Essay on Beall’s God, Gluts and Evil.

	In “God, Gluts and Evil”, Beall presents a novel approach to the logical problem of evil, through employing a glut-theoretic approach rooted in non-classical logic. Beall suggests that by incorporating dialetheism (the believe that sentence can have both a true and false value) and accepting true contradictions – gluts – in the theological understanding of some of God’s attributes, we can reconcile the coexistence of an omnipotent, omniscient, and omnibenevolent God with the existence of evil in the world. This essay will aim to critically examine Beall’s proposal within the context of two paraconsistent logic systems (FDE and LP) and consider the philosophical implications of Beall’s approach in traditional theism. 

	The logical problem of evil has challenged the coherence of traditional theism. It posits the apparent contradiction between the existence of an all-powerful, all-knowing, and all-good God and the presence of evil in our world. Beall resolves this contradiction by first affirming the traditional formulation of the problem of evil, with involves the following propositions: 

God is omniscient and knows how to eliminate evil. (O) 
God is omnipotent and has the power to eliminate evil. (K) 
God is omnibenevolent and desires to eliminate evil. (R)
 Evil exists in the world. (E)
	In classical logic, given the theological premises of God and the existence of evil, the simultaneous truth of these propositions appears inconsistent, leading to the conclusion that either one of (1) - (3) is false, or (4) is false. The entailment relation that should follow from (1) to (3) is as follows: 
Evil does not exist in the world.  (¬E) 
Given (1) to (3), O ∧ K ∧ R ⊢ ¬E  
However, given that (4) is true, it follows that (5) must be false. Given the entailment relation that is present in (6), (5) must be true following from (1) to (3). There is a contraction in (4) and (5). Beall attempts to prevent the entailment in (6) by changing (1) and (2) from statements that are true, into gluts, in which case the falsity component in gluts will filter out the otherwise valid logical entailment in classical logic.
Beall's argument relies on paraconsistent logic, which permits the coexistence of contradictory statements without collapsing into triviality—where every statement becomes provable. In paraconsistent logic, the principle of explosion (ex contradictione quodlibet) is rejected, allowing contradictions to exist without rendering the system incoherent and unusable. 
Beall justifies why (1) and (2) are gluts by pointing out paradoxes that exist in theology surrounding (1) and (2). For example, the paradox of the stone is listed as one example in which (1) exhibits glutty properties. The paradox of unknowability is another example in which (2) exhibit glutty properties. By accepting these contradictions, Beall argues that the falsity that is present in (1) and (2) prevents (6) from being true, thereby resolving the logical problem of evil through the filtering effect of falsity. 
However, it is unclear if Beall has a robust reason for considering why (1) and (2) should exhibit glutty properties. Accepting that God's attributes are both true and false raises semantic issues regarding the meaningfulness of these predicates. If "God is omnipotent" and "God is not omnipotent" are both true, the term "omnipotent" loses its definitive meaning, leading to semantic confusion. In classical logic, predicates must have clear truth values to maintain coherence in discourse. The acceptance of gluts for divine attributes requires a robust justification, especially since these attributes are traditionally considered perfections in theology. Beall attempts to circumvent this by claiming that axiomatically God is perfection, hence claims about whether (1) and (2) will undermine the perfectness of God is unfounded as long as an argument for why perfection should not be axiomatic has not been suggested, but this is still unsatisfactory, given the lack of semantic clarity as to what (1) and (2) would mean if they are both considered gluts. 
For example, the monotheism inherent in theology is not assured if (1) and (2) are considered gluts. It becomes possible for the existence of multiple different theologies, given the fact that premises (1) and (2) are crucial for the entailment that monotheism is true. The same reasoning that can be used to explain contradictions within theology (such as the problem of evil) can be used to explain contradictions across theology. Given that, an acceptance of (1) or (2) as glutty can lead to the conclusion that it is logically possible for there to be multiple coexisting monotheistic theologies, which is a radical solution for any theology that involves a god with properties (1) to (3). 
This instability affects not only theological discourse but also the meaningfulness of worship and religious practice. Believers rely on the understanding that God's attributes are coherent and trustworthy. If these attributes are contradictory, it undermines the basis for faith and devotion, or it requires a radical rethinking and restructuring of their beliefs in view of the fact that God contains contradictory properties through paraconsistent logic.  
From a wider perspective, the use of gluts in theology has the risk of reducing many theological arguments to trivialities. This has already been demonstrated by Chowdhury (2020), who applied Beall’s conception of gluts to Islamic theology to resolve the longstanding debate between traditionalist Islamist viewpoints about the perfectness of the Quran. There has also been a similar effort by Beall to resolve the issue of free will using gluts, amongst other contradictions present in Chrisitian theology (Beall 2023). Such discourse over the truthfulness of apparently contradictory statements, and the subsequent ideas that have arisen from trying to resolve such contradictions, has been an important driver of theology (and other fields of philosophy). On the contrary, accepting some of these statements as gluts almost seems to reduce most of these philosophical inquiries to trivialities.
Additionally, the proposal does not provide a positive explanation for the existence of evil but rather blocks the logical entailment that would necessitate its non-existence. This approach seems more like an evasion than a solution. The contradictions in God's attributes do not illuminate why evil exists; they merely prevent the classical inference from proceeding. This lack of explanatory power weakens the efficacy of Beall's proposal in addressing the problem of evil; it invites criticism of his solution as being incomplete as it does not deal with the stronger, more problematic evidential problem of evil. Beall himself acknowledges this, when he admits that “the apparent problem is not principally a logical inconsistency (which, on the current approach, is just one of many logical possibilities); it’s rather an unwavering commitment to (7) [evil existing in the world] ‘just being false’” (2023). 
Furthermore, alternatives have been proposed to resolve the contradiction in (1) and (2), such as the free will defence by Plantinga (1974), which offers an explanation for the logical problem of evil without introducing gluts into (1) and (2). Rather, (1) and (2) are redefined in terms of logical possibility, which would resolve the apparent paradoxes in (1) and (2) through the use of modal logic rather than paraconsistent logic, which is a more widely accepted logical system to resolve the problem of evil. 
Beall also did not specify which paraconsistent logical system he is committing to using to prove why (6) is defeated by falsity filtering effect, but it seems likely that the logic system he is applying is either LP or FDE, which both block disjunctive syllogism. While it is not necessary for diathesism to commit to a particular paraconsistent logical system, analysing his argument through these paraconsistent logical systems can be helpful in understanding his argument.
For FDE, we can consider (1) to (4) from the perspective of FDE semantics. (1) to (2) have the truth-value of B, (3) has the truth-value of T. Considering the entailment (6):
(O ∧ K) has the truth-value of Both
(O ∧ K) ∧ R has the truth value of Both
	The entailment (6) requires that whenever the premises are designated (i.e., T or B), the conclusion (5) must be designated. However, given (8), the possible designations for (5) is either B or T. Given that (5) can be B or T, (4) can coexist with (5) if (5) is Both. Rather than denying the entailment (6), it allows for (6) to simultaneously exist with (4) without contradiction. 
	The same can be considered for LP. Using prior designations of (7), the entailment (6) holds if the premise is true and the conclusion is true. The difference in LP comes in (8), which needs a modification:
(O ∧ K) ∧ R has the truth value of True. 
	Given that in LP, there are no contradictions if a statement and its negation is true, there is no logical inconsistency in having both (4) and (5) existing within the same logical space. 
	Overall, Beall's proposal has an intuitive appeal that overcomes the complexities of the problem of evil through an acceptance of gluts, but the acceptance of gluts into theodicy itself introduces severe, unresolved problems for theology as a whole. While it remains consistent in FDE and LP paraconsistent logic systems, it is still not wholly clear if these systems offer satisfactory answers to theological questions.



References:
Beall, Jc, and Michael DeVito. Entailment, Contradiction, and Christian Theism. Cambridge University Press, 2023, pp. 30 - 31. 
Plantinga, Alvin. God, Freedom, and Evil. Harper & Row, 1974.
Safaruk Zaman Chowdhury (2020): God, Gluts and Gaps: Examining an Islamic Traditionalist Case for a Contradictory Theology, History and Philosophy of Logic

	


Give a strong critque of this essay from the perspective of a lecturer teaching non-classical logic at a university.