Saturday, January 30, 2016

Evil Is Evidence for Atheism or Theism?

One variety of the argument from evil goes like this:

1. If horrible evils exist, then God does not exist.
2. Horrible evils do exist.
3. Therefore, God does not exist.

How might one justify premise (1)? Where “If P, then Q” is symbolized as P → Q, it is a theorem that Pr(Q|P) ≤ Pr(P → Q), so “Given P, probably Q” entails a high probability for “If P, then Q.” The likelihood that God does not exist given that horrible evils exist is high, so (1) is true.

A theist might argue that evil proves the existence of God because in the absence of God, there would exist no moral dimension to certain states of affairs; the moral property “moral badness” would not be associated with any action because if God does not exist then objective moral values do not exist. The argument might go like this:

1. If God does not exist, then horrible evils do not exist.
2. Horrible evils do exist.
3. Therefore, God exists.

Atheists are divided on the probability of morality existing on atheism; some think morality probably doesn’t exist if atheism is true and would agree with (4) while disagreeing with (5), whereas some atheists agree with (5) and reject (4).

For those atheists who believe that moral values probably don’t exist on atheism and agree with (4), is it possible that evil (if it exists) renders God’s existence unlikely, evil is unlikely on atheism, and yet atheism is probably true?

Yes.

Let’s use the following symbolization key:
• G = God exists
• ¬G = God does not exist
• E = Horrible evils exists
• ¬E = horrible evils do not exist

Consider the logically possible probability distribution values:

¬GGTotal
E0.090.0010.091
¬E0.810.0990.909
Total0.90.11.0

So for example P(¬G & E) = 0.09 in the table above. An important math equation where P(A|B) is the probably of A given B:

 P(A|B) = P(A&B) P(B)

The following are true:

1. P(¬G|E) = 98.9011%
2. P(¬E|¬G) = 90%

So statement (7) implies that premise (1) is probably true, and statement (8) implies that premise (4) is true. So for the atheist that denies objective moral values, he can accept both (1) and (4) are likely true while also maintaining a high probability for ¬G (perhaps via the presumption of atheism) but would of course deny premise (5).

Moreover, statement (7) basically says “The likelihood that God does not exist given that horrible evils exist is high” and so the atheist can affirm that even while denying the existence of evil. Even if the atheist denies the existence of horrible evils, the theist surely believes horrible evils exist, and so a high probability for P(¬G|E) is problematic for the theist in a way that isn’t for the atheist.