How does postulating a spirit leaving the body add predictive power?
It doesn't, because it's not meant to. Spirit leaving the body is barely a proto-theory, never mind a falsifiable hypothesis.
At this point we're still collecting observations. If there turn out to be observations which need to be explained, theory building can start at that point.
It would rather anal to pretend there's nothing at all to explain. The stats suggest that around 10% of people who recover from near death have an NDE. The format is usually - but not always - consistent. So there's certainly something happening.
But there's no definitive information about how externalised these experiences are, or what - if anything - they mean.
And 'just knowing' after the experience, no matter how strongly, doesn't - unfortunately - seem a reliable indication of veracity.
Finding evidence of unusual physical perception seems like a good place to start.
A broad class of plausible models of NDEs assign them some property that is, in effect, verifiable; in semi-Popperian terms, the absence of that property is falsifiable.
This class includes all models in which NDEs enable subjects to report a fact about about the physical world that should be unavailable by ordinary means. Examples include NDE models in which reports of seeing the physical world from a position outside the body are are taken at face value.
Given what we know of the shocking unreliability of eye-witness reports, the standard of evidence for rare NDE observations of this sort must be quite high, but there is no reason why the standard could not be met. Further, in many reasonable models, the standard would be met so routinely and decisively that the matter would never have been in question.
In particular, there is a class of models in which NDEs have a teaching purpose, and the teaching is performed by reasonably knowledgeable and competent agents of some sort. By the nature of "teaching", these models naturally lead to the strong expectation that we would have clear, routine, and age-old evidence. Models in which teachers withhold strongly evidential information seem to me to strain credibility. Words and ideas I offer here may be used freely and without attribution.
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