Let's take a time-binding approach in regard to the original post and the title of this thread. We have words to perform indications - whether that being indicated is physical such as a rock or tree, or that being indicated is something that exists virtually in our symbolic environments.
We make perceptual distinctions distinguing figure and background - a two valued binary distinction, which is a fuction of neurological processing of optical nervous processes and structure. We also make cognitive distinctions that are equally two-valued, something we focus on contrasted with that which is excluded from the focus. And we can swap figure and background. If we don't have a convenient word for the background we use the word 'not' or the prefix 'non'. Another linguistic representation of this distinction is the prefix 'a'.
However, the 'a' is "atheism" is not the prefix 'a' added to the word "theism". "Atheism", going back to the Greek, meant "without gods". The word "theism" was coined much later.
The basic meaning of the prefix a- is “without.” For example, achromatic means “without color.” Before vowels and sometimes h, a- becomes an-: anaerobic. Many of the words beginning with this prefix are used in science, such as aphasia, anoxia, and aseptic.*
The two-valued orientation that says a person must either believe or not believe is hard to overcome. "Agnostic" contrasts with gnosis which can be defined as "direct knowledge of God through awareness of the divine spark within." An agnostic "doesn't know".*
In English, the term atheism was adopted from the French athéisme in about 1587. The term atheist in the sense of "one who denies or disbelieves" predates atheism in English, being first attested in about 1571; the Italian atheoi is recorded as early as 1568. Atheist in the sense of practical godlessness was first attested in 1577. The French word is derived from athée ("godless, atheist"), which in turn comes from the Greek atheos. The words deist and theist entered English after atheism, being first attested in 1621 and 1662, respectively, and followed by theism and deism in 1678 and 1682, respectively. Deism and theism changed meanings slightly around 1700, due to the influence of atheism. Deism was originally used as a synonym for today's theism, but came to denote a separate philosophical doctrine.*
Of possible interest is a correspondence on atheism and Doubt and Faith.