Is it permitted for a Ben-Noach be an atheist?

Question

Avoda zarah is one of the things prohibited by the Seven Noachide Laws. But what about atheism? I know that the 7 Laws are often taken to include a larger number of halachot from the Torah, so would the prohibition against avoda zarah expand to include kefira as well?

Answer 1

Rav Moshe Feinstein, in a t'shuva about allowing children to say a generic prayer in public school (Orach Chayim II #24), refers to the Ramba"m's statement in Mishne Torah that Adam Harishon was given one commandment - belief in God. No'ach and his descendants later got 6 more, adding up to 7. They both conclude that not only the negative aspect of believing in God is necessary - i.e. not serving other deities - but also the positive affirmation of His creation and provenance over the world, when circumstances call for it. Rav Moshe also uses the inference from the words of Ramba"m explained in @Yishai's answer.

Answer 2

Given the Rambam's statement:

Anyone who accepts upon himself the fulfillment of these seven mitzvot and is precise in their observance is considered one of 'the pious among the gentiles' and will merit a share in the world to come.

This applies only when he accepts them and fulfills them because the Holy One, blessed be He, commanded them in the Torah and informed us through Moses, our teacher, that Noah's descendants had been commanded to fulfill them previously.

However, if he fulfills them out of intellectual conviction, he is not a resident alien, nor of 'the pious among the gentiles,' nor of their wise men.

It would seem that the answer is no, it is not permitted.