Renunciation not based on Rebirth
Some may agree that the good life of the Buddhist is not based on the idea of rebirth, but when a Buddhist renounces, however, he does so either to find happiness in the next world or to solve the Samsaric problem of stopping the continuation of rebirth.
This, however, is not found to be the case when we examine Sutras like, Potaliya Sutta, Magandiya Sutta, Mahadukkhanda Sutta, Ariya Pariyesana Sutta and many others. The reasons for renunciation are to be found here and now. There is a Sutta in the Samyutta Nikaya where Mara (Satan) assuming the shape of a Brahmin... drew near to the bhikkhus and said:
“Your Reverences are too young to have left the world.... You are in your early prime now. Have the fun that belongs to natural desires. Enjoy, gentlemen, the pleasures of youth. Do not abandon the present pleasures, and run after pleasures of the future, which involves time."
“Nay, brahmin, we have not abandoned the things of this life to run after matters involving time. It is 'matters of time' brahmin, that we have abandoned, who are running after things of this life. Yea, brahmin, natural desires are ‘matters of time,’ so hath the Exalted One said, full of sorrow and despair; that way lies abundant disaster. But this doctrine is concerned with ‘things of this life,' and is not a 'matter of time'; it bids a man to come and behold, it directs him inward, and could be known by the wise, as a personal experience."
(K.S. I, 147)
The above passage clearly explains, as does several other Sutras, that renunciation does not involve the need for a belief in a next life.