I believe that the logical problem of evil presents a powerful internal critique against the existence of a traditionally conceived monotheistic God (omnibenevolent, omnipotent, omniscient).

The logical problem of evil is an argument that aims to establish a logical contradiction between the existence of an omniscient, omnibenevolent, and omnipotent being (Tri-Omni) and the presence of evil in the world. If successful, this argument would render the existence of such a being logically impossible, as it would involve a contradiction akin to asserting both P and ¬P simultaneously.

The popular focus among scholars is now on the evidential problem of evil and not the logical problem of evil. The evidential problem of evil argues that the existence and nature of evil in the world, including gratuitous or apparently unnecessary suffering, make the existence of an omni-trait God (omnibenevolent, omnipotent, and omniscient) less probable. This problem focuses on the apparent disconnect between the amount, intensity, distribution, and specific instances of evil (e.g., a deer suffering in a forest fire) and the idea of a loving, all-powerful, and all-knowing God who could prevent such evils without compromising a greater good.1 This makes the existence of such a being unlikely on evidential terms.

Some even consider the logical argument debunked following Plantinga's Free Will defence. I disagree. I believe that the free will defence fails for several reasons, such as (a) the possibility of humans having morally significant free will in heaven yet cannot do any wrong, and also (b) God's status as a moral agent with free will yet being ontologically good and not able to do any wrong: both entailing that a world where creatures only do what is good is logically possible on conventional theism.

This entry's main goal is not to argue for this specific case, but rather to demonstrate that, through the logical problem of evil, the concept of 'evil' becomes incoherent under theism.

The Incoherency of ‘Evil’ Under Theism

In the following presentation of the argument, I bypass the free will defense by framing the concept of "good" in the traditional sense—as what ought to be done, in accordance with God's desires. This approach leads to a difficult choice for the theist: either relinquish one of God's Tri-Omni traits or deny the existence of evil altogether.

This is because, under this interpretation, the concept of evil—defined as what ought not to be done, based on God's desires—becomes incoherent when considering an omniscient, omnibenevolent, and omnipotent God who is infallible in His desires. The existence of evil, as understood in this context, contradicts the infallibility of such a being, since all events that He brings into existence align with His desires and therefore ought be done; they are considered good in an all-things-considered sense. In other words, in virtue of what would an evil event be evil if it is permitted in order to bring about a greater good, an all-things-considered good? In this sense it ought be done and is therefore good, not evil.

Key Terms

To better understand this argument, it is essential to define the key terms and concepts involved:

1. Good and evil: ‘Good’ in philosophy is often construed as being analytically equivalent to the action guiding norm, which is to say, what ought be done. And 'evil' is just the opposite of good, that is, what ought not be done. In the context of theism, good and evil are traditionally construed in reference to God's desires. Good actions or events align with God's desires, whereas evil actions or events contradict them.

2. Pro toto: This term refers to something that is "all things considered," taking into account all relevant factors. If something is deemed "all things considered good" or "pro toto good," it means that after taking into account all relevant factors and possible consequences, the action or outcome is still considered to be desirable. Note that I have used ‘pro toto’, ‘all things considered’, ‘greater good’ and ‘ultimately’ as coextensive terms, but have interchanged them to give readers a broader sense of the idea.

3. God's omni properties: These are the qualities attributed to God, such as omnipotence (all-powerful), omniscience (all-knowing), and omnibenevolence (all-good). Infallibility with respect to God's desires means that God cannot err or be mistaken in what He desires.

4. God's instantiation or permission of all logical/actual events: This idea suggests that everything that occurs/exists or can logically occur/exist does so either because God directly causes it (instantiates) or allows it to happen (permits).

5. Maximally good: This term implies that God is the greatest possible good, without any flaws or imperfections and he will only do what is all things considered good. It is interchangeable with ‘omnibenevolence’.

The Argument in Plain English

1. Good is coextensive with what ought to be done.

2. Evil is coextensive with what ought not to be done.

3. Under theism, good/evil is construed in reference to God's desires.

4. God's Omni properties include His infallibility with respect to His desires.

5. God is maximally good.

6. God instantiates or permits all actual and logically possible events.

7. If God is maximally good, is infallible with respect to his desires, good/evil is construed in reference to His desires, and He instantiates or permits all actual and logically possible events, then all events, including evil events, ought to happen are are therefore ultimately (i.e., all things considered) good.

8. All events, including evil events, ought to happen and are therefore ultimately good.

9. If all events, including evil events, ought to happen and are ultimately good, and evil is what ultimately ought not happen, then it is logically impossible for there to be any evil in the world on theism.

10. It is logically impossible for there to be any evil in the world on theism.

11. If it is logically impossible for there to be any evil in the world on theism, and good/evil is construed in reference to God's desires on theism, then the existence of evil is incoherent on the theistic framework.

12. The existence of evil is incoherent on the theistic framework.

13. To resolve the incoherence, a theist must either deny the existence of evil or give up on one of God's omni properties.

To use an analogy, imagine a situation where getting pricked by a needle is considered bad because it causes pain. However, if the needle prick is necessary for administering a life-saving vaccination, then the pain caused by the needle is outweighed by the greater good of the vaccination. In this case, the needle prick, which is initially considered bad, ought to happen and is therefore ultimately good.

Consider the Holocaust, which is widely regarded as a horrific and evil event. Within the context of the argument, if the Holocaust was necessary to bring about some greater good (such as the allowance of free will), then it ought to have occurred, making it good and not evil (given that that evil is analytically equivalent to the converse of that, i.e. what ought not be done). God must have permitted the Holocaust to occur for the sake of this greater good, and therefore the Holocaust ought to have happened, and what ought to happen cannot be evil. It is counterintuitive to say, "I believe that X is all-things-considered good, but it ought not to happen." If something is deemed "all-things-considered good" or "pro toto good," it means that after taking into account all relevant factors and possible consequences, the action or outcome is still considered to be desirable.

The idea is that, whatever the ‘greater good’ is, free will, the lessons learned, the ability to appreciate things etc., if it necessitates an evil event to first occur, then that evil ought be done, and is therefore a good event and not an evil event. If something is done for the sake of the ‘greater good’ (such as getting pricked by a needle) then it ought be done, and what ought be done is coextensive with what is good. On the theistic framework, then, the existence of evil is simply incoherent because all events God permits ought be done, all things considered. The only way to get out of this problem, it seems to me, is for the theist to deny the existence of evil or give up on one of God's omni properties. 

Argument in Formal Logic

Let's assign propositional variables to the main ideas in the argument:

P1: Good is coextensive with what ought to be done (G).

P2: Evil is coextensive with what ought not to be done (E).

P3: Under theism, good/evil is construed in reference to God's desires (T).

P4: God's Omni properties include His infallibility with respect to His desires (I).

P5: God is maximally good (M).

P6: God instantiates or permits all actual and logically possible events (P).

C1: Under theism, all events, including evil events, are ultimately good and ought to have happened (C1).

C2: It is logically impossible for there to be any evil in the world on theism (C2).

C3: The existence of evil is incoherent on the theistic framework (C3).

Now we can express the argument using propositional variables and logical operators:

1. (G)

2. (E)

3. (T)

4. (I)

5. (M)

6. (P)

7. ((M ∧ I ∧ T ∧ P) → C1) [If God is maximally good, is infallible with respect to his desires, good/evil is construed in reference to His desires, and He instantiates or permits all actual and logically possible events, then all events, including evil events, are ultimately good and ought to have happened]

8. (C1) [From 3, 4, 5, 6, and 7, modus ponens]

9. ((C1 ∧ E) → C2) [If all events, including evil events, are ultimately good and ought to have happened, and evil is what ought not to be done, then it is logically impossible for there to be any evil in the world on theism]

10. (C2) [From 2 and 8, and 9, modus ponens]

11. ((C2 ∧ T) → C3) [If it is logically impossible for there to be any evil in the world on theism, and under theism, good/evil is construed in reference to God's desires, then the existence of evil is incoherent on the theistic framework]

12. (C3) [From 3 and 10, and 11, modus ponens]

This structure represents the idea that given the premises P1-P6, the conclusions C1, C2, and C3 logically follow.

Truth Table

To create a truth table for this argument, we need to list all possible truth values for the six premises (P1-P6) and then determine the truth values for the conclusions (C1, C2, C3) based on those premises. Since there are six premises, there are 2^6 = 64 possible combinations of truth values.

Here's the truth table:

In this table, "T" represents true, and "F" represents false. The first six columns represent all possible combinations of truth values for the premises (P1-P6). The next column evaluates the logical conjunction (M ∧ I ∧ T ∧ P) and, subsequently, determines the truth values for C1, C2, and C3 based on the truth values of the premises and the logical operators specified in the argument.

The argument is valid because, in every row of the truth table where all premises are true, the conclusions C1, C2, and C3 are also true. Therefore, if the premises are accepted as true, the conclusions necessarily follow.

Possible Objections and Replies

There are some possible objections to this argument:

1. Objection: Permissive vs Perfect Will distinction

One objection is the distinction between God's permissive will and His perfect will. According to this view, while God permits evil events to occur, He does not necessarily desire them in the same way as He desires good events. Instead, He may allow evil events for a greater purpose, such as preserving free will or achieving a greater good that would not be possible without the existence of evil.

Reply to objection 1:

The argument addresses this by stating that if an evil event is necessary to bring about a greater good, then that evil event ought to be done and is therefore good, not evil. This counter-objection circumvents the distinction between God's permissive will and His perfect will, it operates within the theistic framework where the greater good is understood in relation to God's nature and desires. Within this framework, it is assumed that God, being maximally good and infallible, would only allow evil events to occur if they were necessary to achieve a greater good, as part of His ultimate plan.

2. Objection: Challenging good-ought tie up

Another potential objection is questioning the absolute coextensiveness of "good" and "ought," arguing that there might be cases where what is good is not necessarily what ought to be done, or vice versa. This could apply in situations involving moral dilemmas or conflicting moral obligations, where what ought to be done is not straightforward.

Reply to objection 2: This objection is not relevant, given that the argument is focused on the pro toto sense of good, encompassing the "all things considered good" concept. When considering the pro toto sense of good, the relationship between good and ought is more straightforward. If an evil event is necessary for achieving a greater good, then is it ought to be done; and therefore good. So the Holocaust ought to have happened because it brings about a great good (e.g., creaturely free will and God’s intervention would otherwise breach this greater good).

3. Objection : The concept of God's providence and mysteriousness

Some theists may argue that human understanding is limited, and thus, we cannot fully comprehend the divine plan or God's ultimate purposes. The notion of providence suggests that God has a plan that goes beyond human understanding, and the existence of evil might be part of this larger plan. This objection posits that we cannot be sure if our interpretation of good and evil is aligned with God's divine intentions, and therefore, it might be premature to declare evil as incoherent within the theistic framework.

Reply to objection 3:

I will reply to this by explicating Stephen Law's paper "Skeptical Theism and Skepticism About the External World and Past". It it, he focuses on the implications of accepting skeptical theism for our broader epistemic commitments. Law engages with the following two skeptical theist's claims:

1. The "No Good Reason" claim: We have no good reason for supposing that God would not allow the evils that we observe in the world.

2. The "No See-um" claim: If we are unable to identify a reason for God to allow an evil, this is not good evidence that there is no such reason.

Law argues that if we accept these two claims, we risk undermining our confidence in inductive reasoning and our beliefs about the external world and the past. He develops his argument by drawing parallels between skeptical theism and two forms of skepticism: skepticism about the external world (hinge skepticism) and skepticism about the past (inductive skepticism).

Hinge skepticism is the idea that we cannot have any knowledge about the external world. Law compares this to skeptical theism by pointing out that, in both cases, we are acknowledging that our understanding and knowledge might be limited. All these forms of skepticis hinge on the recognition of our cognitive limitations and the possibility of hidden reasons or factors that we cannot grasp. Accepting skeptical theism due to our limited understanding means that our understanding may also be limited in other areas, such as our knowledge about the external world and the past.

Inductive skepticism is the view that we cannot be certain about the truth of our beliefs based on past experiences. Law contends that skeptical theism undermines our confidence in inductive reasoning, as it suggests that there may be hidden reasons or factors beyond our comprehension that render our inductive conclusions incorrect or unreliable. This leads us to doubt our knowledge of the past, resulting in inductive skepticism.

In the paper, Law uses several thought experiments to illustrate his points. For example, he introduces the character of "Paul," who is presented with various scenarios that raise doubts about the reliability of his beliefs about the external world and the past. Law argues that if Paul accepts skeptical theism, he should also accept skepticism about the external world and the past, as both hinge on similar epistemic concerns.