If you are going to discuss Atheism, Agnosticism, and Theism, you probably ought to do so by first defining what you mean by the terms. Theism and Agnosticism are both relatively easy to define. Theism can be reasonably said to be a belief in some form of deity. Agnosticism is generally accepted to be the position that we either do not or can not know for sure whether any deities exist or do not exist. Atheism is much harder to define. I think this page has some good discussion of different "forms" of Atheism:
Negative and positive atheism - Wikipedia, the free encyclopedia
I've never seen a good rational arguement for positive atheism. To assert that no deities exist is to assert full knowledge of everything which would imply that you are some form of deity yourself since full knowledge of the universe would not be possible for a human. To make the assertion, "There is no deity anywhere in existence," is to implicitly refute your own assertion.
I can understand the statement, "I believe there is no deity." I can understand the statement, "I do not believe there is a deity." I cannot understand the statement, "There is no deity."
Careful philosophers note that a crucial element is missing in this kind of discussion. For a proposition such as "God exists", there are actually four possibilities: theism, atheism, agnosticism, and non-cognitivism. The last is the one that usually gets left out of the discussion, but is the most important.
To answer a question, the questioner and the answerer must have an understanding as to what the question means. For the proposition "God exists" this boils down to what is meant by "God". The non-cognitivist position is that the proposition is not sufficiently defined to allow an answer which would be understood by the parties of the discussion in the same way. Personally I am a non-cognitivist regarding the proposition "God exists". My usual response is "Which God?"
Now if I ask you "Do you believe in Jupiter?" You will answer "No" and I can confidently state that both you and I are atheists with respect to the existence of Jupiter.
In general terms, all questions of the form "Do you believe in X?" require a common understanding as to what X exactly is.
Something along those lines is brought up on the wikipedia page I linked to. Non-cognitivism is, I think, a form of Negative Atheism. A person who either chooses not to think about deities or who has never heard of any deity, does not believe in any deity. That person doesn't assert that there is not any deity, they simply do not think about deities at all (or at least not for any significant amount of time.) This is also known as Implicit Atheism as opposed to Explicit Atheism.
First, thanks for a well thought out response! Non-cognitivism is an outgrowth of logic rather than philosophy of religion. As such, it makes no judgment of a proposition that might be implied but is not stated. So I don't think it is a form of Negative Atheism. My personal faith is a form of philosophical Taoism which holds that personified deities (those that exhibit human emotions and characteristics such as favoritism, anger, pride, susceptability to cajolery, etc) are human constructs designed for social control. They are a sociological phenomena, not a religious one. So my personal beliefs are Negative Atheist toward almost all deities in your framework. But that is not a universal characteristic of a non-cognitivist position with regard to any particular proposition of god-talk.
Anyone who does not believe that all deities exist can fit into one of these categories of Atheism with respect to any given description of a deity. To your example, I don't think many people believe in Jupiter any more. Even among Christian sects, the God one sect describes is not necessarily the same God that another sect describes. Some of the most vehement disputes I have witnessed about God were between two Christians.
My experience is very similar to yours. There is more dispute over the "true" God than over the general proposition of the existence of a deity.
That said, unless you are "Atheist" with regards to all deities (or at least every one you had ever heard or thought of) you would not describe yourself as Atheist in general.
I do not consider myself an atheist in a general sense. My objection is to a large class of proposed deities, and to some others I am a non-cognitivist. I see no harm in the "Clock-maker God" of the Deists of the 16th century, nor of the "smaller gods" of hearth and home. No one ever went to war over these "gods", although quite a few witches were burned for believing in them (but that is a reflection on those who hunted, not the hunted).
I would finish with one note. When you ask the wrong question, you usually get bad results. The Abrahamic religions ask "What does God want us to do?" and has therefore spawned a great deal of evil in the world. One is hard pressed to conceive of a crime against humanity not committed in the name of those religions. And of course those faiths are mutually exclusive in many cases and in a state of violent conflict against each other. In contrast, the Eastern traditions (Vedic religions, Buddhism, Taoism, Confucianism, Jainism and so forth) are less exclusive. A Chinese proverb states that every Chinese wears a Confucian hat, a Taoist robe, and Buddhist sandals. Each of these faiths starts from a different question, "How should a wise person live their life and treat other people?"
