arguing that any attempt to find his contradictory Christology guilty of irrationalism will ultimately rely on a standard account of logic and some principles which connect such an account with a theory of rational acceptance-rejection behavior. At this point, Beall rightly claims that, even though these are very difficult and controversial issues, there is a lot of work in philosophy of logic which questions either the standard account of logic or the principles which are used to connect such an account with a theory of rational acceptance-rejection behavior. And, if so, it is far from being clear whether Anderson’s objection succeeds. Beall writes:

If one charges that that – the [true] contradiction [of Christ] – is irrational, then let the objector state her grounds for saying as much. I have little doubt that the objector’s ‘grounds’ will ultimately point to the standard account of logic, and also point to principles tying the given account of logic to (a theory of) rational acceptance–rejection behavior. While these are difficult matters to adjudicate, there is enough work in the philosophy of logic (and theories of rational acceptance–rejection behavior) to question the strength of such legs in the objector’s charge. (Beall, 2021, 82)Footnote 1

3 Contradictory Christology and its mystery

As it is not difficult to imagine, Beall’s contradictory Christology has been welcomed with a lot of worries. Given the topic of this paper, one of these worries is particularly salient, and it concerns the mystery which is supposed to characterize the union of Christ’s two contradiction-entailing natures, that is, the divine nature and the human nature. Countless theologians have rightly claimed that this hypostatic union is meant to be mysterious – the very fact that someone can be God and man is meant to be puzzling and inexplicable. Far from being something which is easily reconcilable, this item of faith is meant to represent an obstacle on which our rationality is destined to stumble. The fact that Jesus Christ is both divine and human has to be shocking as shocking is the very idea that God himself hanged on a cross at the top of mount Golgotha.

As we have already seen, Beall claims that, given an appropriate sub-classical logic, we can take the contradictions which are entailed by Conciliar Christology as true. With an appropriate sub-classical account of logic, Beall argues, we can reason about such contradictions, and develop our theologies without being in danger of sliding into illogical thinking. Having said that, someone might think that, if we can simply take these contradictions as true, it is not clear how they can be puzzling and inexplicable anymore. And, if we can reason about such inconsistencies, and if can use them to develop our theologies, the mystery of the incarnation seems to vanish. Doesn’t Beall overlook that inescapable mystery which is supposed to characterize Christ and His two natures?

In dealing with this worry, Beall argues that the answer to the aforementioned question is negative, for Beall claims that what is mysterious is not that Christ has inconsistent properties. The mystery, thus, does not lie in the fact that Christ is, let’s say, immutable and mutable. This is nothing more than a contradiction which happened to be true. What is mysterious, though, is how Christ has inconsistent properties. The mystery, thus, lies in how Christ is, let’s say, immutable and mutable. In other words, Beall believes that, even if we have the formal tools which are necessary for reasoning about true contradictions and even if we can employ such tools while reasoning about the contradictions concerning Jesus Christ, we still lack a proper explanation of how such contradictions occurred. And, if this is correct, the mystery of the hypostatic union is preserved by Beall’s contradictory Christology, and the previous worry does not arise. Beall presents this train of thoughts in the following way:

On my contradictory Christology the mystery is not that Christ is contradictory; for that, after all, is just the clear and obvious starting line – the clear and pressing ‘problem’ with which we all begin. The mystery is rather one of implementation or mechanism: how the contradiction was pulled off. We have precise (largely mathematical) models of how to think about the contradiction; but these models are at best guides to the truths that follow (or don’t follow) from Christ’s contradictory being; they don’t provide an explanation of how the actual contradiction was realized. How a contradiction is truly realized in a world that in most other respects is truly described by consistent theories remains mysterious at its core. (Beall, 2021, 45)

At this point, the reader might want to know the reasons why Beall’s account of mystery is particularly interesting. Why are we discussing it? Is there something special in how Beall understands the concept of mystery and its theological employment? Well, it is possible to answer these questions by starting to note that, even though it is unquestionable that the concept of mystery plays an essential role in the Christian tradition, the vast majority of philosophers and theologians disagree with Beall, for they believe that such a mystery lies in the fact that Christ has inconsistent properties. While Beall identifies the mystery in how Christ is, let’s say, both immutable and mutable, many Christan thinkers believe that our thinking is thrown out of its joint as soon as we begin to ponder the possibility of Christ being, let’s say, both immutable and mutable. As soon as we try to grasp what this means, a great number of theologians and philosophers agrue, our thinking seems to stop making sense and our language appear to fail us in delivering any meanful content or any content we can rationally believe. Flag holders of this idea are McCabe, Turner, Davies and Anderson. There is no doubt that all these thinkers have developed (variations of) these ideas in great details. However, Anderson appears to be particularly interesting and important for the narrative of the present work. The reason being that, even though we will not discuss how Anderson’s account of theological language can highlight our inability to grasp the Divine, we will nonetheless show that a careful comparison between Anderson’s discussion of theological language and Beall’s contradictory Christology can help us to uncover an hidden and, therewith, underdiscussed assumption of the latter. This paper will also show that our comparison between Anderson and Beall might push us to enlarge our views about how language might work when it is employed in developing a tenable Christology.

4 Anderson’s MACRUE and Beall’s hidden assumption

In light of what we have already discussed in Section 2, it is possible to summarize the two main commitments of Beall’s contradictory Christology as follows:

  1. (i)

    Given Conciliar Christology or, more precisely, the “scripture, stamped at Chalcedon, and otherwise uniformly recognized as core christological doctrine’’ (Beall, 2021, 145), both (1) and (2) are true.

    1. (1)

      Christ is immutable.

    2. (2)

      Christ is mutable.

  2. (ii)

    (1) and (2) are genuinely contradictory. They (and the conjunction of them) are both true and false.

    James Anderson’s position can be easily characterized when contrasted with Beall’s. In particular, Anderson agrees with Beall on (i), but disagrees with him on (ii). According to Anderson (2007), given what Conciliar Christology says, both (1) and (2) are true, but.

  3. (iii)

    (1) and (2) are merely apparently contradictory. They are just true.

In this and the next Sections, we review Anderson’s view on the fundamental problem of Christology, focusing on Anderson’s following semantic argument for (iii)Footnote 2: First, the combination of (1) and (2) is a case of Merely Apparent Contradiction Resulting from Unarticulated Equivocation (following Anderson, henceforth MACRUE). Second, the language used to state (1) is analogical. In this section, we see the first part of his semantic argument and, through this, reveal a hidden assumption in Beall’s inconsistent Christology.

The heart of the idea that (1) and (2) constitutes a case of MACRUE is very simple. To make the point clear, here we use (n1), the negation of (1), instead of (2):

  • Christ is immutable.

  • (n1) Christ is not immutable.

(1) and (n1) are merely apparently contradictory if they “involve an equivocation on one or more of the terms employed” (Anderson, 2007, 226). Anderson claims this is the case. For the sake of discussion, let us suppose that ‘immutable’ is equivocally used in (1) and (n1): ‘immutable’ used in (1) has a different meaning than `immutable’ used in (n1). Once we articulate this equivocation, as illustrated in (1’) and (n1’), the contradiction disappears:

  • (1’) Christ is immutable1.

  • (n1’) Christ is not immutable2.

In this way, if ‘immutable’ in ‘Christ is immutable’ is not used exactly in the same way as in ‘Christ is not immutable’, they are merely apparently contradictory.

Anderson’s MACRUE strategy enables us to point out an implicit assumption in Beall’s inconsistent Christology. For Beall, `immutable’ and other terms in (1) and (n1) are univocal: ‘immutable’ in ‘Christ is immutable’ is used exactly in the same way as in ‘Christ is not immutable’. The same holds for ‘Christ’ and ‘is’. As we have seen in Section 3, if this is not the case, (1) and (n1) are not genuinely contradictory, as contrary to what Beall claims.

By comparing Anderson and Beall, the following question naturally arises: Is `immutable’ (or any other terms) univocal or equivocal in (1) and (n1)? Anderson suggests that the apparent contradiction itself motivates us to understand it as equivocal.Footnote 3 But, if this is the only reason to hold that `immutable’ is equivocal in (1) and (n1), this sounds question-begging for proponents of contradictory Christology, according to which (1) and (n1) are genuinely contradictory and we can rationally believe the contradiction. On the other hand, simply assuming that the words in (1) and (n1) are univocal to reach the conclusion that they are genuinely contradictory begs the question for proponents of consistent Christology. Is there any good (non-question-begging) reason to suppose that the words in (1) and (n1) are univocal? Or is there any good (non-question-begging) reason to suppose that the words in (1) and (n1) are equivocal? In the next section, we claim that it is reasonable to seek a compromise between those two positions.

5 Both literal and analogical

For this purpose, first consider a reason to hold that some of the words in (1) and (n1) are equivocal. One way to support the equivocation is to show that a word in (1) is used with a different meaning than its literal meaning (while supposing that it is used in (n1) with its literal meaning). Echoing Thomas Aquinas, Anderson claims this is the case. He says:

According to … Thomas Aquinas, words predicated of creatures (such as `good’) cannot be applied univocally to God on account of the vast ontological difference between the Creator and the creation; … [W]hen we affirm that `Socrates is wise’ and `God is wise’ we do not employ the predicate `is wise’ in precisely the same sense. … When we affirm that `God is wise’, the predicate `is wise’ is analogous to that in the affirmation `Socrates is wise’; there is both similarity and difference of meaning, since Socrates’ wisdom resembles God’s wisdom in some respects but by no means all. (Anderson, 2007, 233-234)

God’s divine nature is so far beyond our nature that the predicate `is wise’, which is tailored to describe human wisdom, cannot capture God’s wisdom. In this sense, God goes beyond the descriptive capacity of our language. As many Thomists have confirmed, we cannot `define’ God in terms of any positive characterization with our language (Davies, 2011; McCabe, 2005; Turner, 2014). Having said that, the Bible is full of positive characterizations of God. How is this possible? When we apply, say, the predicate `is wise’ to God, the best we can do is to employ it analogically. It is used only analogically, and thus, the meaning that it has when it is applied to God is different from the meaning that it has when it is applied to a human. According to Anderson, this happens whenever we talk about God’s nature (Anderson, 2007, 235). Once we admit that Christ has a divine nature, it follows that any predicate in our language is applicable only analogically to Christ as well. This consideration provides us the following way of articulating the equivocation in (1) and (n1), where the subscript a indicates `immutable’ with an analogous meaning and l with its literal meaning:

  • (1e) Christ is immutablea.

  • (n1e) Christ is not immutablel (We assume this to treat the pair of (1) and (n1) as a case of equivocation.)

With this articulation, (1) and (n1) are only apparently contradictory, and thus they can be just true, as Anderson claims.

So far we have discussed a reason for why the word `immutable’ in (1) and (n1) is equivocal. However, once we focus on Christ’s human nature, we can exploit the consideration above to present a reason for why the word `immutable’ in (1) and (n1) is univocal. Since Christ is a human being, there is nothing preventing us from applying words like `wise’ or `immutable’ with precisely the same meaning as when they are applied to a human. So `Christ is immutable’ is false in its literal sense, as `Socrates is immutable’ is false in its literal sense. We can explicitly reflect this univocality as follows.

  • (1u) Christ is immutablel.

  • (n1u) Christ is not immutablel.

It follows from this formulation that (1) and (n1) are genuinely contradictory. And thus, if both of them are true, as Beall claims, they are both true and false.

In this way, we have a reason for the equivocation in (1) and (n1) and a reason for the univocality in (1) and (n1). On the one hand, given the divine nature of Christ, `immutable’ in (1) is used only analogous to its literal use. If it is used literally in (n1), `immutable’ in (1) and (n1) is equivocal. On the other hand, given the human nature of Christ, `immutable’ in (1) is used in the same literal sense as it is used in (n1), so it is univocal in (1) and (n1).

Now, according to Conciliar Christology and, in particular, the Chalcedonian doctrine, Christ has both the divine nature and the human nature, which both Anderson and Beall accept.Footnote 4 Then it follows that we have both a reason for univocality and a reason for equivocality. However, of course the univocality of `immutable’ in (1) and (n1) and its equivocality in (1) and (n1) conflict with each other. Given the conflict between univocality and equivocality, we have four options:

  1. (i)

    The conflict defeats both the reason for univocality and the reason for equivocality.

  2. (ii)

    The conflict defeats the reason for univocality but does not defeat the reason for equivocality.

  3. (iii)

    The conflict defeats the reason for equivocality but does not defeat the reason for univocality.

  4. (iv)

    The conflict defeats neither the reason for univocality nor the reason for equivocality.

On the one hand, Anderson would argue for (ii). Such an argument would be that equivocation makes us possible to avoid the genuine contradiction, but that univocality doesn’t. However, again, this begs the question for proponents of inconsistent Christology. On the other hand, Beall would argue for (iii). Beall would argue against the theoretical complication of the kind that Anderson proposes by appealing to simplicity and epistemic neutrality (Beall, 2021, 146–147). While simplicity and epistemic neutrality matter, it would not be crucial. It may show that a simple, univocal treatment of the apparent contradictions is better than a complicated, equivocal treatment of them in some respects. However, this per se doesn’t give us enough reason to reject the equivocation of the apparent contradictions. It does only when one of the two options, (ii) and (iii), is correct and the other should be rejected. This argument thus works only if we neglect option (iv). This consideration naturally leads us to the following questions: Why do we neglect option (iv)? That is exactly because univocality and equivocation conflict with each other. However, both reasons per se look good, from both historical and philosophical view points, as we have seen. We have a good reason to hold that `immutable’ in `Christ is immutable’ is used analogically, given his divine nature. We have a good reason to hold that `immutable’ in `Christ is immutable’ is used literally, given his human nature. And, since Christ has both natures, why don’t we conclude that `immutable’ in `Christ is immutable’ is used both analogically and literally at the same time? This view can be taken as a way to compromise between Anderson’s and Beall’s views, in the sense that the view accepts the key tenets of both views. Given this, even though option (i) is certainly a possible one, it is too destructive.

In what follows, let us pursue option (iv) and briefly compare it with Anderson’s view and Beall’s view: What does follow from the idea that (1) is both literal and analogical? Note that our purpose is not to argue for option (iv) against other options; rather, to explore option (iv) as an unexplored area of the theoretical landscape. For this purpose, we propose that `immutable’ is a case of multiple denotation (Priest, 2016). Priest (2016) discusses the noun phrase `the denotation of this term plus one’ and claims that it has more than one denotation: n and n + 1. We apply this idea to predicates. `Immutable’ can be used to mean its literal denotation and analogical denotation at the same time. To make clear the point and what results from this, let us engage in a bit of formal semantics.

For simplicity, let us consider only one-place predicates and focus on extensional semantics. In a standard semantics, a model assigns a predicate only one extension as its denotation. Let us assume that the extension of a predicate is a function from the domain to the set of truth values {t, f}:

$$[[P]]=g:D\to \{t,f\}$$

This gives us the following truth condition of atomic sentences of the form Pa:

$$[[Pa]]=g([[a]])$$

Based on this standard classical setting, we can give a multiple denotation semantics for predicates. Such a semantics assigns more than one denotation to a predicate. Formally, the interpretation of a predicate is a set of a function from the domain to the set of truth values.

$$[[P]]\subseteq \{g:D\to \{t,f\}\}$$

Accordingly, the truth condition of an atomic sentence assigns a set of truth values to it: Given that \([[P]]=\{{g}_{1}, \, {g}_{2}, \, \dots , \, {g}_{n}\}\), then.

$$[[Pa]]=\{{g}_{1}([[a]]), \, {g}_{2}([[a]]),\dots ,{g}_{n}([[a]])\}$$

In this setting, \([[Pa]]\) is \(\{t\}\), \(\{f\}\), or \(\{t, \, f\}\), which corresponds to true, false, and both true and false, respectively.

From the discussion so far, it follows that `immutable’ is equivocal: it has not only its literal meaning but its analogical meaning. Such equivocation is dissolved when its subject is fixed. When it is combined with the subject `God’, the predicate is used with its analogical meaning. When it is combined with that subject `Socrates’, the predicate is used with its literal meaning. What makes this difference is the nature of the subject. The divine nature of God requires its analogical meaning, and the human nature of Socrates allows us to use it with its literal meaning. Now let us make such sensitivity explicit. Let n(x) be the nature of x. To make explicit that `immutable’ is sensitive to the nature of its subject, let us assume that `immutable’ has an inarticulate slot for the nature of its subject, and thus, that a sentence of the form `x is immutable’ has the following form:

$${{\text{immutable}}}_{({\text{n}}({\text{x}}))}({\text{x}})$$

The interpretation of `immutable’ is sensitive to the nature of its subject:

$$[[{\mathrm{immutable}}_{(\mathrm n\left(\mathrm x\right))}]]\;=\;g_ l,\;\mathrm{when}\;\mathrm n\left(\mathrm x\right)\;\mathrm{is}\;\mathrm{divinity},\;g_a,\;\mathrm{when}\;\mathrm n\left(\mathrm x\right)\;\mathrm{is}\;\mathrm{humanity}$$

gl represents the literal meaning of `immutable’ and ga its analogical meaning. We thus have the following truth assignments to `God is immutable’ and `Socrates is immutable’ respectively:Footnote 5

$$[[{{\text{immutable}}}_{({\text{n}}({\text{God}}))}({\text{God}})]]=t$$
$$[[{{\text{immutable}}}_{({\text{n}}({\text{Socrates}}))}({\text{Socrates}})]]=f$$

So far is classical. Let us now consider when the predicate is applied to Christ. Christ has two natures: both divinity and humanity. To do justice to this dual nature of Christ, we redefine n(x) be a set of x’s natures: n(God) = {divinity}, n(Socrates) = {humanity}, and n(Christ) = {divinity, humanity} (let us here put aside the complication involved trinity which may suggest that God has these two natures). Corresponding to the possible multiplicity of the nature of a subject, the interpretation of `immutable(n(x))’ is multiplied:

$$[[\text{immutable}_{\text{(n(x))}}]]= \{g_i|i\in \text{n(x)}\}$$

Applying the multiple denotation semantics, we have the following truth assignment to `God is immutable’, `Socrates is immutable’, and `Christ is immutable’, respectively.

$$[[\text{immutable}_{\text{(n(God))}}(\text{God})]]=\{g_a ([[\text{God}]])\}=\{t\}$$
$$[[\text{immutable}_{\text{(n(Socrates))}}(\text{Socrates})]]=\{g_l ([[\text{Socrates}]])\}=\{f\}.$$

\([[\text{immutable}_{(\text{n(Christ))}}(\text{Christ})]]=\{{g}_{a}([[\text{Christ}]]),{g}_{l}([[\text{Christ}]])\}=\{t, \, f\}\)Footnote 6

The result shows that, under the present semantics, the forth option leads to a version of inconsistent Christology. Let us briefly compare this result with Anderson’s view and Beall’s. On the one hand, this potentially poses a problem for Anderson’s consistent Christology. This suggests that merely appealing to analogical language and unarticulated equivocation is not enough to show that the contradiction about Christ is merely apparent and not real. To arrive at the conclusion, one needs to show that `immutable’ is only analogically used when it is applied to `Christ’. However, it seems too difficult to show this, given that Christ has not only the divine nature but also the human nature. On the other hand, the resulting version of inconsistent Christology is different from Beall’s. According to Beall’s view, `immutable’ is univocal. It is only literally used when it is applied to `Christ’. His claim is that `Christ is immutablel’ is both true and false. In the present account, when `immutable’ is applied to `Christ’, it is interpreted as both literal and analogical. The claim is that, say, `Christ is immutableal’ is both true and false. As we have seen, `Christ is immutablel’ is false: When `immutable’ is literally used, we focus on the human nature of Christ and, thus, He is not immutable in any literal sense. Beall’s version of inconsistent Christology claims that `Christ is immutablel’ is true as well. The present account is not committed to this. The formal semantics presented above is, in fact, incompatible with the claim that `Christ is immutablel’ is both true and false. However, it is important to note that this is due to the limitation of the technical details of the semantics, not to any philosophical consideration. We can revise the semantics so that it is compatible with the claim that `Christ is immutablel’ is both true and false. See Conclusion of the paper.

It is natural to ask at this point how the proposed compromise between Beall’s and Anderson’ views treats the `univocal’ and `equivocal’ dispute between them. It is up to how we interprete (n1). On the one hand, if we interpret `immutable’ in (n1) as ` immutableal’, `immutable’ in (1) and (n1) are univocal.

  • (1al) Christ is immutableal

  • (n1al) Christ is not immutableal

On the other hand, if we interpret `immutable’ in (n1) as ` immutablel’ (as we stipulate when we interpret Anderson’s equivocation view), `immutable’ in (1) and (n1) are equivocal.

  • (1al) Christ is immutableal

  • (n1l) Christ is not immutablel

Even though we tend to prefer the former interpretation, to conclude so we need to scrutinize how `not’ works in (n1), which goes beyond the scope of the present paper. So we leave the question whether `immutable’ in (1) and (n1) is univocal or equivocal as an open question. It is worthwhile mentioning that even though (1al) and (n1l) are not genuinely contradictory in the strict sense that they don’t consititute a pair of a sentence and its negation, the equivocation presented in (1al) and (n1l) doesn’t help us to avoid the conjunction of them to be both true and false: If (1al) is both true and false, and (n1l) is true, then the conjunction of them is both true and false, given LP.

It is important here to emphasize the differene between a predicate with multiple denotations and a merely ambiguous predicate. An ambiguous expression is used in a sentence with one of its meanings. For example, when I say `I went to a bank yesterday’, `bank’ is used to mean a financial bank or a river bank, rather than to mean a financial bank and a river bank. On the other hand, `the denotation of this term plus one’, the term with multiple denotations, is used to mean n and n + 1, rather than n or n + 1. To claim that when `immutable’ is applied to `Christ’, it is used as a predicate with multiple denotations is to claim that it is used to mean its literal and analogical meanings. The predicate `immutable’ would thus be taken as a three-way ambiguous predicate: with its literal meaning, with its analogical meaning, and with its literal and analogical meanings.

This point shows how the present proposal is different from any of ``qua’’ responses to fundamental problem summarized in Pawl (2020, Section 7.4). All responses discussed there consider only two parameters, that is, qua-human and qua-divine. Within this terminology, the present proposal can be taken as considering the third parameter, that is, qua-human-and-divine. Note that the third parameter solves the problem of the qua-response concerning the predicate ``two-natured’’ (cf. Pawl, 2020, 51). The problem is that, even though Christ is two-natured, neither Christ is two-natured-qua-human nor Christ is two-natured-qua-divine. The third parameter enables us to interpret `Christ is two-natured’ as `Christ is two-natured-qua-human-and-divine’.

6 Conclusion

Comparing Beall’s contradictory Christology with Anderson’s MACRUE view, we have pointed out the following implicit assumption in Beall’s view: The predicates that appear in the pairs of sentences that illustrate the fundamental problem are univocal. Even though this assumption has a good reason given the human nature of Christ, it is also the case that the view that such predicates are equivocal has a good reason if we focus on the divine nature of Christ. In this paper, as a way to do justice to the dual nature of Christ – he has both human and divine natures – attested in Conciliar Christology, we presented a semantic explication of how the predicates used to state the fundamental problem are both literal and analogical. Such semantics treats those predicates as cases of multiple denotations. The proposed semantics shows that the apparent inconsistency derived from the dual nature of Christ is genuinely contradictory, but in a different way from Beall’s contradictory Christology.

Before closing this paper, we should mention a limit of the present semantic exposition. In the multiple denotation semantics presented in this paper, a denotation of a predicate is defined as a function from the domain to the set of two truth values {t, f}. Because of this setting, the semantics precludes the possibility that Christ is immutable is literally both true and false (formally, gl([[Christ]]) = t and gl([[Christ]]) = f, which is impossible given gl is a function), which Beall claims that it is the case. Technically, the following revision of the present semantics suffices to semantically implement Beall’s claim: to add the new value b (which represents both true and false) in the range of extension functions, or use relation, rather than function, to define extensions. Once we accept one of those ways of revising the semantics, we get a different version of multiple denotation semantics. Interestingly, a result of such a revision is that (1) (and thus (n1)) is plurivalent: (1) is both true and false (given the univocality of `immutable’ in (1) and (n1) and their truth), but (1) is just true (given that `immutable’ is equivocal in (1) and (n1)). We leave it a topic of future research to explore this option in details.