In Other Philosophy
Aquinas, using Scholasticism, treats the "Best of all possible worlds" problem in the Summa Theologica (1273):
Objection 1: It seems that God does not exist; because if one of two contraries be infinite, the other would be altogether destroyed. But the word "God" means that He is infinite goodness. If, therefore, God existed, there would be no evil discoverable; but there is evil in the world. Therefore God does not exist.
He counters this in general by the quinque viae, and in particular with this refutation:
Reply to Objection 1: As Augustine says (Enchiridion xi): "Since God is the highest good, He would not allow any evil to exist in His works, unless His omnipotence and goodness were such as to bring good even out of evil." This is part of the infinite goodness of God, that He should allow evil to exist, and out of it produce good.
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