An Impossible (or
Penrose) Triangle
Three Types of Contradictions
Writing in 1955, the late Oxford don J.L. Mackie claimed that evil is logically inconsistent with God’s existence.
In its simplest form the problem is this: God is omnipotent; God is wholly good; and 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.[1]
Consider the following set of propositions: {God is omnipotent; God is wholly good; evil exists}. Mackie claimed that the set is somehow contradictory. But how?
The Christian philosopher Alvin Plantinga pointed out that there are three ways for a set of propositions to be inconsistent or contradictory.[2]
First, a set is explicitly contradictory if one of the members of the set is the denial or negation of another member of the set. For example, consider set A:{God exists; God does not exist}. Set A is explicitly contradictory.
Second, a set is formally contradictory if it is possible to deduce an explicit contradiction in its members by the laws of logic. Consider, for example, set B: {If all men are mortal, then Socrates is mortal; All men are mortal; and Socrates is not mortal}. Set B is not explicitly contradictory. But the first two members of that set entail Socrates is mortal. When we add Socrates is mortal to set B, we get an explicit contradiction. Because the proposition, "Socrates is mortal," follows from the first two members of the set by modus ponens, set B is formally contradictory.
Third, a set S is implicitly contradictory if there is a necessary proposition p such that the result of adding p to S is a formally contradictory set. Plantinga asks us to consider the following set, which I'll call set C: {George is older than Paul; Paul is older than Nick; and George is not older than Nick}. As Plantinga points out, set C is neither explicitly nor formally contradictory, but it is implicitly contradictory because it is not possible that all three members of set C are true. Why is it not possible? Because, as Plantinga says, the following proposition is necessarily true: "If George is older than Paul, and Paul is older than Nick, then George is older than Nick." If we add that proposition to set C, then we get an explicit contradiction.
To sum up: a set of propositions is either explicitly contradictory or it isn't. If it is, then one member of the set denies another member of the set. If it isn't explicitly contradictory but there is a contradiction, then one or more propositions must be added to the set. If the additional proposition(s) can be deduced from the members of the set by the laws of logic alone, then the set is formally contradictory. If the additional proposition(s) are instead necessary truths (or propositions deduced from necessary truths), then the set is implicitly contradictory.
Let's now turn to the question of whether there is a contradiction, in any of these three senses, between atheism and moral obligation.
Does the Atheist Contradict Himself?
According to Plantinga, the atheist who runs an argument from evil has contradicted himself by accepting a contradictory pair of propositions. This pair, of course, is:
(1) God does not exist;
and
(2) Genuine moral obligation exists.
Call this set D; the claim is that D is an inconsistent set. But how?
Is There an Explicit Contradiction?
Plantinga's first type of contradiction is an explicit contradiction; for a set to be explicitly contradictory, one of its members must be the negation of another member. But the negations of (1) and (2) respectively are:
(1') God exists.
and
(2') Genuine moral obligation does not exist.
But neither (1') nor (2') are in set D, so set D is clearly not explicitly contradictory.
Is There a Formal Contradiction?
Remember that Plantinga's second type of contradiction, formal contradiction, requires that we use only the laws of logic to deduce a new proposition which, once added to the set, forms an explicit contradiction. But no laws of logic permit us to deduce the negation of one of the propositions in set D from the other member. So set D isn't formally contradictory either.
Is There an Implicit Contradiction?
This leaves Plantinga's third and final option, namely, that atheism and moral obligation are somehow implicitly contradictory. When Plantinga explains why he thinks set D is contradictory, I think we may reasonably interpret him as claiming that it is implicitly contradictory. In his words:
A naturalistic way of looking at the world, so it seems to me, has no place for genuine moral obligation of any sort; a fortiori, then, it has no place for such a category as horrifying wickedness. … There can be such a thing only if there is a way rational creatures are supposed to live, obliged to live; and the force of that normativity--its strength, so to speak--is such that the appalling and horrifying nature of genuine wickedness is its inverse. But naturalism cannot make room for that kind of normativity; that requires a divine lawgiver, one whose very nature it is to abhor wickedness.[3]
This passage suggests that we add the following proposition to set D:
(3) Genuine moral obligation requires a divine lawgiver.
So if Plantinga thinks that set D is implicitly contradictory, then he must hold that (3) is not merely true, but necessarily true.
But is it? What does it mean to say that some action, call it X, is a "moral obligation"? That we are required to perform X, presumably. But anyone who does not know what moral obligation means will be equally in the dark about what it means for an action to be required. So let's start by considering what it means to have an obligation of any type. There are many types of obligations: moral, legal, religious, game, etiquette, and so forth. Depending on the type of obligation, an obligation's source might be rules or social roles.[4] So one idea might be that the source of moral obligations or requirements is moral rules, and the only suitable candidate for a moral rule is divine law. But "required by divine law" is not a necessary condition for X to be a moral obligation. To see this, consider how divine law could create moral obligations. Divine law could create moral obligations if and only if there is a prior moral obligation to obey divine law. But if there is a prior moral obligation to obey divine law, then that obligation itself must not be the result of a divine law. Furthermore, if the source of that prior moral obligation isn't divine law, then why can't there be additional moral obligations which are also not the result of divine law? Thus, "required by divine law" is not a necessary condition for moral obligation. But that entails that (3) is not necessarily true and so can't be used to show that set D is implicitly inconsistent.
Conclusion
In summarizing his refutation of Mackie's logical argument from evil, Plantinga writes:
... 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 [... Mackie's set of 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.[5]
What's sauce for the goose is sauce for the gander. One wonders, therefore, why Plantinga and so many other theistic philosophers and apologists who confidently assert that set D 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 Plantinga, who brilliantly refuted Mackie's argument from evil, fails to apply the same standards to his "theistic argument from evil" as he applied to Mackie's argument from evil. In the case of Mackie's argument from evil, Plantinga argued that as long as it is even possible that God and evil may co-exist, there is no logical contradiction between God exists and evil exists. But he ignores the parallel objection to his theistic argument from evil: as long as it is even possible that moral obligation exists and God does not, there is no logical contradiction between atheism and moral obligation.
I am confident that, if Plantinga were to read and reply to this post, he would deny that it is even possible that God does not exist, perhaps citing his modal ontological argument in support. In turn, allow me to respond as follows. First, I'm inclined to agree with Plantinga that God, at least as Plantinga defines "God," is the kind of being who either necessarily exists or necessarily doesn't exist. Thus, if theism is true, it's necessarily true; if theism is false, it's necessarily false. Second, the reader needs to keep in mind that when Plantinga, in the context of his modal ontological argument, refers to possibility, he's referring to what's known as "metaphysical possibility," not "strict logical possibility." This distinction matters because something could be strictly logically possible (in the sense of not being self-contradictory, like a 'round triangle' or a 'married bachelor') and, at the same time, not metaphysically possible. This leads to my third point. As Graham Oppy has argued, there is a parody of Plantinga's modal ontological argument which, if successful, shows that God necessarily does not exist.[6] It's far from obvious that Plantinga's argument is correct and the parody is incorrect. Thus, I don't think we know with certainty that theism is necessarily true or that theism is necessarily false. For this reason, I think we should assume that both God's existence and God's non-existence are epistemically possible. And so it is at least epistemically possible that moral obligation exists and God does not. Therefore, I have shown that Plantinga has given no good reason to think that set D is contradictory.
Notes
[1] J.L. Mackie, “Evil and Omnipotence” Mind 64 (1955): 200-212, https://doi.org/10.1093/mind/LXIV.254.200.
[2] Alvin Plantinga, God, Freedom and Evil (Grand Rapids, MI: Eerdmans, 1974), pp. 13-16.
[3] Alvin Plantinga, “A Christian Life Partly Lived” in Kelly James Clark (ed.), Philosophers Who Believe: The Spiritual Journeys of 11 Leading Thinkers (Downers Grove: InterVarsity Press, 1997), 45-82. Italics are mine.
[4] Nicholas Wolterstorff, Justice: Rights and Wrongs (Princeton, NJ: Princeton University Press, 2008), p. 279.
[5] Plantinga 1974, pp. 23-24.
[6] Graham Oppy, Ontological Arguments and Belief in God (Cambridge: Cambridge University Press, 1995), pp. 70-78.
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