are there different types of theodicies?
Yes, Biblical theodicy, Augustinian theodicy, Irenaean theodicy, Origenian theodicy.
Theodicy
The biblical account of the justification of evil and suffering in the presence of God has both similarities and contrasts in the Hebrew Bible and the New Testament. 
what is the  augustinian theodicy? The Augustinian theodicy, named for the 4th- and 5th-century theologian and philosopher Augustine of Hippo, is a type of Christian theodicy designed in response to the evidential problem of evil. when was it designed? Plantinga's adapted Augustinian theodicy, the free will defence – which he proposed in the 1980s – attempts to answer only the logical problem of evil. what was the theodicy about? It attempts to explain the probability of an omnipotent (all-powerful) and omnibenevolent (all-good) God amid evidence of evil in the world. and what is a theodicy? Theodicy () means vindication of God. It is to answer the question of why a good God permits the manifestation of evil, thus resolving the issue of the problem of evil.
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Theodicy [SEP] Biblical theodicy
The biblical account of the justification of evil and suffering in the presence of God has both similarities and contrasts in the Hebrew Bible and the New Testament. For the Hebrew Bible, the Book of Job is often quoted as the authoritative source of discussion. It is generally accepted that God's responsive speeches in Job do not directly answer Job's complaints; God does not explain Himself or reveal the reason for Job's suffering to him; instead Yahweh's speeches focus on increasing Job's overall understanding of his relationship with God. This exemplifies Biblical theodicy. There is general agreement among Bible scholars that the Bible "does not admit of a singular perspective on evil...