According to Buddhism, all component or conditioned things are impermanent and in a constant state of flux. Therefore in opposition, the existence of an unchanging and independent self, in this world, is denied since it goes against the Buddhist principle of selflessness (anatta). Buddhists hold that the notion of a permanent self is one of the main root causes for the wars and conflicts in human history, and that by living by anatta or not-self, we may go beyond our mundane desires. The ineffable state of Nirvana is solely recognized as being distinct. Conventionally speaking though, the soul or self for Buddhists is spoken of socially but under the conviction that we are dependent on others and not independent unchanging selfs. At death the body & mind disintegrates, but if the disintegrating mind contains any remaining traces of karma, it will cause the continuity of the consciousness to bounce back an arising mind to an awaiting being (i.e. a fetus developing the ability to harbor conciousness). Thus Buddhists teach that a reborn being is neither entirely different nor exactly the same.
The Hindu concept of atman is what reincarnates, standing as the highest divine self or ray in each human being. In Buddhist thought this is denied. Buddhism and Hinduism both reach the conclusion that there is a continuity between lives, yet their tenets on what it is that goes from life to life vary. In one there is a higher self (or atma), in the other there is only thought-processes or tendencies that is reborn.
See also: Shunyata
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