What logical arguments do they have?
Before I answer, allow me to say this: some of them wish they had no arguments. Actually, "arguments" aren't actually that important for them, they just wish they had no reasons to think there's no God. Just saying!
Moving on...they have a whole list of logical arguments, most of which are based in the (apparent) lack of logic on God's thought. As in...let's say God wanted to create a universe in which humans could live and use their free will with the objective of accepting or rejecting God. Obviously, since God invent all the rules that operate inside the universe, He could have chosen ANY possible way those rules would apply. In so being, it's hard to understand this like these: Why would God
- Create the whole universe from a ridiculously small point, which could lead humans to think the beginning of the universe implied simplicity, not complexity?
- "Build" humans with the exact same material used to build the whole universe (i.e, atoms, particles and all that stuff), which could lead them to think they had the same value of everything in the universe?
- Allow mental illnesses, which clearly interfere with the whole use-your-free-will-to-choose-God-or-reject-God thing?
- Allow humans to die before a certain age, which interferes with the exact same thing?
- Allow animals to hunt and eat humans as if they were some chicken, which could lead them to think they were as animals as any other animal?
- Allow humans to rot like any regular animal and plant, which could lead them to think hey were as animals as any other animal?
- And why, oh why would He allow extraordinary coincidences to happen, which is WAY likely to make humans think intelligence is not obligatory to create a complex situation/monument/piece of art/whatever
Actually, I myself have talked about some of these lacks of logic in this topic:
http://discussions.godandscience.org/vi ... 33&t=39825. Which is natural, since these lacks of logic are the main thing that keep me away from believing in the God of the Bible. Yes, even more than the spontaneous creation theory.