This is an expansion on the last segment of W08 and the stuff from earlier in the lecture that leads up to it. Since it concerns what many philosophers of religion now perceive to be the critical weakness of the LPOE–prompting them to move to an inductive/evidential rather than a strictly logical formulation of the Problem–it bears a bit of re-emphasizing. (Warning: this is a longish post. I originally wrote it to help students from a previous year who said that they found the material hard to follow. This might not apply to you in this semester. But since I wrote it, might as well.)

Almost from the beginning of his article, Mackie signals the high ambition of his project–to show not merely that “religious beliefs lack rational support”, but that they are “positively irrational”. He will do so by showing that “several parts of the essential theological doctrine are inconsistent with one another”. And consequently, on the very standard assumption that it is irrational for someone to hold an inconsistent set of beliefs, the Theist “can maintain his position as a whole only by a much more extreme rejection of reason”, i.e., by saying that her faith is, in a manner of speaking, against reason.

Now, even though Mackie talks about “religious beliefs” and “theological doctrine”, we can be more precise in our understanding of his intended opponent. As he puts it, “the problem of evil, in the sense in which I shall be using the phrase, is a problem only for someone who believes the following three propositions: (a) God (who exists) is omnipotent, (b) God (who exists) is omnibenevolent, and (c) evil exists in the world. Let’s call this person, defined by her believing that the three mentioned propositions are true, for short, Believer, and her opponent, Atheist. But how exactly is the LPOE a problem for Believer? This is where a good bit of carefulness is needed. Mackie has this to say:

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 [i.e., the three beliefs that define Believer]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’, ‘evil’, and ‘omnipotent’… From these it follows that the propositions that a good omnipotent thing exists, and that evil exists, are incompatible. (pp. 200-201)

Despite his initial statement–“There seems to be some contradiction between these three propositions” (though note the qualifying “seems”)–Mackie is careful enough not to assert that the three propositions actually contradict each other. Rather, they are “incompatible”, or inconsistent. There isn’t actually a “p and not-p” among the three propositions. Rather, you can derive a “p and not-pfrom them with the help of some other premises. Hence Mackie says, “the contradiction does not arise immediately: to show it we need some additional premises”.

Mackie offered his candidate “additional premises” at the top of p. 201. In lecture, we discussed how with any two of the three propositions in Believer‘s belief set, plus the additional premises, you can derive the negation of the third remaining proposition, thus deriving a contradiction. But we need to probe this move a bit more, for it is no accident that Mackie called the additional premises “quasi-logical rules”. For not all additional premises are good enough for the job that Mackie intended for them. Specifically, they can’t be merely true premises. They have to be logically necessary as well.

To explain the point, let’s go back to the two examples I used in class involved the six minions:

Proposition Set A:

  • (1) Abel is older than Baker.
  • (2) Baker is older than Charlie.
  • (3) Charlie is older than Abel.

Proposition Set B:

  • (1) Angeline is older than Bernice.
  • (2) Bernice is older than Cheryl.
  • (3) Cheryl has more years of schooling than Angeline.

Only Proposition Set A is, properly speaking, inconsistent. Proposition Set B isn’t. You can derive a contradiction from Set A with the help of some additional logically necessary premises. You can’t do that for Set B. But let’s consider Set A first:

(1) Abel is older than Baker.

(2) Baker is older than Charlie.

(3) Charlie is older than Abel.

(4) If X is older than Y, then it’s not the case that Y is older than X.

(5) If X is older than Y, and Y is older than Z, then X is older than Z.

(6) Abel is older than Charlie (from (1), (2) and (5)).

(7) It’s not the case that Charlie is older than Abel (from (4), (6))—which contradicts (3).

By adding, or making explicit the two additional premises (4) and (5), we can derive the contradiction “(7) and (3)”. But the two additional premises are not just true, they are logically necessary. I’ll say more about what it means for (4) and (5) to be logically necessary later, but for now, I need you to grasp this key point first: Because the additional premises are not just true but logically necessary, we can legitimately conclude that Proposition Set A is itself inconsistent.

But if those additional premises were not logically necessary, but only true, we can’t conclude in that way. This was what happened in Proposition Set B:

(1) Angeline is older than Bernice.

(2) Bernice is older than Cheryl.

(3) Cheryl has more years of schooling than Angeline.

(4) If X is older than Y, and Y is older than Z, then X is older than Z.

(5) If X has more years of schooling than Y, then it’s not the case that Y has more years of schooling than X.

(6) If X is older than Y, then X has more years of schooling than Y.

(7) Angeline is older than Cheryl (from (1), (2) and (4))

(8) Angeline has more years of schooling than Cheryl (from (6), (7))

(9) It’s not the case that Cheryl has more years of schooling than Angeline (from (5), (8))—which contradicts (3).

Now, the additional premises (4) and (5) are logically necessary. (4) is the same as previously in Set A. (5) is also very similar. (6) is the problem. Conceivably, (6) is true; but it is not logically necessary. Again, I’ll say more about what it means for it not to be logically necessary but the key point to grasp here (which is really a counterpart to the previous key point) is this: Because at least one of the additional premises is at best true, but not logically necessary, we cannot legitimately conclude that Proposition Set B is itself inconsistent. What you have shown is that {R} conflicts with {S}. In other words, If you believe that {R} is true, then you shouldn’t believe that {S} is true (and vice versa).

The upshot is this. If Mackie’s additional premises are not logically necessary, then he hasn’t shown that the three propositions in Believer’s belief are inconsistent, only that they conflict with at least one of his additional premises. If Believer wants to continue to believe in the three propositions, she shouldn’t also believe in the truth of the additional premises (and vice versa). Mackie is fully aware of this–this is why he explicitly calls his additional premises “quasi-logical rules connecting the terms ‘good’, ‘evil’, and ‘omnipotent’.”

So now we need to explain what it means for a proposition to be not just true, but logically necessary. There is more than one way for something to be logically necessary. For our purposes, let’s start from the contrast between the following two propositions from our minion examples:

Logically Necessary: (5) If X has more years of schooling than Y, then it’s not the case that Y has more years of schooling than X.

At best True, but not Logically Necessary: (6) If X is older than Y, then X has more years of schooling than Y.

Let’s take for granted that both statements are true. But what’s the difference between them?

Here’s a difference: if (5) is true, it’s purely because if one thing has more of something than another, then it follows immediately that the other thing doesn’t have more of the same thing than it. All of that is just part of what it means for anything to have more of something than another, assuming standard meanings to those words, and the rules of standard logic. It doesn’t matter whom we are referring to. It doesn’t matter specifically how much older one this is over the other. It doesn’t matter what context this is. In every context, for every pair of items, and for every specific difference of age, it will be the case that (5) is true, as long as we are assuming standard meanings to the words and standard logic; in fact, (5) can’t even be false. This how (5) is not just true, but logically necessary–it’s truth is a matter of logic and meaning alone.

Proposition (6) is different. Even granting that the statement is true, and assuming standard meanings of the words involved, it does matter, for instance, specifically how much older is one than the other: if X is only 6 months older than Y, you shouldn’t have too much confidence that X has more years of schooling than Y; on the other hand, if X is 75 years older than Y, then your confidence is correspondingly increased. It matters what the context is and thus whom we are talking about: if we are talking about people living in a war torn country or undeveloped society somewhere, where no schools have been running for the longest time, or ever, (6) is false–because nobody has any years of schooling. In contrast, if we are talking about typical people from a regimented and education-crazy society such as Singapore, then typically, the older person will have more years of schooling than the younger. The long and short is that (6) may well be true. But it could be false. If it’s true, it’s truth is not just a matter of logic and meaning alone, even assuming standard meanings to the words involved, but requires the cooperation of the world, so to speak. This is how (6) is at best true, but not logically necessary.

So the critical question for the Logical Problem of Evil is this: Are Mackie’s additional premises not just true, but logically necessary? Before I say a bit more about that, let me first consider a rejoinder. Does it matter? What if the additional premises are just plain vanilla true, even if not logically necessary? If we did manage to show that a contradiction can be derived from the propositions in Believer’s belief set plus these true additional premises, haven’t we done an important thing already–we have shown that Believer’s belief set conflicts with something true, and so is false. Isn’t this good enough?

In one sense it is, but in a deeper sense, not. Suppose the additional premise is true, then, yes, the POE did managed to achieve something–it has shown, to Atheist’s own satisfaction, that Believer’s belief set conflicts with something that he–Atheist–holds to be true. But no, it is not enough if the ambition of the LPOE is to show that the Theist is positively irrational. The additional premise can’t just be true–as in taken by Atheist to be true; they have to be premises Believer has to accept (or is otherwise irrational).

There are different ways this can happen, and some of these are more ambitious than others, and the most stringent, most incontrovertible way, is to show that the premise is logically necessary. If the premises in question are logically necessary, then–granted standard logic and granted that all concerned avoid the nuclear option of playing the God-can-do-the-logically-impossible card–yes, Believer has to accept the premises. Not accepting them reveals her to be illogical and thus irrational, on par with refusing to accept that if someone has more apples than another, then it’s not the case that the latter has more apples than the former, given standard meanings of those words.

Back to Mackie’s additional premises. They are (see top of p. 201 of the reading):

(M4) Good is opposed to evil, in such a way that a good thing always eliminates evil as far as it can.

(M5) There are no limits to what an omnipotent thing can do.

If all parties agree to avoid the nuclear option of playing the God-can-do-the-logically-impossible card, then we can take (M5) out of the discussion given a suitable qualification. By “no limits”, we don’t mean to include the logically impossible. So the expansion of what it means for a being to be omnipotent that it can do all logically possible things is acceptable to both Believer and Atheist.

The real question concerns (M4)–and unsurprisely, most of the “attempted solutions” Mackie considered in his article directly or indirectly target that premise. While I have my own opinions about this I don’t really want to settle the issue for you one way or another. What I do want is that you appreciate the reasoning that gets us to this point. (Anything else beyond that is, strictly speaking, gravy.) But suffice it to say that (M4) may well be true, but it is far from being obviously and incontrovertibly logically necessary. And a way to focus the situation is to ask ourselves the following question. Imagine the following proposition:

(BB) Some evils are such that their existence is logically necessary for the existence of goods that outweigh them.

(Labeled ‘BB’ for ‘Believer’s Beef’.) Is (BB) true or false? Maybe it’s true, but that’s not obvious; maybe it’s false, but that’s not obvious either. Here’s the rub: it may be true. It is not logically impossible. In fact, (BB) and (M4) conflicts with each other–if one is true, the other is false. For all we care, either could be true, and neither is logically necessary. But as long as (BB) is not logically impossible–it could be true–then (M4) is not logically necessary either. (Note: to defuse the Logical Problem of Evil, Believer doesn’t even have to show that BB is actually true; she only needs to show that (BB) is logically possible. But I’ll skip that subtlety.)

In short, Atheist has his work cut out for him if he sticks to the Logical Problem of Evil as aiming to show that there is an inconsistency in Believer’s belief set–he owes us an account of how (M4) is not just true or defensible against various objections; he needs to show us that (M4) is logically necessary, something Mackie hasn’t even tried to do in the article. (Though to be fair, he did try to show that (M4) is the sort of thing that Believer should accept, that Believer’s possible objections against it aren’t good enough. But that’s still short of the stated target.)

Commenting on the general issue, Michael Tooley (an Atheist philosopher and proponent of a more modern, and inductive version of the Problem of Evil), has this to say:

If a premise such as [e.g., something like (M4)] cannot, at least at present, be established deductively, then the only possibility, it would seem, is to offer some sort of inductive argument in support of the relevant premise. But if this is right, then it is surely best to get that crucial inductive step out into the open, and thus to formulate the argument from evil not as a deductive argument for the very strong claim that it is logically impossible for both God and evil to exist, (or for God and certain types, or instances, of evil to exist), but as an evidential (inductive/probabilistic) argument for the more modest claim that there are evils that actually exist in the world that make it unlikely that God exists. (“The Problem of Evil” in Stanford Encyclopedia of Philosophy)

If you are interested to find out more, check out the writings of Alvin Plantinga, the philosopher of religion who did some of the most important recent work on this very area. One relatively accessible version is found in his short book God and Other Minds. Plantinga and Tooley actually co-wrote a book, Knowledge of God, where they contributed alternate chapters debating with each other.