noahidism - Must a non-Jew accept the Noachide laws as binding?

In order for a non-Jew to fulfill his obligation to follow the 7 Noahide Laws, is it required that he accept those laws as binding, or is it sufficient if he coincidentally happens to follow the 7 Laws without thinking about it.

This question is inspired by this answer.

EDIT:

After thinking a bit about this question, I think the question itself might be illogical. If the answer to "Is it required that he accept those laws as binding" is "yes," then it is impossible to "coincidentally happen to follow the 7 Laws without thinking about it." So I guess the first clause of the question is really my question.

Answer

The Rambam states in הלכות מלכים הלכה יא

כל המקבל שבע מצות בני נח ונזהר לעשותן הרי זה מחסידי עומות העולם. ויש לו חלק עולם הבא. והוא שיקבל אותן ויעשה אותן מפני שצוה בהן הקב"ה בתורה והודיענו על ידי משה רבינו שבני נח מקודם נצטוו בהן. אבל אם עשען מפני הכרע הדעת אין זה גר תושב ואיו מחסידי עומות העולם ולא מחכמיהם.

Melachim uMilchamot 8:11 translates this as

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.

The term מקבל (accepts on himself) implies that he accepts it as obligatory. This is similar to the way the Bnai Yisrael "accepted" the Torah at Har Sinai. That is, once it was accepted, it was obligatory from then on. Similarly, the fact that the non-Jew who accepts the sheva mitzvos must accept that they are mitzvos (commandments) shows that he must regard them as obligatory and from Hashem as brought down by Moshe just as the 613 mitzvos of the Torah are binding on Bnai Yisrael.

Wikipedia at Seven Laws of Noah besides pointing to the Rambam and the chabad translation, also points to the Encyclopedia Talmudis discussion of the matter. It goes into more detail but has details that are irrelevant to the question as asked. Look there if you want to see more or want to see references to the Encyclopedia Talmudis.