The unsolvable chain of evidence. For a past life memory to be verified, you'd need a documented fact from a deceased person's life that the current person could not possibly know through normal means, and you'd have to rule out fraud, cryptomnesia (hidden memory), and genetic or collective unconscious
transmission. For the afterlife, you'd need a verifiable, two-way
communication with a specific, identifiable deceased consciousness. The hard problem is that any piece of evidence (e.g., a child knowing a dead person's secret) can be explained by lesser hypotheses (telepathy between living minds, chance, subconscious inference). The signal can never be isolated from the noise of unknown psychic phenomena or pure
coincidence.
*Example: A child recalls being a pilot named James who died in a WWII crash, giving specific coordinates. Investigators find wreckage there of a plane piloted by a James. The hard problem: This is astonishing, but is it proof of reincarnation? Alternative explanations include: 1) The child psychically tapped into the
collective memory/historical record of the event (clairvoyance, not past life). 2) Extreme coincidence plus
confabulation. To prove a past life, you must first disprove all forms of present-life psychic ability, which is itself unproven. The conclusion is always one unproven assumption stacked on another.*
Hard Problem of Past Lives & Afterlife.