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Atheist existentialism or atheistic existentialism is a kind of existentialism which strongly diverged from the Christian works of Søren Kierkegaard and has developed within the context of an atheistic worldview.
The philosophy of Søren Kierkegaard provided existentialism's theoretical foundation in the 19th century. Atheist existentialism began to be recognized after the 1943 publication of Being and Nothingness by Jean-Paul Sartre, and Sartre later explicitly alluded to it in Existentialism is a Humanism in 1946. Sartre had previously written in the spirit of atheistic existentialism, (e.g. the novel Nausea (1938) and the short stories in his 1939 collection The Wall). Simone de Beauvoir likewise wrote from an atheist existentialist perspective.
The term atheistic existentialism refers to the exclusion of any transcendental, metaphysical, or religious beliefs from philosophical existentialist thought. Atheistic existentialism can nevertheless share elements (e.g. anguish or rebellion in light of human finitude and limitations) with religious existentialism, or with metaphysical existentialism (e.g. through phenomenology and Heidegger's works).
Atheistic existentialism confronts death anxiety without appealing to a hope of somehow being saved by a God (and often without any appeal to supernatural salvations like reincarnation). For some thinkers, existential malaise is mostly theoretical (as it is with Jean-Paul Sartre) while others are quite affected by an existentialistic anguish (an example being Albert Camus and his discussion of the Absurd).
Sartre once said "existence precedes essence". What he meant was that, first of all, man exists (e.g. appears on the scene) and only afterwards defines himself. If man, as the existentialist conceives him, is indefinable, it is because at first he is nothing. Only afterward will he be something, and he himself will have made what he will be. Thus, there is no human nature, since there is no God to conceive it. Not only is man what he conceives himself to be, but he is also only what he wills himself to be after this thrust toward existence.
Major works 
The novel Nausea is, in some ways, a manifesto of atheistic existentialism. Sartre deals with a dejected researcher (Antoine Roquentin) in an anonymous French town, where Roquentin becomes conscious of the fact that nature, as well as every inanimate object, are indifferent towards him and his tormented existence. Furthermore, they show themselves to be totally extraneous to any human meaning, and no human can see anything significant in them.
Camus writes of dualisms, between happiness and sadness, as well as life and death. In Le Mythe de Sisyphe (The Myth of Sisyphus), such dualism becomes paradoxical, because humans greatly value their existence while at the same time being aware of their mortality. Camus believes it is human nature to have difficulty reconciling these paradoxes, and indeed, he believed humankind must accept what he called "the Absurd". On the other hand, Camus is not strictly an existential atheist because the acceptance of the Absurd implies neither the existence of a god nor the nonexistence of a god.
Despair, Optimism, and Rebellion 
In his essay “Despair, Optimism, and Rebellion”, Evan Fales submits three atheist existential stances towards life (which are not mutually incompatible). He argues that a certain dignity, and commitment to truth, is captured by Bertrand Russel when he says that “…only on the firm foundation of unyielding despair, can the soul’s habitation henceforth be safely built”. Fales believes that despair is only one possible reaction, or else component, of the atheist existentialist attitude.
Fales proposes that another attitude is the Optimism of Secular Humanists: their moral systems are objective, man-made, and grounded to some extent in naturalistic facts; they derive meaning in their lives by defending those morals, and other aspects of a good life (beauty, pleasure, mastery, etc.). Fales adds that atheist optimists must be careful to avoid fatalism (not to be confused with determinism) when faced with the grimmer sides of human nature, especially in the absence of divine retribution - a task he says secular humanists realize by seeing their short life and great challenges as serving to deepen their moral obligations to make at least a small contribution. Fales also describes what he calls the optimists’ “negative thesis” when he writes “The infantilization of humankind in relation to God is one of the most disturbing features of Christian religious sensibility, especially in the context of moral judgment.” The path of optimism, to Fales, thus means affirming man-made morality, but also challenging ideologies that say morality could be anything else.
Since Rebellion is practiced against something, Fales warns that the atheist is not rebelling against the God they reject, so much as an indifferent universe. Fales continues: ”But, if there is a God, and that God is the God of Abraham, Isaac, Jacob, and Jesus, then I affirm that there is one stance that is legitimate and justified. It is rebellion.”
See also 
- Enc. Britannica, art. "Atheistic Existentialism"
- About Atheistic Existentialism
- Atheistic existentialism
- The absurd in atheistic existentialism