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Of all of the arguments against the Bible from a stance of pure logic which I have ever heard, the only one which seems to be able to stand up to honest, logical scrutiny in even the smallest way is the Problem of Evil.
Clearly, from a Biblical standpoint, we can say that our free will, given to us by God, causes the sufferings that man brings on other men. The common rebuttal to this: that God's omniscience would cause Him to know the things we will do and thus render free will an illusion, can be shown to be invalid through some simply logical reasoning. Namely, that it is sound logic to say that "correlation does not prove (nor imply) causation", and that God's knowledge of our actions (even if it is beforehand) correlating with our choice to undertake said actions, by no means proves the causation of our actions on the part of God. We are still left with bearing the responsibility for said actions and their consequences, as God's foreknowledge of our choice does not compel us to choose that option. Furthermore, the idea that God exists "outside of time" lends support to this argument (although it is unnecessary in this argument).
Unfortunately, this argument cannot be used to explain the suffering found in nature (animals hurting animals), nor can it explain natural disasters. Is there a theologian or apologetic scholar who has written to explain a way to rationalize this? Is there anyone here who has studied this in depth and can offer a rationalization?