This is indeed “independent of Buddhism” because it involves both an ātmavāda and a sassatavāda. Which is why they talk about reincarnation rather than rebirth.
Normally at this stage of an argument on Sutta Central, participants cite numerous passages from the Pāli suttas to prove their point. To the best of my knowledge there are no stories in Pāli of children remembering their past lives. Children are notably absent from the Pāli most of the time (apart from the occasional dead infant). Does anyone have any such stories from Pāli suttas to share?
To the best of my knowledge, in Pāli no one other than the Buddha is able to exercise this advanced magical power of having knowledge of past lives (pubbenivāsānussati). While it is true that theoretically any arahant could also perform this magic, in practice none do. Moreover, arahants are not reborn after they die. So no child could possibly possess this advanced Buddha-magic. If the Pāli texts are any guide.
To the best of my knowledge this idea that children might remember a past life is not present in any Buddhist tradition of any time or place until the modern era. The one exceptions is Tibet where is it inextricably linked to issues of monastic governance and succession. And there, the sprul sku is a bodhisatva choosing to reincarnate (however that is supposed to work): in which case there is no reason that their memories would be selective or that such memories would fade as the child matured. If they possess the power of pubbenivāsānussati then they ought to clearly remember all of their past lives, like the Buddha.
As far as I can tell, this phenomenon of children aged 4-6 remembering their past lives (and subsequently forgetting them) seems to be begin with 20th century Western materialists (around the time of the Tibetan diaspora?), and in every case there is continuity of personality across lifetimes. They insist on an entity that survives death unchanged. This is, by definition, an ātmavāda and a sassatavāda. I’m sure I don’t need to restate the Buddhist arguments against these kinds of views.
The other problem with Stevenson and co is that they aren’t really doing science. The minimal requirement of doing science is that it results in a causal explanation of the phenomenon in question; and that the explanation can be used to make testable predictions. Moreover, any proposed causal explanation has to be consistent with other widely accepted causal explanations, or it has to replace them. So an explanation of reincarnation that, for example, relied on breaking the laws of thermodynamics would not be considered science, unless it also proposed a new way of understanding thermodynamics that allowed for the breaking of the rules under specified circumstances.
And, to be clear, the persistence of coherent information structures like memories beyond the death of the brain that encoded them, very definitely violates the laws of thermodynamics.
The so-called science of reincarnation is an example of the aesthetic fallacy. Although they use many of the external forms of science, they don’t produce causal explanations and they don’t make testable predictions. Ergo, what they are doing may appear to the uninitiated to be science, but it is not science.
I remain open to reviewing any explanation of rebirth that is consistent with other scientific insights and capable of making a testable prediction, just as soon as one of their predictions is accurate and precise to 5σ (the usual standard in scientific publishing). And don’t worry about it being left-field. I’m a great fan of novel and heterodox scientific explanations such as Chiara Marletto’s Constructor Theory, or Karl Friston’s Free Energy Principle. I only stipulate that the explanation and the confirmed prediction it makes be published in a mainstream scientific journal before being presented in simplified form to a lay readership. This should not be that hard given how much “evidence” there is.
The problem remains that if reincarnation is real in the way that Stevenson and co assert it is (in their self-published works), then the Buddhist anātman view of rebirth has been decisively proven wrong. Religious Buddhists would be better off sticking to the story that science—as the embodiment of materialism—has nothing to offer Buddhism.
If you have never practiced science, if you have only ever read about science in books, then you don’t know what you are talking about. Until one has practiced science for a number of years under the instruction of a qualified teacher, one really has no hope of understanding science well enough to apply it or to assess a novel scientific explanation.