1. First, “reincarnation” is a bad translation for “attabhāvapaṭilābha”.
– Reincarnation implies an “everlasting entity” taking different forms in different births.
As we discussed in the post, “Anattā in Anattalakkahana Sutta – No Soul or an Ātma”, “atta” has a mundane meaning and a transcendental (lokuttara) meaning.
2. In the mundane sense, “attabhāva” can imply a certain birth or existence, say as a human, a deva, or an animal. Even when a human is reborn he can be said to have “another attabhava”.
– However, as we saw in that post, in reality there is “attā” like a “soul” being reborn (this is again why reincarnation is a bad translation).
3. Therefore, one needs to be careful in determining in what sense the term “attabhāva” is used in a particular instance.
– In the sutta that y not referred to (“Saṅgīti Sutta (DN 33)“), Ven. Sariputta just listed those four types of “attabhāva”, likely to be in the lokuttara sense; he did not elaborate on the four categories. I don’t have time to look into that right now. May be others can comment on that.
– English translation at the same website: “The Recital (DN 33)“.
4. The Buddha provided explanations for both mundane and lokuttara versions in the “Poṭṭhapāda Sutta (DN 9)“.
– English translation there: “To Poṭṭhapada (DN 9)“. I have not read that, so I am not sure how good the translation is.