Michael Egnor, a neurosurgeon and intelligent design advocate has issued this challenge to Atheists. Here are my answers to the questions he asks.
1. Why is there anything?
The problem with this question is that it assumes there is an reason for the existence of "anything". The evidence we have, to the contrary, seems to give rise to the idea that existence may have simply been a big cosmic accident. Why does everything have to have a reason?
2. What caused the universe?
Once again, we've come across the assumption that something caused the universe, when in reality it may have simply just happened. Even if there was a cause, we couldn't test it (or prove it), so therefore you couldn't accept that the universe has a "cause".
The best explanation for how the universe actually came into being that we have is what is colloquially known as Big Bang theory (note: the term Big Bang is a misnomer, and was actually given to the theory by a detractor). We can't know a cause, but we can know a how.
3. Why is there regularity (law) in the universe?
Once again, note the why.
Cynically, I would argue otherwise (that there is nothing regular about the universe, just compare relativity to quantum mechanics). If he's asking why we have deduced various laws of nature, then its because those laws of nature are just simple generalizations about a natural process. There is regularity because nature tends to act in the same ways every time. Solids displace their own weight in water, electrons orbit atoms in shells, nature selects for the most adaptive species; these are things that happen in nature not for any specific reason (if there was one, there would be no way to find it), but because it just happens.
4. Of the Four Causes in nature proposed by Aristotle (material, formal, efficient, and final), which of them are real? Do final causes exist?
The only causes that are observable or measurable are the material and formal cause. The other two are non-scientific philosophical ideas in that they postulate that nature has purpose, or principles guiding its purpose. As I've said before, they are not testable and therefore cannot be shown to exist. So, only the material and formal cause are real, and no, final causes do not exist.
5. Why do we have subjective experience, and not merely objective existence?
Because we can only perceive what our brains interpret. There is no way in nature to have an "objective existence". But, this does not mean that we cannot objectively determine the universe around us. Science lets us do that.
6. Why is the human mind intentional, in the technical philosophical sense of aboutness, which is the referral to something besides itself? How can mental states be about something?
I don't even think that's a question.
7. Does Moral Law exist in itself, or is it an artifact of nature (natural selection, etc.)
There's no such thing as "moral law" because morals are subjective, and depend on circumstance. However, current evolutionary understanding indicates that "morals" (i. e., a general sense of right and wrong) developed naturally because they might allow for greater group survival. In that sense, morals are in fact an artifact of nature.
8. Why is there evil?
Define evil. Is it evil to kill someone? Maybe, is it evil to kill someone in self defense? I wouldn't think so. Evil, like morality, is extremely subjective. To ask why there is evil, we would need a good definition of evil.
So, lets just say for argument that evil is just the act of doing bad things: killing, stealing, raping, mortgage fraud, etc. Those behaviors develop naturally. Some behaviors are good, some are bad. The bad ones tend to get weeded out because of natural selection, but they may persist. It could be said that evil is just evolutionary psychology gone wrong.