1. If God does not exist, then objective moral values and duties do not exist.
2. Objective moral values and duties exist.
3. Therefore, God exists.
In his writings, Dawkins seems to understand that, without God, there is no objective good or evil (thus granting premise 1). Yet Dawkins goes on to condemn behavior that he regards as immoral (thus granting premise 2). Dawkins's denial of God's existence therefore shows that he is positively irrational.