The Buddha denied the existence of the soul. But he is also said to have affirmed the doctrine of karma and rebirth. At once a question arises. If there is no soul, how can there be karma? If there is no soul, how can there be rebirth? Did he use the terms in a different sense than the sense in which they were used by the Brahmans of his days? If so, in what sense? Did he use them in the same sense in which the Brahmans used them? If so, is there not a terrible contradiction between the denial of the soul and the affirmation of karma and rebirth? This contradiction needs to be resolved.
First of all, it should be clear that the Buddha never used the terms in the same sense as it means in Hinduism. As far as Buddhism is concerned, there is no soul. Karma doesn't mean the hereditary passing of deeds and there results from life to life, in the context of Buddhism. Karma means action and reaction. For example, if I jump on mud, the mud will splash on me. Similarly, the meaning of rebirth doesn't mean the continuous birth of an eternal soul. This concept is a Hindu doctrine.