A privative, named from Latin privare, "to deprive", is a particle that negates or inverts the value of the stem of the word.
“Atheism” is typically defined in terms of “theism”. Theism, in turn, is best understood as a proposition—something that is either true or false. It is often defined as “the belief that God exists”, but here “belief” means “something believed”. It refers to the propositional content of belief, not to the attitude or psychological state of believing. This is why it makes sense to say that theism is true or false and to argue for or against theism. If, however, “atheism” is defined in terms of theism and theism is the proposition that God exists and not the psychological condition of believing that there is a God, then it follows that atheism is not the absence of the psychological condition of believing that God exists (more on this below). The “a-” in “atheism” must be understood as negation instead of absence, as “not” instead of “without”. Therefore, in philosophy at least, atheism should be construed as the proposition that God does not exist (or, more broadly, the proposition that there are no gods).
Departing even more radically from the norm in philosophy, a few philosophers and quite a few non-philosophers claim that “atheism” shouldn’t be defined as a proposition at all, even if theism is a proposition. Instead, “atheism” should be defined as a psychological state: the state of not believing in the existence of God (or gods). This view was famously proposed by the philosopher Antony Flew and arguably played a role in his (1972) defense of an alleged presumption of “atheism”. The editors of the Oxford Handbook of Atheism (Bullivant & Ruse 2013) also favor this definition and one of them, Stephen Bullivant (2013), defends it on grounds of scholarly utility. His argument is that this definition can best serve as an umbrella term for a wide variety of positions that have been identified with atheism. Scholars can then use adjectives like “strong” and “weak” to develop a taxonomy that differentiates various specific atheisms. Unfortunately, this argument overlooks the fact that, if atheism is defined as a psychological state, then no proposition can count as a form of atheism because a proposition is not a psychological state. This undermines his argument in defense of Flew’s definition; for it implies that what he calls “strong atheism”—the proposition (or belief in the sense of “something believed”) that there is no God—is not really a variety of atheism at all. In short, his proposed “umbrella” term leaves strong atheism out in the rain.
The word 'atheism', however, has in this contention to be construed unusually. Whereas nowadays the usual meaning of 'atheist' in English is 'someone who asserts that there is no such being as God', I want the word to be understood here much less positively. I want the originally Greek prefix 'a' to be read in the same way in 'atheist' as it customarily is read in such other Greco-English words as 'amoral', 'atypical', and 'asymmetrical'. In this interpretation an atheist becomes: not someone who positively asserts the non-existence of God; but someone who is simply not a theist. Let us, for future ready reference, introduce the labels 'positive atheism' for the former doctrine and 'negative atheism' for the latter.