The Inductive Argument from Evil
REBUFFED WITH HIS DEDUCTIVE ARGUMENT, the atheologian often turns to the inductive argument from the existence of evil. 1 Rowe calls it "the evidential form of the problem of evil: the form of the problem which holds that the variety and profusion of evil in our world, although perhaps not logically inconsistent with the existence of [God], provides, nevertheless, rational support for the belief that the theistic God does not exist." 2 This echoes Hume's earlier comment: "However consistent the world may be . . . with the idea of such a Deity, it can never afford us an inference concerning his existence."3 Or to put it another way, the pain and suffering which occur in our world make it unlikely or improbable that a God who is good, omnipotent, omniscient, loving, and personal exists.
How is this unlikelihood or improbability to be understood? Is there any way of formulating the inductive argument or improbability more precisely? Since atheologians have appealed to a standard theorem of probability calculus called Bayes' Theorem 4 elsewhere in philosophical theology--for example, to suggest that the teleological argument serves to make improbable rather than probable God's existence 5--it is appropriate that we here employ Bayes' Theorem to reconstruct the atheologian's thesis that it is improbable that God exists given the amount of evil in the universe.
Bayes' Theorem can be formulated as follows, where