(Philosophy of Religion students take note: I have made two posts re. Mackie's essay - this one and one below.)
Here’s “the Logical Problem of Evil,” as formulated by the philosopher J.L. Mackie. This has been called "Mackie’s triad":
i. God is all-powerful.
ii. God is wholly good.
iii. Evil exists.
These three are thought to be logically inconsistent. This means one cannot affirm - simultaneously - the truth of all three statements.
b. Mackie adds some explanatory rules to make the inconsistency more obvious. Mackie believes that:
iv. A good being would always stop evil from happening. This means that a good being always eliminates evil as far as it can.
v. An all-powerful being is able to stop evil from happening. It can do anything. There are no limits to what an omnipotent being can do.
With these two explanatory rules added, Mackie thinks the logical inconsistency is obvious. Thus, for Mackie, to believe in the existence of God is positively irrational (= illogical).
Mackie's argument can be put in the form of what is called a logically "inconsistent triad". In this argument form, three propositions are inconsistent with each other such that one cannot hold all three at the same time without holding a contradiction. Holding such a contradiction would be like believing that:
a. This object is round.
b. This object is square.
It’s impossible to consistently or rationally believe both of these at the same time. Thus Mackie's argument from the problem of evil is an argument that seeks to demonstrate that the traditional theistic definition of God is logically incompatible with the existence of evil. It concludes that God cannot possibly exist if evil exists. Mackie argues that the theist cannot rationally believe in God's existence given the existence of evil.
Now NO ONE ACCEPTS THIS ARGUMENT AS A PROOF OF GOD’S NON-EXISTENCE TODAY. (See William Rowe's footnote #1 at the end of his essay in Pojman, Philosophy of Religion.) WHY NOT?
ANSWERING THE LOGICAL PROBLEM OF EVIL
Mackie's strictly logicl argument today as largely discredited. The problem with this argument is that it assumes something false. This has to do with Mackie's first explanatory hypothesis (# iv. above). It assumes that a good being would prevent every evil it can under any circumstances. This assumption is false. It seems clear that there are circumstances in which even a perfectly good being would allow some evil. These are cases where allowing those evils are necessary for bringing about certain kinds of good things. In other words, all that is needed to refute Mackie's logical argument is to show that there is at least one instance where suffering is needed in order to produce a greater good.
Therefore it seems impossible to conclusively prove that there is no good reason for some particular evil. This is because we can see that there are good reasons for certain kinds of evil. Some evil may be necessary for the realization of a greater good. Therefore, there is no way to conclusively (i.e., with logical necessity) prove that God does not exist on the basis of evil.
Most – nearly all – philosophers agree on this. Again, see the atheist William Rowe's work on this. The argument has shifted from the logical argument from evil to what is called “the evidential argument from evil.” That's what Rowe's essay is all about. Instead of a strictly logical argument such as Mackie's we now have an inductive, probableistic argument.
For arguably the best book on the evidential argument from evil see Daniel Howard-Snyder's The Evidential Argument from Evil.