According to Buddhist thought, the soul does not retain its attributes at death any more than a wave retains its identity when it dissipates in the ocean. An analogy often used to illustrate Buddhism’s perspective of the cycle of birth and rebirth is that of a candle that lights another candle as it flickers and becomes extinguished.
Buddhist belief in the process of birth and rebirth is validated by the testimony of Lord Buddha Himself, who upon enlightenment came to know all the details of His hundreds or thousands of past lives. He stated that His present life would be His last. Although Lord Buddha would not include God in His teachings and did not claim to be divine, His followers came to worship Him.
Buddhists pay Him homage, if not as God, then as the Enlightened One and Hindus see Buddha as the ninth incarnation of Lord Vishnu, the Preserver.
Read more about Birth and Rebirth in the Buddhist Religion in On Hinduism, by Irina Gajjar.
Because the Gita and other scriptures consider reincarnation a self-evident doctrine, they do not make arguments to support its truth. This is much the case with most of the doctrines that are a part of scared Vedic literature. However, philosophers and teachers have made many arguments in support of their perspectives or interpretations of both doctrine and scripture. They have taught that reincarnation explains many things.
It explains why some people suffer while others do not or why some children are born with exceptional talent. It accounts for memories and emotions that seem to come out of the blue and it accounts for reports of extraordinary experiences in other dimensions.
It accounts for thousands of near death experiences reported but those who went to other realms and returned to tell what they saw and heard. Rather than rejecting these reports because they go beyond what is strictly possible, Hinduism considers many of them truthful and valuable testimony.
Quote starts with “Because the Gita and other scriptures consider….” and ends with “many of them truthful and valuable testimony.”
SeeOn Hinduism, by Irina Gajjar, Chapter Six, Karma and Reincarnation.