www.alphadictionary.com

theodicy

The justification or vindication of God in view of the existence of evil.

The word was coined by the philosopher Leibniz in 1710.

Anyone know if there's a like term for using the existence of evil as justification for denying the existence of God?

Was it toward the end of the 17th century that 'God' became beneficent rather than vengeful? Explaining the need to coin such a word?