Notes: Is Evil Evidence?

Mike Almeida of the University of Texas at San Antonio aims to deliver a blow to the evidential argument from evil. Skeptics have wielded suffering and evil as evidence against God's existence, while others have marshaled goodness and beauty as evidence in God's favor. Almeida argues in his 2022 paper that if we accept S5 modal logic (the most widely endorsed framework for understanding metaphysical necessity), then this entire evidential line of argument collapses into logical contradiction.¹ If Almeida's thesis is sound, then counterintuitively, earthquakes and genocides might constitute evidence for God's existence, while moral perfection and eliminated suffering might be evidence against it, at least until we were to know with certainty whether God exists or not.

Summarizing Almeida's thesis

1. The traditional God (omnipotent, omniscient, and morally perfect) either necessarily exists or is impossible since there's no middle ground.

2. In S5 modal logic, every possible state of affairs trivially entails whatever is metaphysically necessary, including whether God exists or not.

3. Therefore, if God is necessary, every state of affairs (including evil) entails God's existence.

4. If God is impossible, every state of affairs entails God's non-existence.

5. Since we don't know which is true without already knowing whether God exists, no evidence can be "independent" or provide meaningful support either way.

6. Almeida concludes that evidence is irrelevant to rational belief about God's existence. Therefore, "evil is not evidence" (nor is anything else).

Definitions and technical terms

• □Fx: The conjunctive property of essential moral perfection, omnipotence, and omniscience

• Traditional God: An entity that exemplifies □Fx in absolutely every possible world

• S5 modal logic: The most widely defended logic of metaphysical necessity

• Non-trivial evidence: Evidence that is independent and genuinely informative (as opposed to trivial evidence)

• Epistemic probability P(□FG|S): The probability of God's existence given evidence S

• ∃S and ∀S: Quantifiers ranging over all possible states of affairs

• ◊: Possibility operator ("possibly")

• □: Necessity operator ("necessarily")

• S: State of affairs variable/constant

Classic argument against God's existence

• Premise: There exist states of affairs that do not entail God's existence.

  • Examples: Jones's prolonged illness, Smith's debilitating injury

  • Formula: ∃S∼□(S → □FG)

• S5 theorem application: If some state doesn't entail God exists, then some state entails God doesn't exist.

• Conclusion: God is impossible (□∼□FG).

Classic argument for God's existence

• Premise: There exist states of affairs that do not entail God's non-existence.

  • Examples: Great goods in the world, Jones's lifelong health

  • Formula: ∃S∼□(S → ∼□FG)

• S5 theorem application: If some state doesn't entail God doesn't exist, then some state entails God exists.

• Conclusion: God is necessary (□□FG).

The contradiction

• Logical impossibility: Both conclusions cannot be true simultaneously.

• Implication: The assumption that there can be evidence both for and against God's existence is false.

The triviality mechanism

• Fundamental result: ∀SP(□FG|S) = 1 ∨ ∀SP(∼□FG|S) = 1

  • Every state of affairs constitutes conclusive evidence for God's existence, OR

  • Every state of affairs constitutes conclusive evidence against God's existence

• No Independent Evidence: Whether a state constitutes evidence for or against God depends entirely on whether God exists.

• In S5, either ∀S□(S → □FG) or ∀S□(S → ∼□FG), which means

• All states trivially entail God exists, OR

• All states trivially entail God doesn't exist.

Counterintuitive consequences

• Evil as evidence for God: Earthquakes, hurricanes, genocides could constitute conclusive evidence for God's existence.

• Good as evidence Against God: Improvements in well-being could constitute conclusive evidence against God's existence.

• Epistemic independence: Discovering terrible possible worlds tells us nothing about God's existence.

• Epistemic limitation: We cannot determine evidential value until we know whether God exists.

My reaction

I think the argument proves too much and it seems to reduce to absurdity if seemingly gratuitous evil that serves no purpose or end would be evidence for God. In logic, entailment is a strict relationship where a hypothesis H is true by logical necessity if the evidence E is true (i.e., E logically implies H). For example, if E is "All swans are white and this is a swan," then H ("This swan is white") is entailed. However, in many real-world scenarios, evidence does not strictly entail a hypothesis. For instance, observing a white swan supports the hypothesis "All swans are white," but does not entail it, as there could be non-white swans elsewhere. Entailment is not the kind of relation to capture the probabilistic or defeasible nature of most evidential relationships.

Probabilistic reasoning argues that evidential support is a matter of degree, not an all-or-nothing logical relation. Logical entailments can provide certainty, but more flexible non-entailing relations accommodate partial or indirect evidence, which is common in fields like medicine and social sciences. This isn't a new problem in the field of philosophy because many metaphysical topics are underdetermined, as in the available evidence is insufficient to uniquely support one hypothesis or theory over its rivals. So relations like likelihood, inference to the best information (IBE), and corroboration can bolster a hypothesis, but can't guarantee the truth of the proposition it favors.

I think the argument might show entailments like those put forth in the atheistic the logical argument from evil, which states that certain kinds (or sometimes any kind) of evil are incompatible with the existence of God, can't be evidence. Alternatively, it could mean the premise (that evil and God can’t coexist) is either false or underdetermined, so we can only evaluate the argument’s conclusion using probabilistic reasoning or by IBE. If evil doesn’t logically preclude God’s existence (as many theists argue), it fails as deductive evidence. However, evil can still be meaningful evidence through non-entailment relations like likelihood or IBE, which accommodate underdetermination and uncertainty.

It’s clear that the debate over evil as evidence against God’s existence is far from settled. I suggest we continue to explore these stances with an open mind, seeking common ground where we can. One thing entailed (pun intended) would be a more nuanced dialogue that respects the strengths and limitations of each perspective.

Image credit

1. Mike Almeida, “Evil is not evidence,” Religious Studies (2022), https://www.cambridge.org/core/journals/religious-studies/article/evil-is-not-evidence/630C8588C7F9E4F2BC960A447B817F11.