Rebirth. If there is no self, then what is reborn?

Not sure if this answers your question or not, but it may be of interest nontheless. Quotes are from here: http://shinranworks.com/the-major-expositions/chapter-on-practice/ Quotes are by T'an-luan, a chinese monk who is credited by Honen as being the founder of Pure Land buddhism in china:

Question: In the Mahayana sutras and treatises it is frequently taught that sentient beings are in the final analysis unborn, like empty space. Why does Bodhisattva Vasubandhu express aspiration for “birth”? Answer: The statement, “Sentient beings are unborn, like empty space,” is open to two interpretations. First, what ordinary people see – such as sentient beings, which they conceive as real, or the acts of being born and dying, which they view as real – is ultimately non-existent, like imaginary “tortoise fur,” or like empty space. Second, since all things are “born” from causal conditions, they are actually unborn; that is, they are non-existent, like empty space. The “birth” to which Bodhisattva Vasubandhu aspires refers to being born through causal conditions. Hence it is provisionally termed “birth.” This does not mean that there are real beings or that being born and dying is real, as ordinary people imagine. Question: In what sense do you speak of birth in the Pure Land? Answer: For the provisionally-called “person” in this world who practices the five gates of mindfulness, the preceding thought is the cause of the succeeding thought. The provisionally-called “person” of this defiled world and the provisionally-called “person” of the Pure Land cannot be definitely called the same or definitely called different. The same is true of preceding thought and succeeding thought. The reason is that if they were one and the same, then there would be no causality; if they were different, there would be no continuity. This principle is the gate of contemplating sameness and difference; it is discussed in detail in the treatises. Here ends the explanation of the three gates of mindfulness manifested in the first stanza.

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