A couple of people didn't understand my recent post on atheism, so let me elaborate. Theism is belief in a personal deity (whom I will call "God"). Atheism is disbelief in a personal deity. The theist affirms, and the atheist denies, that God exists. Theism and atheism are logical contradictories, which means that one of them is true and the other false. What I said in my post is that there are three possible arguments (or argument types) in favor of atheism. The first is that God is impossible, like a married bachelor. The idea is that the properties ascribed to God, such as omnipotence, omniscience, and omnibenevolence, cannot be instantiated. If God is impossible, then obviously God does not exist.
Some atheists admit that God is possible (i.e., that the concept of God is instantiatable), but deny that God exists. There are, in general, two types of argument: deductive and inductive. A deductive argument for atheism says that God's existence is impossible, given certain premises. An inductive argument for atheism says that God's existence is improbable, given certain premises. If I make a deductive argument for atheism, I am telling my interlocutors that certain of their beliefs (represented as premises) preclude belief in God. In other words, you can't believe p, q, and r and still believe in God. If I make an inductive argument for atheism, I am telling my interlocutors that certain of their beliefs (represented as premises) give them reason (thought not a conclusive reason) to disbelieve in God.
All arguments for atheism fall into one of these three categories, and no argument falls into more than one.
Keith Burgess-Jackson, J.D., Ph.D. 