A Solution to the Logical Problem (Alleged Contradiction) of Evil

The Claim of Contradiction
According to John Mackie (The Miracle of Theism. OUP 1982) the theist accepts a group or set of three propositions; this set is inconsistent. The propositions are

(1) God is omnipotent
(2) God is wholly good
(3) Evil exists.

Call this set A; the claim is that A is an inconsistent set. But what is it for a set to be inconsistent or contradictory?  We may conclude there is an explicit contradiction only if one of the members is the denial or negation of another member (e.g. God is not omnipotent; God is not wholly good; Evil does not exist). As it stands, there is no explicit contradiction since each proposition is merely referring to a different state of affairs.

How to Demonstrate a Logical Contradiction
Contrast this with another set that is obviously contradictory. Call it set B:
(4) If all men are mortal, then Socrates is mortal
(5) All men are mortal
(6) Socrates is not mortal

The contradiction in this set may not be explicit but unlike set A, we can apply the rules of logic to deduce an explicit contradiction from the set.

From (4) and (5) and using the law modus ponens (if p, then q; p; therefore q) we deduce
(7) Socrates is mortal.
The result of adding (7) to B is set [(4), (5), (6), (7)].
This set is clearly contradictory since (6) is the denial of (7).

The conclusion is that any set which shares this characteristic with set B is formally contradictory.

A formally contradictory set is one from whose members an explicit contradiction can be deduced by the law of logic. But so far, the atheist has not provided a logical deduction that explicitly contradicts set A.

The atheist can resort to another procedure to demonstrate a contradiction.
Consider set C, whose members are

(8) George is older than Paul
(9) Paul is older than Nick
(10) George is not older than Nick
This set is neither explicitly nor formally contradictory; we can’t just by using the laws of logic, deduce the denial of any of these propositions from the others. And yet there is a good sense in which it is inconsistent or contradictory. For clearly it is not possible that its three members all be true. It is necessarily true that

(11) If George is older than Paul, and Paul is older than Nick, then George is older than Nick

And if we add (11) to set C, we get a set that is formally contradictory; (8), (9), and (11) yield, by the laws of ordinary logic, the denial of (10).

The atheist may therefore claim that set A is implicitly contradictory. All he needs to do is provide a necessary proposition p to set A and then by using the laws of logic, he can deduce an explicit contradiction from p together with the members of A.
These necessary propositions or additional premises may be the following:

(12) A good thing always eliminates evil as far as it can
(13) There are no limits to what an omnipotent being can do.

And, of course, if the atheist means to show that set A is implicitly contradictory, then he must hold that (12) and (13) are not merely true but necessarily true.

But, are there? Take (13) first? What does it mean to say a being is omnipotent? Does this mean there are no limits to what this almighty being could do? Most theistic philosophers would argue omnipotence does not have nonlogical limits but omnipotence cannot bring about logically impossible states of affairs or cause necessarily false propositions to be true, like square circles or married bachelors.

With the above caveat we may initially suppose that (13) is necessarily true.

But consider the case of my friend Paul who foolishly drove out in a blizzard and got stranded nearby. I happened to have spare petrol in my garage which I have stored for emergencies. But I was unaware of the plight of my freezing friend as I was having an engrossing dinner conversation with friends in my cozy home. I failed to deliver petrol to Paul. Nevertheless, no one can deny that I was doing a “good thing”. I was simply unaware of Paul’s plight. And if the case described is possible – a good person’s failing through ignorance to eliminate a certain evil he can eliminate – then (12) is by no means necessarily true.

The atheist may retort and offer a revise form of (12):
(12a) Every good thing always eliminates every evil that it knows about and can eliminate.

{(1), (2), (3), (13), (12a)}, you’ll notice, is not a formally contradictory set – to get a formal contradiction we must add a proposition specifying that God knows about every evil state of affairs. But most theists do believe that God is omniscient or all-knowing; so if this new set – the set that results when we add to set A the proposition that God is omniscient – is implicitly contradictory then the atheist should be satisfied and the theist confounded. (And, henceforth, set A will be the old set A together with the proposition that God is omniscient.)

Answering or Eliminating the Atheist’s Claim of Contradiction Given God’s Omniscience

But is (12a) necessarily true?

Supposed a poisonous snake bit my foot in one of my jungle hikes. The pain was horrific. The doctor advised me to endure the pain that remains barely bearable despite medication. There is nothing he can do to stop the pain short of amputating my knee and he assured me that the pain will stop in a few days. Now the pain in my foot is an evil state of affairs but the doctor can eliminate this evil only by bringing about a greater evil (amputation). No one will doubt the doctor is a good person for failing to end the pain in my foot.  Therefore (12a) is false; it is not a necessary truth or even a truth that every good thing eliminates every evil it knows about and can eliminate.

A slightly different kind of case shows the same thing. A really impressive good state of affairs G will outweigh a trivial evil E – that is, the conjunctive state of affairs G and E is itself a good state of affairs. And surely a good person would not be obligated to eliminate a given evil if he could do so only by eliminating a good that outweighed it. Therefore (12a) is not necessarily true; it can’t be used to show that set A is implicitly contradictory.

These difficulties might suggest another revision of (12); we might try

(12b) A good being eliminates every evil E that it knows about and that it can eliminate without either bringing about a greater evil or eliminating a good state of affairs that outweighs E.

Is this necessarily true? It takes care of the second of the two difficulties afflicting (12a) but leaves the first untouched. We can see this as follows. First, suppose we say that a being properly eliminates an evil state of affairs if it eliminates that evil without either eliminating an outweighing good or bringing about a greater evil. It is then obviously possible that a person finds himself in a situation where he could properly eliminate an evil E and could also properly eliminate another evil E’, but couldn’t properly eliminate them both.

Consider the familiar dilemma of deciding who to save when the boat carrying you, your mother and your wife capsized. You could possibly save both of them but you could effectively save only one. That you save only one in the end does not show you are not a good person.

So neither (12a) nor (12b) is necessarily true. The atheist may insist that God cannot be excused in such dilemmas since he should be able to do both. That is to say, an omnipotent and omniscience being is able and will eliminate both evils. Perhaps this is so; but it is not strictly to the point. The fact is the counterexamples show that (12a) and (12b) are not necessarily true and hence can’t be used to show that set A is implicitly inconsistent. What the reply does suggest is that perhaps the atheist will have more success if he works the properties of omniscience and omnipotence into (12). Perhaps he could say something like

(12c) An omnipotent and omniscient good being eliminates every evil that it can properly eliminate.

And suppose, for purposes of argument, we concede the necessary truth of (12c). Will it serve the atheist’s purposes? Not obviously. For we don’t get a set that is formally contradictory by adding (13) and (12c) to set A. This set (call it A’) contains the following six members:

(1) God is omnipotent
(2) God is wholly good
(2’) God is omniscient
(3) Evil exists
(12c) An omnipotent and omniscient good being eliminates every evil that it can properly eliminate
(13) There are no nonlogical limits to what an omnipotent being can do.

Now if A’ were formally contradictory, then from any five of its members we could deduce the denial of the sixth by the laws of ordinary logic. That is, any five would formally entail the denial of the sixth. So if A’ were formally inconsistent, the denial of (3) would be formally entailed by the remaining five. That is, (1), (2), (2’), (12c), and (13) would formally entail
(3’) There is no evil

But they don’t; what they formally entail is not that there is no evil at all but only that

(3”) There is no evil that God can properly eliminate

So (12c) doesn’t really help either – not because it is not necessarily true but because its addition [with (13)] to set A does not yield a formally contradictory set.

We can proceed with further examples and counter-examples, but I suppose the analysis given so far is sufficient to help the theist grasps the strategy to counter the alleged logical contradiction of evil. Strictly speaking, it would suffice for the theist just to demonstrate that set A has not been shown to be implicitly inconsistent. Our logical analysis shows that the logical problem of evil (alleged contradiction) can been sufficiently (successfully) addressed.

Some theists (Augustine, Leibniz) are prepared to go even further and add a further claim that set A is implicitly consistent and possible in a broadly logical sense.

The logical procedure is – to show that a set S is consistent when you think of a possible state of affairs (it needn’t actually obtain) which is that such that if it were actual, then all the members of S would be true.

First we conjoin proposition (1), (2), and (2’) and henceforth call the result (1):

(1) God is omniscient, omnipotent, and wholly good

The problem, then, is to show that (1) and (3) (evil exists) are consistent. This could be done, as we’ve seen, by finding a proposition r that is consistent with (1) and such that (1) and (r) together entail (3). One proposition that might do the trick is

(14) God creates a world containing evil and has a good reason for doing so.

If (14) is consistent with (1), then it follows that (1) and (3) (and hence set A) are consistent. Accordingly, one thing some theists have tried is to show that (14) and (1) are consistent.

For example, the theist can claim that creating a better, more perfect universe requires the existence of free, rational, and moral agents; and some of the free creatures God created went wrong. But the universe with the free creatures it contains and the evil they commit is better than it would have been had it contained neither the free creatures not this evil.

As all things philosophical go, the atheist may choose to contest this additional claim, but as far as the requirement of logic goes, all the theist is required is to suggest a proposition r that is consistent with (1) and in conjunction with it entails (14). The theist does not need to claim to know or even believe that r is true. And here of course, he is perfectly within his rights. His aim is to show that (1) is consistent with (14); all he need do then is find an r that is consistent with (1) and such that (r) entail (14); whether r is true is quite beside the point

To be sure, to go beyond the requirement of logical coherence (which hopefully has been demonstrated above) and to be able to articulate (r) – to say what God’s reason is – would be more satisfying, but that would take us into the discipline of Biblical theology. We shall stay with the modest goal, which is, to demonstrate that set A has not been shown to be implicitly inconsistent.

This post constitutes part 2 on the problem of evil. For part one LINK

The ideas and analysis in this post are plagiarized from Alvin Plantinga, God, Freedom and Evil (Eerdmans. 1974). O blessed theft!


  1. huangtze says:

    Dr Ng: I’m using a new email,pls contact me through :hokkea2@gmail.com.
    By the way,do you have any article paper for the forum on 17th of September which you can send me?
    Thank you
    God bless

  2. Could a logical conclusion of (1)God is omnipotent & (2) God is wholly good and add (3) God is omniscient be that (4) the universe is optimized? God thus knows what to do and is fully capable of accomplishing it and would not make any missteps or take any useless actions (perfect efficiency). The question then becomes: Optimized based on what criteria? (5) God is love where love is agape–a love given by choice without conditions. Since God is love, maximizing love gives glory to God. Since love involves choice, the introduction of potential for poor choices exist. Thus the potential for evil can exist. One could also show that loving an enemy introduces greater love than loving a friend or family member. Thus (1) thru (5) and (6) Love requires freedom to choose (7) Freedom allows potential for evil therefore (1) thru (6) can exist without being contradicted by (8) Evil exists. Further God has both perfect will and permissive will and God has foreordained certain events (Jesus Christ birth, crucifixion, and resurrection) where He intercedes into the affairs of men to ensure that world events do not exceed the boundaries of His permissive will and thwart His overall plan. Somehow Optimization involves the perfect efficiency [(1) thru (3)] of maximizing of God’s glory (love), and maximizing freedom of choice (potential introduction of evil) through the minimizing of God’s unsolicited intervention (only done necessarily to ensure God’s permissive boundaries remain intact). The remaining variable is a subset of choice (prayer) where prayer solicits God’s intervention into circumstances where God may not have intervened had prayer not been offered. Thus God allows the affairs of mankind to operate within His boundaries of X and Y. Within these boundaries God maximizes love (His glory) within the confines of man’s choices, allowing human prayer/submission to enable Him to further improve Optimization. This requires a bit of Open theism where quantum indeterminacy is real–e.g. God designed this universe where it cannot be known with omniscience a particles position and momentum (Heisenberg uncertainty principle) and thus the universe operates on probabilities as opposed to actuals (more like a cloud than a clock as John Polkinhorne describes). Sorry for the long discourse, but is this heading in a logical/viable direction?