In a widely discussed piece entitled “Evil and Omnipotence” John Mackie repeats this claim:
“I think, however, that a more telling criticism can be made by way of the traditional problem of evil. Here it can be shown, not that religious beliefs lack rational support, but that they are positively irrational, that the several parts of the essential theological doctrine are inconsistent with one another….” [John Mackie, “Evil and Omnipotence,” in The Philosophy of Religion, ed. Basil Mitchell (London: Oxford University Press, 1971), 92.]
Is Mackie right? Does the theist contradict himself? But we must ask a prior question: just what is being claimed here? That theistic belief contains an inconsistency or contradiction, of course. But what, exactly, is an inconsistency or contradiction? There are several kinds. An explicit contradiction is a proposition of a certain sort—a conjunctive proposition, one conjunct of which is the denial or negation of the other conjunct.
For example: Paul is a good tennis player, and it’s false that Paul is a good tennis player.
(People seldom assert explicit contradictions). Is Mackie charging the theist with accepting such a contradiction? Presumably not; what he says is:
“In its simplest form the problem is this: God is omnipotent; God is wholly good; yet evil exists. There seems to be some contradiction between these three propositions, so that if any two of them were true the third would be false. But at the same time all three are essential parts of most theological positions; the theologian, it seems, at once must adhere and cannot consistently adhere to all three.” [Ibid., 92-93.]
According to Mackie, then, the theist accepts a group or set of three propositions; this set is inconsistent. Its members, of course, are,
(1) God is omnipotent
(2) God is wholly good
and
(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? Following our definition of an explicit contradiction, we might say that a set of propositions is explicitly contradictory if one of the members is the denial or negation of another member. But then, of course, it is evident that the set we are discussing is not explicitly contradictory; the denials of (1), (2), and (3), respectively are
(1′) God is not omnipotent (or it’s false that God is omnipotent)
(2′) God is not wholly good
and
(3′) There is no evil
none of which are in set A.
Of course many sets are pretty clearly contradictory, in an important way, but not explicitly contradictory. For example, set B:
(4) If all men are mortal, then Socrates is mortal
(5) All men are mortal
(6) Socrates is not mortal.
This set is not explicitly contradictory; yet surely some significant sense of that term applies to it. What is important here is that by using only the rules of ordinary logic—the laws of propositional logic and quantification theory found in any introductory text on the subject—we can deduce an explicit contradiction from the set. Or to put it differently, we can use the laws of logic to deduce a proposition from the set, which proposition, when added to the set, yields a new set that is explicitly contradictory. For by using the law modus ponens (if p, then q; p; therefore q) we can deduce
(7) Socrates is mortal from (4) and (5). The result of adding (7) to B is the set {(4), (5), (6), (7)}. This set, of course, is explicitly contradictory in that (6) is the denial of (7). We might say that any set which shares this characteristic with set B is formally contradictory. So a formally contradictory set is one from whose members an explicit contradiction can be deduced by the laws of logic. Is Mackie claiming that set A is formally contradictory?
If he is, he’s wrong. No laws of logic permit us to deduce the denial of one of the propositions in A from the other members. Set A isn’t formally contradictory either.
But there is still another way in which a set of propositions can be contradictory or inconsistent. Consider set C, whose members are
(8) George is older than Paul
(9) Paul is older than Nick
and
(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).
I said that (11) is necessarily true; but what does that mean? Of course we might say that a proposition is necessarily true if it is impossible that it be false, or if its negation is not possibly true. This would be to explain necessity in terms of possibility. Chances are, however, that anyone who does not know what necessity is, will be equally at a loss about possibility; the explanation is not likely to be very successful. Perhaps all we can do by way of explanation is give some examples and hope for the best. In the first place many propositions can be established by the laws of logic alone—for example
(12) If all men are mortal and Socrates is a man, then Socrates is mortal.
Such propositions are truths of logic; and all of them are necessary in the sense of question. But truths of arithmetic and mathematics generally are also necessarily true. Still further, there is a host of propositions that are neither truths of logic nor truths of mathematics but are nonetheless necessarily true; (11) would be an example, as well as
(13) Nobody is taller than himself
(14) Red is a color
(15) No numbers are persons
(16) No prime number is a prime minister
and
(17) Bachelors are unmarried.
So here we have an important kind of necessity—let’s call it “broadly logical necessity.” Of course there is a correlative kind of possibility: a proposition p is possibly true (in the broadly logical sense) just in case its negation or denial is not necessarily true (in that same broadly logical sense). This sense of necessity and possibility must be distinguished from another that we may call causal or natural necessity and possibility. Consider
(18) Henry Kissinger has swum the Atlantic.
Although this proposition has an implausible ring, it is not necessarily false in the broadly logical sense (and its denial is not necessarily true in that sense). But there is a good sense in which it is impossible: it is causally or naturally impossible. Human beings, unlike dolphins, just don’t have the physical equipment demanded for this feat. Unlike Superman, furthermore, the rest of us are incapable of leaping tall buildings at a single bound or (without auxiliary power of some kind) traveling faster than a speeding bullet. These things are impossible for us—but not logically impossible, even in the broad sense.
So there are several senses of necessity and possibility here. There are a number of propositions, furthermore, of which it’s difficult to say whether they are or aren’t possible in the broadly logical sense; some of these are subjects of philosophical controversy. Is it possible, for example, for a person never to be conscious during his entire existence? Is it possible for a (human) person to exist disembodied? If that’s possible, is it possible that there be a person who at no time at all during his entire existence has a body? Is it possible to see without eyes? These are propositions about whose possibility in that broadly logical sense there is disagreement and dispute.
Now return to set C. What is characteristic of it is the fact that the conjunction of its members—the proposition expressed by the result of putting “and’s” between (8), (9), and (10)—is necessarily false. Or we might put it like this: what characterizes set C is the fact that we can get a formally contradictory set by adding a necessarily true proposition—namely (11). Suppose we say that a set is implicitly contradictory if it resembles C in this respect. That is, a set S of propositions is implicitly contradictory if there is a necessary proposition p such that the result of adding p to S is a formally contradictory set. Another way to put it: S is implicitly contradictory if there is some necessarily true proposition p such that by using just the laws of ordinary logic, we can deduce an explicit contradiction from p together with the members of S. And when Mackie says that set A is contradictory, we may properly take him, I think, as holding that it is implicitly contradictory in the explained sense. As he puts it:
“However, the contradiction does not arise immediately; to show it we need some additional premises, or perhaps some quasi-logical rules connecting the terms ‘good’ and ‘evil’ and ‘omnipotent.’ These additional principles are that good is opposed to evil, in such a way that a good thing always eliminates evil as far as it can, and that there are no limits to what an omnipotent thing can do. From these it follows that a good omnipotent thing eliminates evil completely, and then the propositions that a good omnipotent thing exists, and that evil exists, are incompatible.” [Ibid., 93.]
Here Mackie refers to “additional premises”; he also calls them “additional principles” and “quasi-logical rules”; he says we need them to show the contradiction. What he means, I think, is that to get a formally contradictory set we must add some more propositions to set A; and if we aim to show that set A is implicitly contradictory, these propositions must be necessary truths—“quasi-logical rules” as Mackie calls them. The two additional principles he suggests are
(19) A good thing always eliminates evil as far as it can
and
(20) There are no limits to what an omnipotent being can do.
And, of course, if Mackie means to show that set A is implicitly contradictory, then he must hold that (19) and (20) are not merely true but necessarily true.
But, are they? What about (20) first? What does it mean to say that a being is omnipotent? That he is all-powerful, or almighty, presumably. But are there no limits at all to the power of such a being? Could he create square circles, for example, or married bachelors? Most theologians and theistic philosophers who hold that God is omnipotent, do not hold that He can create round squares or bring it about that He both exists and does not exist. These theologians and philosophers may hold that there are no nonlogical limits to what an omnipotent being can do, but they concede that not even an omnipotent being can bring about logically impossible states of affairs or cause necessarily false propositions to be true. Some theists, on the other hand—Martin Luther and Descartes, perhaps—have apparently thought that God’s power is unlimited even by the laws of logic. For these theists the question whether set A is contradictory will not be of much interest. As theists they believe (1) and (2), and they also, presumably, believe (3). But they remain undisturbed by the claim that (1), (2), and (3) are jointly inconsistent—because, as they say, God can do what is logically impossible. Hence He can bring it about that the members of set A are all true, even if that set is contradictory (concentrating very intensely upon this suggestion is likely to make you dizzy). So the theist who thinks that the power of God isn’t limited at all, not even by the laws of logic, will be unimpressed by Mackie’s argument and won’t find any difficulty in the contradiction set A is alleged to contain. This view is not very popular, however, and for good reason; it is quite incoherent. What the theist typically means when he says that God is omnipotent is not that there are no limits to God’s power, but at most that there are no nonlogical limits to what He can do; and given this qualification, it is perhaps initially plausible to suppose that (20) is necessarily true.
But what about (19), the proposition that every good thing eliminates every evil state of affairs that it can eliminate? Is that necessarily true? Is it true at all? Suppose, first of all, that your friend Paul unwisely goes for a drive on a wintry day and runs out of gas on a deserted road. The temperature dips to—10°, and a miserably cold wind comes up. You are sitting comfortably at home (twenty-five miles from Paul) roasting chestnuts in a roaring blaze. Your car is in the garage; in the trunk there is the full five-gallon can of gasoline you always keep for emergencies. Paul’s discomfort and danger are certainly an evil, and one which you could eliminate. You don’t do so. But presumably you don’t thereby forfeit your claim to being a “good thing”—you simply didn’t know of Paul’s plight. And so (19) does not appear to be necessary. It says that every good thing has a certain property—the property of eliminating every evil that it can. And if the case I described is possible—a good person’s failing through ignorance to eliminate a certain evil he can eliminate—then (19) is by no means necessarily true.
But perhaps Mackie could sensibly claim that if you didn’t know about Paul’s plight, then in fact you were not, at the time in question, able to eliminate the evil in question; and perhaps he’d be right. In any event he could revise (19) to take into account the kind of case I mentioned:
(19a) Every good thing always eliminates every evil that it knows about and can eliminate.
{(1), (2), (3), (20), (19a)}, 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 Mackie 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.)
But is (19a) necessary? Hardly. Suppose you know that Paul is marooned as in the previous example, and you also know another friend is similarly marooned fifty miles in the opposite direction. Suppose, furthermore, that while you can rescue one or the other, you simply can’t rescue both. Then each of the two evils is such that it is within your power to eliminate it; and you know about them both. But you can’t eliminate both; and you don’t forfeit your claim to being a good person by eliminating only one—it wasn’t within your power to do more. So the fact that you don’t doesn’t mean that you are not a good person. Therefore (19a) 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.
We can see the same thing another way. You’ve been rock climbing. Still something of a novice, you’ve acquired a few cuts and bruises by inelegantly using your knees rather than your feet. One of these bruises is fairly painful. You mention it to a physician friend, who predicts the pain will leave of its own accord in a day or two. Meanwhile, he says, there’s nothing he can do, short of amputating your leg above the knee, to remove the pain. Now the pain in your knee is an evil state of affairs. All else being equal, it would be better if you had no such pain. And it is within the power of your friend to eliminate this evil state of affairs. Does his failure to do so mean that he is not a good person? Of course not; for he could eliminate this evil state of affairs only by bringing about another, much worse evil. And so it is once again evident that (19a) is false. It is entirely possible that a good person fail to eliminate an evil state of affairs that he knows about and can eliminate. This would take place, if, as in the present example, he couldn’t eliminate the evil without bringing about a greater evil.
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 (19a) is not necessarily true; it can’t be used to show that set A is implicitly contradictory.
These difficulties might suggest another revision of (19); we might try
(19b) 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 (19a) 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 find 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. You’re rock climbing again, this time on the dreaded north face of the Grand Teton. You and your party come upon Curt and Bob, two mountaineers stranded 125 feet apart on the face. They untied to reach their cigarettes and then carelessly dropped the rope while lighting up. A violent, dangerous thunderstorm is approaching. You have time to rescue one of the stranded climbers and retreat before the storm hits; if you rescue both, however, you and your party and the two climbers will be caught on the face during the thunderstorm, which will very likely destroy your entire party. In this case you can eliminate one evil (Curt’s being stranded on the face) without causing more evil or eliminating a greater good; and you are also able to properly eliminate the other evil (Bob’s being thus stranded). But you can’t properly eliminate them both. And so the fact that you don’t rescue Curt, say, even though you could have, doesn’t show that you aren’t a good person. Here, then, each of the evils is such that you can properly eliminate it; but you can’t properly eliminate them both, and hence can’t be blamed for failing to eliminate one of them.
So neither (19a) nor (19b) is necessarily true. You may be tempted to reply that the sort of counterexamples offered—examples where someone is able to eliminate an evil A and also able to eliminate a different evil B, but unable to eliminate them both—are irrelevant to the case of a being who, like God, is both omnipotent and omniscient. That is, you may think that if an omnipotent and omniscient being is able to eliminate each of two evils, it follows that he can eliminate them both. Perhaps this is so; but it is not strictly to the point. The fact is the counterexamples show that (19a) and (19b) 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 atheologian will have more success if he works the properties of omniscience and omnipotence into (19). Perhaps he could say something like
(19c) 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 (19c). Will it serve Mackie’s purposes? Not obviously. For we don’t get a set that is formally contradictory by adding (20) and (19c) 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
(19c) An omnipotent and omniscient good being eliminates every evil that it can properly eliminate
and
(20) 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′), (19c), and (20) 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 (19c) doesn’t really help either—not because it is not necessarily true but because its addition [with (20)] to set A does not yield a formally contradictory set.
Obviously, what the atheologian must add to get a formally contradictory set is
(21) If God is omniscient and omnipotent, then he can properly eliminate every evil state of affairs.
Suppose we agree that the set consisting in A plus (19c), (20), and (21) is formally contradictory. So if (19c), (20), and (21) are all necessarily true, then set A is implicitly contradictory. We’ve already conceded that (19c) and (20) are indeed necessary. So we must take a look at (21). Is this proposition necessarily true?
No. To see this let us ask the following question. Under what conditions would an omnipotent being be unable to eliminate a certain evil E without eliminating an outweighing good? Well, suppose that E is included in some good state of affairs that outweighs it. That is, suppose there is some good state of affairs G so related to E that it is impossible that G obtain or be actual and E fail to obtain. (Another way to put this: a state of affairs S includes S’ if the conjunctive state of affairs S but not S’ is impossible, or if it is necessary that S’ obtains if S does.) Now suppose that some good state of affairs G includes an evil state of affairs E that it outweighs. Then not even an omnipotent being could eliminate E without eliminating G. But are there any cases where a good state of affairs includes, in this sense, an evil that it outweighs? [More simply the question is really just whether any good state of affairs includes an evil; a little reflection reveals that no good state of affairs can include an evil that it does not outweigh.] Indeed there are such states of affairs. To take an artificial example, let’s suppose that E is Paul’s suffering from a minor abrasion and G is your being deliriously happy. The conjunctive state of affairs, G and E—the state of affairs that obtains if and only if both G and E obtain—is then a good state of affairs: it is better, all else being equal, that you be intensely happy and Paul suffer a mildly annoying abrasion than that this state of affairs not obtain. So G and E is a good state of affairs. And clearly G and E includes E: obviously it is necessarily true that if you are deliriously happy and Paul is suffering from an abrasion, then Paul is suffering from an abrasion.
But perhaps you think this example trivial, tricky, slippery, and irrelevant. If so, take heart; other examples abound. Certain kinds of values, certain familiar kinds of good states of affairs, can’t exist apart from evil of some sort. For example, there are people who display a sort of creative moral heroism in the face of suffering and adversity—a heroism that inspires others and creates a good situation out of a bad one. In a situation like this the evil, of course, remains evil; but the total state of affairs—someone’s bearing pain magnificently, for example—may be good. If it is, then the good present must outweigh the evil; otherwise the total situation would not be good. But, of course, it is not possible that such a good state of affairs obtain unless some evil also obtain. It is a necessary truth that if someone bears pain magnificently, then someone is in pain.
The conclusion to be drawn, therefore, is that (21) is not necessarily true. And our discussion thus far shows at the very least that it is no easy matter to find necessarily true propositions that yield a formally contradictory set when added to set A. [In Alvin Plantinga, God and Other Minds (Ithaca, NY: Cornell University Press, 1967), chap. 5, I explore further the project of finding such propositions.] One wonders, therefore, why the many atheologians who confidently assert that this set is contradictory make no attempt whatever to show that it is. For the most part they are content just to assert that there is a contradiction here. Even Mackie, who sees that some “additional premises” or “quasi-logical rules” are needed, makes scarcely a beginning towards finding some additional premises that are necessarily true and that together with the members of set A formally entail an explicit contradiction.
Alvin Plantinga, God, Freedom, and Evil (Grand Rapids, MI: Eerdmans, 1977).