Negative atheism, also called weak atheism and soft atheism, is any type of atheism where a person does not believe in the existence of any deities but does not necessarily explicitly assert that there are none. Positive atheism, also called strong atheism and hard atheism, is the form of atheism that additionally asserts that no deities exist. Sometimes positive atheism goes by the term gnostic atheism to contrast with agnostic atheism, which is more correlated with weak atheism, and to stand opposite Gnostic theism on simple charts mapping different belief systems.
The terms "negative atheism" and "positive atheism" were used by Antony Flew in 1976 and have appeared in George H. Smith's and Michael Martin's writings since 1990.
Because of flexibility in the term god, it is possible that a person could be a positive/strong atheist in terms of certain conceptions of God, while remaining a negative/weak atheist in terms of others. For example, the God of classical theism is often considered to be a personal supreme being who is omnipotent, omniscient, omnipresent, and omnibenevolent, caring about humans and human affairs. One might be a positive atheist for such a deity, while being a negative atheist with respect to a deistic conception of God by rejecting belief in such a deity but not explicitly asserting it to be false.
Positive and negative atheism are frequently used by the philosopher George H. Smith as synonyms of the less-well-known categories of implicit and explicit atheism, also relating to whether an individual holds a specific view that gods do not exist. "Positive" atheists explicitly assert that it is false that any deities exist. "Negative" atheists assert they do not believe any deities exist, but do not necessarily explicitly assert it is true that no deity exists. Those who do not believe any deities exist, but do not assert such non-belief, are included among implicit atheists.