Lesson · Identity, Modality and Freedom · God and evil

The Problem of Evil as an Inconsistent Set

That God is all-powerful, all-knowing and wholly good, that evil exists, and that a being like that eliminates evil cannot all be true. The consistency lab confirms there is no model, shows that every sentence is needed for the clash, and then shows what the free-will defence changes, and what the evidential version asserts instead.

Open the interactive lesson Practice

o, k, g: omnipotent, omniscient, good e: evil exists bridge: (o ∧ k ∧ g) → ¬e five sentences, no model: drop or weaken one weaker bridge: (o ∧ k ∧ g) → ¬u

Five sentences, and the one that is weakened

Core ideas

What this lesson establishes

This lesson uses the same method as the free-will triad and the fission case. What is new is the sentence that does the connecting, and the observation that arguing for consistency is a matter of finding a model.

The set has five sentences

Write o, k and g for the three attributes, e for “evil exists”, and a bridge premise (o ∧ k ∧ g) → ¬e for “a being with all three attributes eliminates evil”. The lab finds no model, and all five are needed.

A defence needs only a model

To show the five sentences do not contradict, it is enough to describe a possible way for them all to be true. A defence changes the bridge so that it no longer says that evil cannot exist, and the lab finds a model.

The evidential problem asserts a different sentence

The weakened bridge says such a being eliminates unnecessary evil, written u. The evidential argument asserts that some evil is unnecessary, u, and then the set has no model again. Its support is probabilistic and the set is not.

The material

Five sentences and what each response does

The set, the exits, the defence as a model, and the premise that the evidential argument adds.

The problem is old and has been stated many times. J. L. Mackie's version has three claims, that God is omnipotent, that God is wholly good, and that evil exists, joined by two principles he called quasi-logical: a good being eliminates evil as far as it can, and there are no limits to what an omnipotent being can do. The set below is the one later statements settle on. It adds omniscience, since a being that could not know of an evil could not be faulted for leaving it, and it folds the two principles into one bridge. Each of the first three sentences is part of the traditional idea of God, the fourth is a fact, and the fifth connects them.

1. o God is omnipotent 2. k God is omniscient 3. g God is wholly good 4. e evil exists 5. (o ∧ k ∧ g) → ¬e such a being eliminates evil

From 1, 2 and 3 the antecedent of 5 is true, so ¬e follows, which contradicts 4. The lab confirms there is no row of the table that satisfies all five, and the smallest inconsistent subset it reports is the whole set. Dropping any one gives a model, and the drop menu shows each.

Each deletion is a position that has been held. Dropping sentence 1 or 2 gives a God who is limited in power or knowledge. Dropping 3 gives a God who is not good, and dropping 4 says that evil is an illusion, which most readers think denies a fact. Dropping 5 is the interesting move, because it keeps all of the traditional attributes and the fact, and says that a being with those attributes might still permit evil.

The defence as a model

The bridge is not a logical truth. It says a good being eliminates evil as far as it can, and it is plausible only if there is no reason a good being would have for permitting some. The free-will defence supplies one. Perhaps a world with free creatures is better than one without, and perhaps any free creature might misuse its freedom, and then some evil is necessary for the greater good. Write u for “there is evil that is not necessary for any greater good”. The weakened bridge is (o ∧ k ∧ g) → ¬u: such a being eliminates the unnecessary evil.

With that bridge the lab finds a model. It makes o, k, g and e true and u false. The model shows the five sentences can all be true together, and that is all a defence claims. Alvin Plantinga's version does not assert that the story about freedom is true or likely, only that it is possible, and a possible way for all the sentences to hold is what a model is.

That is also its limit. A defence settles the logical problem and does not show that God exists or that the story is probable. It establishes that the contradiction is not forced. The lab can check the model, and whether u is false is not something it can check.

This is where the evidential problem enters. Instead of the bridge, it asserts u: that there are evils, such as the suffering of an animal in a forest fire that no one sees, that look as if no greater good required them. Add u to the weakened bridge and the three attributes, and the lab finds no model again. The logic of the clash is the same as before. What differs is where the support for the offending sentence comes from: for u it is an estimate of how likely it is, given what we can see, and the estimate is exactly what the lab does not compute. The reply that we are poorly placed to see what a being with unlimited knowledge would see is a reply to that estimate, not to the logic.

Interactive

Consistency and what must go

Every model, and every minimal inconsistent subset

Weaken the bridge, then assert the unnecessary evil

The first set is the five sentences of the text, with a tilde for not. Drop each one in turn and read the model. The second preset replaces the last sentence by the weaker bridge, using the letter u. The third adds the claim that there is unnecessary evil, and the clash returns.

Set of sentences

Sentences, separated by semicolons

Give one up

Models—

Verdict—

Smallest inconsistent subset—

A model—

Up to 8 sentences over up to 6 sentence letters. Type ~ for not, & for and, | for or, -> for if-then, or use the symbols.

Method

Treating a problem of evil as a set

Five moves, in this order, for the logical problem and for its variants.

Write each commitment as a sentence

Include the bridge. The attributes and the fact are uncontroversial as sentences. The bridge is where the argument is carried.

Ask for a model, and for the smallest inconsistent subset

If there is no model, the subset names the sentences among which one must be given up. When the subset is the whole set, no sentence is idle.

Delete each sentence once

Name the position each model represents and what it gives up, such as a limited God, or the denial that evil exists.

Weaken the bridge and test again

Replace the bridge by a weaker conditional, such as one about unnecessary evil, and ask again for a model. A model shows consistency, which is all a defence claims.

Find what the argument now asserts

If the weakened set is consistent, the argument that remains must assert a sentence that restores the clash. Name it, and say what supports it.

Deletions, weakenings and assertions

Score 0 / 0

Choose the answer you can justify.

From the logical to the evidential problem

The three attributes o, k, g, evil e, and unnecessary evil u.

o, k, g, e and (o and k and g) implies not e: no model every one of the five is in the smallest subset weaken to (o and k and g) implies not u o, k, g, e with u false: a model the defence has shown the set is consistent now assert u: the clash returns, no model

The first change is a deletion and the second an assertion, and each is read off a table. The first shows that a defence can be given. The second shows what the evidential argument needs, a sentence whose support is not in the table.

Common mistakes

Believing the problem of evil is a probabilistic argument onlyThe logical problem has no probabilities in it. The five sentences have no model, and the lab reports it by checking every row. The probabilistic version is a second argument, which asserts that unnecessary evil is likely; it appears in the third preset as the sentence u, and what the lab can say about it is only that, if it is true, the set has no model.

Thinking a defence shows that God exists, or that evil is justifiedThe lab finds a model for the weakened set, and that shows the sentences can all be true together. It shows nothing about whether they are, and a model in which u is false is a possibility and not a finding. A defence answers an argument that the attributes are impossible, and no more.

Treating the bridge as a logical truthThe sentence (o ∧ k ∧ g) → ¬e is false in the lab's model for the second set, where all three attributes and e are true. It is an assumption about what a good being does, and the free-will defence is a reason to reject it. The argument for the problem has to defend the bridge, and the lab cannot do that for it.

Check your understanding

✓

Finish when you can write the problem of evil as a set, find its smallest inconsistent subset, and state what each response changes.

You should be able to write the five sentences, report the verdict, delete each sentence in turn and name the position it yields, weaken the bridge and say what a model for it shows, and name the sentence the evidential argument asserts. A response named without the sentence it alters has not been placed.

Note: A consistency check is silent on whether any of the five sentences is true, whether the weakened bridge is plausible, and whether a given evil is necessary for a greater good. The first is metaphysics, the second is a question about goodness, and the third is where the evidential debate lives.