I have always had problems with the definition of 'atheism' proposed by the mast majority of modern atheists. I have also always had issues with the definition of 'theism' proposed by moderns theists. We have the following historical definitions from Noah's 1828 Dictionary:
"A'THEISM, n. The disbelief of the existence of a God, or Supreme intelligent Being. [.] Atheism is a ferocious system that leaves nothing above us to excite awe, nor around us, to awaken tenderness."
"THE'ISM, n. [from Gr. God.] The belief or acknowledgment of the existence of a God, as opposed to atheism. Theism differs from deism, for although deism implies a belief in the existence of a God, yet it signifies in modern usage a denial of revelation, which theism does not."
Notice the word 'Disbelief' in this definition of Atheism. Observe also that under Theism it is broad enough to include polytheism but is distinct from deism in that it affirms the possibility of Revelation (A key feature of personhood).
Disbelief is defined here with more verbal force in that it would be a positive rejection of more than what we now generally consider. Because of this issue with the definition an ex-atheist philosopher named Antony Flew tried to precise the definition by making more appropriate distinctions. The result was a distinction between a positive atheist and a negative atheist in a paper he wrote called the "The Presumption of Atheism". In it the definition he proposed for a negative atheism was done by trying to precise the word 'disbelief'. He said:
"the word ‘atheist’ has in the present context to be construed in an unusual way. Nowadays it is normally taken to mean someone who explicitly denies the existence . . . of God . . . But here it has to be understood not positively but negatively, with the originally Greek prefix ‘a-’ being read in this same way in ‘atheist’ as it customarily is in . . . words as ‘amoral’ . . . . In this interpretation an atheist becomes not someone who positively asserts the non-existence of God, but someone who is simply not a theist."
(A Companion to Philosophy of Religion, ed. Philip Quinn and Charles Taliaferro [Oxford: Blackwell, 1997], s.v. “The Presumption of Atheism,” by Antony Flew)
As a result many and most modern atheists have imbibed or adopted this definition along with some form of verificationism. The strange thing about this definition precising is that it ignores the fact of quiescent beliefs. They are beliefs that you are in possession of but are not always held consciously. An analogy would be like the way your computer stores information when you turn it off and the information is still there when you turn it back on. The big problem with this definition is that it is virtually identical to having a belief that is quiescent instead of not present at all. Thus we could make the same distinction as theists. Namely that of positive theism and negative theism. We could then precise our definition and still fit into the semantic domain of 'disbelief' with lack of belief being the quiescence state of our possessed belief in God. We could say for example that while we are asleep our possessed belief in God is quiescent. This will not suffice alone though because we need to accommodate the deism distinction while agreeing that beliefs are cognitive. We could precise our Mono-theistic definition for (Negative) theism to the (Negative) atheist thus:
"The presence of the belief or acknowledgment of the existence of a God who can make possible revelation"
What this results in is that both become trivially true in a validly circular fashion by definition. Because this is the case we would arrive at Presuppositional Atheism and Presuppositional Theism. After all 'Presumption' as Antony Flew called it is just another word for 'Presupposition'. These two sorts will have to basically argue against the existence of the presence or non-presence of a belief. How would anyone be able to do that? I will let you think about that but this is all to say such a negative definition seems like it could be used as a clever and deceptive tactic to always leave open an escape hatch. As such both definitions seem to have a deficiency.
2 Consider it all joy, my brethren, when you encounter various trials,
3 knowing that the testing of your faith produces endurance.
4 And let endurance have its perfect result, so that you may be perfect and complete, lacking in nothing.
5 But if any of you lacks wisdom, let him ask of God, who gives to all generously and without reproach, and it will be given to him.
6 But he must ask in faith without any doubting, for the one who doubts is like the surf of the sea, driven and tossed by the wind.
7 For that man ought not to expect that he will receive anything from the Lord,
8 being a double-minded man, unstable in all his ways.
(Jam 1:2-8 NAU)