What one has here, however, is not just a puzzle, since the question can, of course, be recast as an argument for the non-existence of God. Thus if, for simplicity, we focus on a conception of God as all-powerful, all-knowing, and perfectly good, one very concise way of formulating such an argument is as follows:
- If God exists, then God is omnipotent, omniscient, and morally perfect.
- If God is omnipotent, then God has the power to eliminate all evil.
- If God is omniscient, then God knows when evil exists.
- If God is morally perfect, then God has the desire to eliminate all evil.
- Evil exists.
- If evil exists and God exists, then either God doesn't have the power to eliminate all evil, or doesn't know when evil exists, or doesn't have the desire to eliminate all evil.
- Therefore, God doesn't exist.
That this argument is valid is perhaps most easily seen by a
reductio argument, in which one assumes that the conclusion — (7) — is false, and then shows that the denial of (7), along with premises (1) through (6), leads to a contradiction. Thus if, contrary to (7), God exists, it follows from (1) that God is omnipotent, omniscient, and morally perfect. This, together with (2), (3), and (4) then entails that God has the power to eliminate all evil, that God knows when evil exists, and that God has the desire to eliminate all evil. But when (5) is conjoined with the reductio assumption that God exists, it then follows via modus ponens from (6) that either God doesn't have the power to eliminate all evil, or doesn't know when evil exists, or doesn't have the desire to eliminate all evil. Thus we have a contradiction, and so premises (1) through (6) do validly imply (7).