Islamic Contradictory Theology . . . Is there any such Thing?

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction.

1. Explicit contradictions somehow wear their status—whatever that status might be—on their sleeves. It is sometimes said that contradictions are things it is irrational to accept or to believe, a view that is most plausible when it is only explicit contradictions that are at stake. Implicit contradictions are single statements or pairs which in some way imply, entail, or commit us to explicit contradictions down the line. That something is an implicit contradiction may thus be far from obvious. (Grim in Priest, Beall, and Armour-Garb [42, p. 54]).

2. “For instance, if one claims that \(\mathrm{P(a)} \wedge \lnot \mathrm{P(a)}\), parameterisation holds that one is in effect claiming that \(\mathrm{P}_{\mathrm {1}}\mathrm{(a)} \wedge \lnot \mathrm{P}_{\mathrm {2}}\mathrm{(a)}\) (e.g. elephants are big and not big, because they are big in the context of land animals on Earth, but not big in the context of stars and planets).” [57].

3. PNC is considered, since Aristotle, as a fundamental principle of logic. The predominance of the PNC has prevailed during all the development of occidental culture and civilization, from Aristotle to modern times. But there also have been people proposing a diametrically opposed viewpoint within this same culture. From Heraclitus to Marx via Hegel some people have sustained that contradiction is essential in reality and/or in thought [21, pp. 361–372].

4. See Ripley [59].

5. See Beziau [22] and Slater [66].

6. There are some serious difficulties that arise once you begin fleshing out these understandings. See Ripley [59].

7. It is important to note that at the time of writing this paper, Beall had not published his book entitled ‘The Contradictory Christ’ Beall [16]. The book had already been published when I was revising this paper. Considering this, my reference to Beall’s book is not any substantial sense. Although, I have renewed certain textual quotes from the book. Furthermore, Beall’s book builds on substantial parts of material from the symposium previously published in The Journal of Analytic Theology. Despite this, he presents new aspects of ‘Contradictory Christology’. However, those new aspects are not entirely relevant to my aim in this paper. More importantly, I do not think those new aspects weaken my argument in any direct way. That is because, my argument has very little to do with Beall’s defence of ‘Contradictory Christology’ itself. Instead, my argument is concerned with how the underlying mechanics of ‘Contradictory Christology’ cannot be extended and applied to a given Islamic theological contradiction. Thus, establishing that there can be no such thing as an Islamic contradictory theology.

8. There are, of course, many other systems of sub-classical logics that are more versatile. For instance, FDE logic does not entertain the ‘maximum available truth-values’. There are, in fact, a whole range of logics that admit infinitely many truth values.

9. [18].

10. I acknowledge that Beall [16] is the first of a two-book series. There are of course other existing works. To note a few: Beall [15], Beall and Cotnoir [17], Cotnoir [31], Göcke [40] and Anderson [12].

11. See Ahsan [6].

12. I acknowledge that a corollary of my argument may have some bearing on Beall’s ‘Contradictory Christology’. Beall [15, 16] assumes FDE logic to be the correct account of logic that tolerates ‘Contradictory Christology’. My argument is against FDE logic and alternative systems of sub-classical logics in failing to allow an Islamic contradictory theology. This may have drawbacks on what we assume a correct account of logic to be in virtue of a contradictory theology in general. A contradictory theology, in general, would be inclusive of a contradictory Christian theology such as Beall’s ‘Contradictory Christology’.

13. See part three of Kars [50]. Also see Heck [44].

14. Priest et al. [57] refer to such moves as ‘parameterisation’. “When one is confronted with a seemingly true contradiction, \(\mathrm{A} \wedge \lnot \mathrm{A}\), treat the suspected dialetheia A, or some of its parts, as having different meanings, and hence as ambiguous (maybe just contextually ambiguous). For instance, if one claims that \(\mathrm{P(a)} \wedge \lnot \mathrm{P(a)}\), parameterisation holds that one is in effect claiming that \(\mathrm{P}_{{1}}\mathrm{(a)} \wedge \lnot \mathrm{P}_{\mathrm {2}}\mathrm{(a)}\) (e.g. elephants are big and not big, because they are big in the context of land animals on Earth, but not big in the context of stars and planets).”

15. Notice that phrase “the One in truth.” This reflects a terminological shift from the third to the fourth section of On First Philosophy. Whereas previously al-Kindī spoke only of things that were “accidentally one” as opposed to “essentially one,” now he contrasts things that are “one metaphorically [bi-’l-majāz]” to God, who is “One in truth [al-wāḥ id bi-’l-ḥ aqīqa]” or the “true One [al-wāḥ id al-ḥaqq].” The meaning, however, is the same: what is “metaphorically” one is what is both one and many. The “true One” is only one, not at all multiple. In the rest of On First Philosophy, al-Kindī will therefore try to specify the sense of “oneness” that applies to God. However, he does this largely by enumerating the senses of “one” that do not apply to God. For this reason, al-Kindī’s treatment of how we speak of God—what one might call “theological discourse”—is usually thought of as being thoroughly negative. If this is right then in the end all al-Kindī has to say about God is that we can say nothing: He is utterly ineffable, inaccessible to language or thought. I think it would be more accurate to say that al-Kindī, in these final passages, is surveying the senses in which “one” might be understood, and narrowing down to the correct sense by a process of elimination [1, pp. 53–54].

    Al-Kindī’s one-page description of the “Eternal” [al-Azalī] contains around forty Arabic negative particles. Simply put, God’s being the cause of creation makes Her uncaused, ineffable, unknowable, and utterly transcendent. She is the source of all multiplicity; and She is beyond the multiplicity and unity that belongs to creation. As the true One, She cannot be spoken of in the way creation is spoken of. “God, ‘the true One,’ is completely transcendent, in the precise sense that nothing can be said of Him.” [50, p. 78] Al-Kindī not only negates discursive proofs of the divine essence, but he also closes the door of any non-discursive access to God, including mysticism. God becomes utterly apophatic, inaccessible, and the unknowable ultimate cause and agent [50, p. 81].

16. In this section devoted to “knowledge of the station of the transcendence of divine unity” , makes the philosophical argument that God’s transcendence entails Her exemption from all possible human definitions, attributions, and traits, including Her very unity. Hence, “We can say nothing about the word ‘unity’ when applied to God.” God is made free of any description through the word “unity”; in other words, “oneness” cannot qualify God if God is to be One. Divine unity is like a house that has no door, says ; no one can enter this house, but some can merely peek inside via divine unveiling [50, p. 101].

    on Divine Majesty and Beauty:

    His essence is exalted above all motions and stillnesses, all bewilderment and mindfulness. It is too high to be overtaken by any explanation, express or implied, just as it is too great to be limited and described. ( Translated by Bayrak and Harris in Renard [14, p. 182]).

17. For early , in line with Plotinus (d.270), God was the unknowable absolute One who can be neither comprehended by reason nor accurately described. Their doctrine removed all the attributes, including “being,” from God, and unlike the majority of the , they kept Her essence utterly unknowable and ineffable [50, p. 26].

    Within this cosmology, Ibn al-Wālid’s God is utterly unknowable, far beyond comprehension, limitation, or definition. Discourse cannot reach anything about Her; anything that can be known or spoken of is created. The Originator is not a body, not a substance, not an accident, not a matter, not a form, not in space, not in time, not comparable to anything, not speakable, and so forth [50, p. 55].

18. Abū Ḥāmid al-Ghazālī most famously had a distinctly negative approach to language concerning God. In the Highest Aim [al-Maqṣad al-Asnā], al-Ghazālī adopts all the principles of a philosophical apophaticism. The unknowability of the divine essence is strongly emphasized, again and again underlining that the highest knowledge concerning God is one’s own incapacity to know—docta ignorantia. Not only divine essence but even divine attributes cannot be known to us as much as they relate to the divine essence. We can only imagine divine attributes through comparison with their created counterparts, but their reality is beyond human conception, imagination, and intellection. Contrasting negative and positive language concerning the divine essence, al-Ghazālī finds the former superior. Accordingly, negations contain a latent praise of God more powerful and correct than positively describing Her with qualified attributes:

    Since there is no likeness of Him, none knows His essence other than He. So al-Junayd . . . was right when he remarked: “none knows God except God.” For that reason, He gave even His noblest creature a name, with which He veiled Himself, as He said: “Praise the name of your Lord Most High” [Q.87:1]. So, by God, none knows God except God, in this world, or the next.

    On his deathbed, Dhū al-Nūn was asked, “What do you long for?” He replied: “That I knew Him before I die—be it for an instant.” Now, this confuses the hearts of most of the weak, and leads them to the delusion of negation [nafy] and ineffectualism . . . . I say: if someone were to say “I do not know God,” that would be true. And if they were to say “I know God” that would also be true. . . .

    This would be the case were a person to ask another, “Do you know Abū Bakr, the faithful one?” . . . If one replied, “Who does not know Abū Bakr, or is ignorant about him? Given the visibility, fame, and renown of his name, is it conceivable that anyone in the world doesn’t know him? . . .” This reply would be true. . . .

    But if another were asked, “Do you know him [Abū Bakr, the faithful one],” and replied “Who am I to know the faithful one? Alas, far from it! None knows him except himself, or someone who is like him or above him. Who am I to claim to know him or even hope for that? People like me hear his name and attributes, but as for claiming to know him—that is impossible.” This is also true—indeed, this proposition has an aspect, which comes closer to the due glorification and homage.

    In the following discussion, al-Ghazālī gives other examples as well, in order to point out that the negative language is superior to positive language concerning the divine essence. His association of the negative language with praise, and the principle of unknowability, none knows God except God, clearly resonate with al- Baṭalyawsī, Maimonides, and the Arabic Aristotle among others [50, pp. 124–125].

19. It is worth noting that the sort of unknowability that I am ascribing to the Islamic God is not the kind that is manifested in theology. The feature which distinguishes my idea of unknowability from is that I don‘t think anything is impossible for an absolute transcendent God while they assume it is. The distinction that I am drawing on can be better appreciated in the extract below:

    From the beginning of their movement in the mid- third/ ninth century, had developed a cosmology that was heavily influenced by a set of Neoplatonic ideas and that interpreted God‘s divine unity (tawḥīd) in a radical way. For philosophers and theologians, tawḥīd meant that God is absolutely transcendent and cannot in any way be part of this world. He is beyond being and beyond knowability. God‘s absolute transcendence makes it impossible that He causes anything in His creation, since that would require some immanence on His part. [41, p. 219]

    .

20. God does not inhere in anything, and nothing inheres in Him. He is exalted above being contained by space, and too holy to be bounded by time; on the contrary, He existed before He created time and space. He now has [the attributes] by which He was [previously characterized], and is distinguished from His creatures by His attributes. There is not in His essence what is other than He, nor in what is other than He is there [anything of] His essence. He is exalted above change [of state] and movement. Originated things do not inhere [or subsist] in Him, and accidental [events] do not befall Him. Rather, He does not cease; through the qualities of His majesty He is beyond cessation, and through the attributes of His perfection He is independent of [or does not require] any further increase of perfection. (al-Ghazālī translated by Watt in Renard [38, p. 110]).

21. Heck [44] quotes the same passage from    al-Ghazālī. He goes on to make the following remarks thereafter.

    In other words, the philosophers obtain only ignorance of God through philosophical reasoning, but the mystically aware scholars realize that all existence is one. They do not see God but rather see all things as being with God, coming to know things as they really are through mystical insight beyond philosophical reasoning. Thus, the philosophical scholastic should say, “No one other than God knows God.” But the mystical scholastic can say, “I know only God.” By virtue of learned ignorance (again, Ghazali speaks of it as a comprehension that comes from the inability to comprehend), one sees that what one had previously known through philosophical reasoning to be other than God is not other than God. There is nothing in existence other than God and God’s works. Ghazali thus calls us to view sky, earth, and trees not as they are but as they are with God—in the sense of having their origin in God and so always being with God. As one claims to see only the sun when beholding its rays stretching across the mountains, one can say, “I know only God and I see only God.” All things are lights and traces of God’s unfathomable power [44, p. 119].

22. Though, I acknowledge that there are contradictions that ensue from specific beliefs related to the Islamic God Himself. These are not contradictions that ensue from the conjunction of certain beliefs in God and observable phenomena in the world. A notable example would be pertaining to God’s essence and attributes, which manifests an unequivocal defiance of the law of non-contradiction. This is articulated in Nasafī’s Māturīdī Creed as “God has pre-eternal attributes subsisting in His essence. They are not He and nor other than He.” (Nasafī’s Māturīdī Creed translated by Watt in Reynolds, [53, p. 114]) Focussing on the latter claim of this short excerpt, this article of faith would evidently be deemed false. By standards of classical logic, it would result in a contradiction and thus be ruled out a priori. The logical form of this statement would be represented by way of a double negation as follows: \((\lnot F(a) \wedge \lnot (\lnot F(a))\). This would read as: object a does not have property F and nor does it not have property F. This logical notation can equally be represented as (\(a \wedge \lnot a)\) since according to the equivalence relation any instant of a double negation such as \(\lnot \lnot a\) can be replaced by a without altering the truth value. See Ahsan [11].

23. Aside from the paradoxical representation of both unknowability and ineffability, there is a distinction to be made between them. Hofweber [47] refers to this distinction in the following manner: “Ineffable facts, if there are any, are completely beyond us, unknowable and beyond what we can consider or entertain. Ineffable facts thus can be more hidden from us than merely unknowable ones or merely incomprehensible ones. All ineffable facts are unknowable and incomprehensible, but not the other way round. We will never know whether the number of grains of sand on earth exactly 500 million years ago was odd or even, but we can represent both options. And we might never comprehend or understand why anything exists at all, even though we can easily represent this fact.” [47, p. 251]. Also see Hofweber [48].

24. Given the fact that—“God is a being necessarily existing of Himself (al-mawjud al-wajib al-wujud bi-dhatihi)” (Maqsad 47, M 342–43), it should be clear that this—“peculiar divine property belongs only to God and only God knows it.” Moreover—“it is inconceivable that anyone know it save Him or one who is His like, since He has no like, no other knows it.” On such an account,—“only God knows God” (ibid.). So the resources of philosophy confirm God‘s uniqueness or tawhid: the utter distinction of the One from all else: —“everything the exercise of which is possible,” which does in fact exist from that One—“according to the best ways of order and perfection” (Maqsad 47, M 342) [25, p. 181].

25. I’m thinking of John Hick’s idea of ineffability here. See Hick [45]. Also see Gäb [37].

26. I have formulated both contradictions on Fitch’s paradox of knowability. See Kvanvig [52] and Salerno ed. [64]. I think it manages to represent both theological contradictions more closely to al-Ghazālī’s articulation of the paradox. Moreover, it accurately reveals their self-referential nature.

27. See my forthcoming paper entitled ‘Islamic Mystical Dialetheism Resolving the Paradox of God’s Unknowability and Ineffability’ [10]. Also see Ahsan [2,3,4,5, 7, 8].

28. I am referring to a rejection of the most basic condition of any given formal theory of truth. For instance, Tarski’s notable Convention T, which involves the schema (T). This condition, for Tarski, was the fundamental condition for any truth-theory that entailed sentences of the form: (T) X is true if and only if p.

29. See Ahsan [9].

30. You could consider inflationary and deflationary types of truth theories as types of theories that are metaphysically significance and metaphysically vacuous/trivial respectively.

31. See my forthcoming paper entitled ‘Islamic Mystical Dialetheism Resolving the Paradox of God’s Unknowability and Ineffability’ [10].

32. The notion of “logical space” was first introduced by Wittgenstein during his stay in Krakow in autumn 1914 while he was serving in the Austrian army. The considerations that finally led to the idea of an abstract space whose internal structure represents all the logic that underlies our ordinary language are well preserved in the first two wartime notebooks (MS 101, MS 102). They belong to a rapidly developing series of ideas which also includes an early version of the picture theory of proposition. They form an important part of the preliminary work for the Tractatus, the first draft of which—the so-called Prototractatus (preserved in MS 104)—Wittgenstein started to write down some time later in summer 1915 [54, pp. 15–16].

33. I believe but, for present purposes, shall only assume that FDE is the correct account of logic . . . [15, p. 408].

34. I am using ‘semantic values’ as opposed to ‘truth-valuations’ here. The reason for this is, by ‘semantic values’ I am thinking of the actual meaningful import we may be able to derive from assigned truth-valuations. While my use of ‘truth-valuations’ is a mere assigning of truth-values.

35. Note that it is now very important to distinguish between being false in an interpretation and not being true in it. (There is, of course, no difference in the classical case.) The fact that a formula is false (relates to 0) does not mean that it is untrue (it may also relate to 1). And the fact that it is untrue (does not relate to 1) does not mean that it is false (it may not relate to 0 either) [55, p. 143].

36. See Caret and Hjortland ed. [26]. Also see Russell [62] and Fisher [35].

37. Logical consequence is a relation among claims (sentences, statements, propositions) expressed in a language. An account of logical consequence is an account of what follows from what—of what claims follow from what claims (in a given language, whether it is formal or natural). An account of logical consequence yields a way of evaluating the connections between a series of claims—or, more specifically, of evaluating arguments [19, p. 3].

38. Equivalently, we can think of the logical consequence with a no counter model definition: \(\Gamma \models \mathrm{A}\) if and only if there is no (counter-)model M such that every \(\mathrm{B} \in \Gamma \) is true in M, but A is false in M [26, p. 4].

39. See Russell [60] and Blake-Turner and Russell [23].

40. Let X be any set of L sentences, and A any sentence of L. Fact: if \(X \vdash _{\mathrm {FDE}} A \) then \(X \vdash _{\mathrm {CL}} A, X \vdash _{\mathrm {K3}}A\), \(X \vdash _{\mathrm {LP}} A\) [18, p. 187].

41. Logical pluralism is certainly not confined to Beall and Restall [19]. Among some of the logical pluralists you have: Carnap [27, 28], Shapiro [65], Hjortland [46], and Bueno and Shalkowski [24]. As Eklund [34] mentions, the debate between logical monists and logical pluralists is one of the most central debates that occupies contemporary philosophy of logic.

42. See Kellen [51].

43. On a standard conception, even God is subject to the laws of logic, His omnipotence dulled by the logical impossibility of creating a Rock So Heavy He Himself Cannot Lift It. Even devout theists seem to think that it is not God, but logic, that is the final arbiter of what is possible and what is not. And yet, humble pluralism suggests that when reckoning with impossibly heavy rocks, maybe God should not take Himself to be limited to classical logic [68, p. 110].

44. FDE thus broadens the space of cases acknowledged by the other theories: it broadens the LP [Logic of Paradox] space of cases by the admission of incomplete [paracomplete] cases; it broadens the K3 [Strong Kleene] space of cases by the admission of inconsistent [paraconsistent] cases; and it broadens the CL [Classical Logic] space of cases in both of these ways [18, p. 179].

45. Classical logic contains all of the following theorems and rules of inference:

    Double Negation: \(\mathrm{A} \leftrightarrow (\sim \sim \mathrm{A})\)

    Excluded Middle: \((\mathrm{A\, v} \sim \mathrm{A})\)

    Non-Contradiction: \(\sim (\mathrm{A} \wedge \sim \mathrm{A})\)

    DeMorgan’s Laws: \(\sim (\mathrm{A} \wedge \mathrm{B}) \leftrightarrow (\sim \mathrm{A \,v} \sim \mathrm{B}), \sim \mathrm{(A\, v \,B)} \leftrightarrow (\sim \mathrm{A} \wedge \sim \mathrm{B})\)

    Explosion: \((\mathrm{B} \wedge \sim \mathrm{B}) \rightarrow \mathrm{A}\)

    Monotonicity: If \(\Delta \) entails A, then \(\Delta \), \(\Phi \) entails A.

46. A case is a structure \(\langle D, \delta \rangle \) where D is the domain and \(\delta \)provides denotations of all names, and provides extensions and antiextensions to all predicates. If \(\Pi \) is a predicate, we write \(\varepsilon _{{{\Pi }}^{+}}\) for its extension and \(\varepsilon _{{{\Pi }}^{-}}\) for its antiextension. . . we stipulate also that all objects of the domain (of any case) have a name in our language. In the formal theory, exclusion and exhaustion can be stated concisely as follows: Exhaustion. For any n-ary predicate \(\Pi \), \(\varepsilon _{{{\Pi }}^{+}} \cup \varepsilon _{{{\Pi }}^{-}} = \mathrm{D}^{n}\). Exclusion. For any predicate \(\Pi \), \(\varepsilon _{{{\Pi }}^{+}} \cap \varepsilon _{{{\Pi }}^{-}} = \emptyset \) [18, pp. 203–204].

47. See Priest [56].

48. For responses to the first view see Ahsan [8]. For responses to the second view see my forthcoming paper entitled ‘Islamic Mystical Dialetheism Resolving the Paradox of God’s Unknowability and Ineffability’ [10].

49. See Russell [60,61,62], Blake-Turner and Russell [23], Cotnoir [32, 33] and Franks [36].

50. There are a range of details that need to be specified when proposing a model. First, we need to carefully specify both what object xis being proposed as a model and what object ywe will be using x as a model of. We call the thing being modeled the target system of the model, and we call the object x a model of the target system. After specifying these, we still need to specify the exact way in which x is being seen as similar to y. These assumptions—the assumptions that x is similar to y in these particular ways —are called modeling hypotheses. [18, p. 14].

51. To do this, of course, we must specify the target system of our models—the parts of natural language whose logical consequence relation we are attempting to model, as well as the modeling hypotheses—the particular aspects of the natural language relation of logical consequence that we are supposing are similar to the relations we highlight in our models [18, p. 15].

52. The modelling hypothesis has limitations as Cotnoir [32, 33] has highlighted.

53. An isomorphism is a homomorphism between two structures that is also bijective. In other words, if there is an isomorphism between two structures, then they have exactly the same formal features [30, p. 161].

54. Beall and Logan [18] provide the following example: let’s look at a well-known example of modeling from the sciences: Watson and Crick’s production of an actual tin-and-cardboard double-helical structure as a model of the DNA molecule. The target system of their model was the DNA molecule. The tin-and-cardboard structure they build was their model of the DNA molecule. And, finally, their modelling hypothesis was that the shape of the two structures were generally similar. Importantly, the tin-and-cardboard structure was different in many ways from an actual DNA molecule. In particular, as Ronald Giere has amusingly observed, Watson and Crick were not proposing that their model was similar to an actual DNA molecule in the sense that both were composed of tin and cardboard [18, pp. 14–15].

55. A homomorphism between two structures is a function f from one structure to the other (plus a correlation between functions or relations on the first structure and functions and relations on the second structure) such that the function f is structure-preserving. In other words, if f is a homomorphism between two structures, then, for any relation R on the first structure, and the corresponding relation S on the second structure, we have: R(x, y) if and only if S(f(x), f(y)) and, for any binary function g on the first structure and corresponding function h on the second structure, we have: f(g(x, y)) \(=\) h(f(x), f(y)) [30, p. 139].

56. See Glanzberg [39].

57. See footnotes 15 to 24.

Authors and Affiliations

1. Department of Philosophy, University of Birmingham, Birmingham, UK

   Abbas Ahsan

Corresponding author

Correspondence to Abbas Ahsan.

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