1. I rarely write about Hinduism and Buddhism because it's fairly specialized. Reincarnation is neglected in Christian apologetics because most Christian apologetics is focussed on challenges to Christianity in the West.
2. Before addressing the specifics, I'd like to make a general observation. Not all paranormal claims are mutually consistent. Compare reincarnation with crisis apparitions. There are reports of dead relatives appearing to a loved one to warn them or give them encouragement during a crisis. But if that's true, then how can reincarnation be true? According to a standard paradigm, reincarnation involves a memory wipe. When a person is reborn, they forget their past lives. Start all over again.
That rules out crisis apparitions. The dead relative has moved on. Been reincarnated. Started from scratch in a new body, as a baby. Immersed in a new life history.
They don't remember their loved ones from past lives. At this point they are younger than their children. Reincarnation resets the lifecycle. Your late mother can't appear to you as your late mother. She's now a little girl.
Reincarnation and crisis apparitions can both be false, but they can't both be true. And I think there's unambiguous evidence for crisis apparitions, whereas the evidence for reincarnation is ambiguous at best.
3. To my knowledge, apologists for reincarnation offer three lines of empirical evidence: déjà vu, transgenerational birthmarks, and memories of a past life.
4. Déjà vu
i) I think this is the weakest evidence. Not just weak evidence for reincarnation, but weak evidence that it's even paranormal.
In my own life I've had déjà vu experiences. One time, sitting at a fast food joint, years ago, I suddenly had the intensive feeling that I'd done this before. I'm pretty sure that I hadn't done it before in this life. But since the establishment was built in my lifetime, it wasn't even possible for me to have been there in a past life. So whatever the explanation, it can't be reincarnation.
Likewise, I've lived in at least two consecutive locations where I had déjà vu experiences. But both of them were built in my lifetime, so that can't be chalked up to a past life. And even if they hadn't been constructed in my lifetime, what are the odds that in a past life I lived in both places–not to mention both places in succession?
iii) Moreover, the sensation I've had is more like a time loop than remembering a past life. It's not the sensation that I was in the same place in a different life, but that this life is repeating itself.
iv) Sometimes our minds play tricks on us. That's my explanation.
But assuming for argument's sake that déjà vu demands a paranormal explanation, telepathy is a simpler explanation. What if one person's memories occasionally leak into another person's mind?
5. Transgenerational birthmarks
i) The claim is that babies sometimes reproduce the unique birthmark of a dead person, like an ancestor. In fact, this has become a TV trope:
ii) I haven't studied the literature in sufficient depth to know if such a phenomenon actually exists. Of course, the appeal is circular. If some babies reproduce the birthmarks of a dead person, then those aren't unique birthmarks.
iii) However, let's stipulate for discussion purposes that the phenomenon exists and demands a paranormal explanation. How would reincarnation be an explanation for replicated birthmarks? On a standard paradigm of reincarnation, the soul (mind, consciousness) transfers from the dead body to a new body. A body-swap scenario. But how would that cause any physical traces?
iv) Why would reincarnation duplicate birthmarks rather than duplicating the body? If the body is not a double, why the same birthmarks?
v) What reincarnation have to do with heredity? Why would someone be reborn in the body of a lineal descendent? Isn't reincarnation just the idea that the same soul is reembodied? But that's not a genetic or genealogical relation–as if, to be reincarnated, you must be a reincarnated ancestor. Assuming (ex hypothesi) that reincarnation is true, why can't the soul transfer to a body in a different family tree? To my knowledge, reincarnation is usually treated as independent of lineage.
vi) It would be interesting to know if there's a history of witchcraft or necromancy in these families. If a baby has the birthmarks of a dead ancestor, is that a family curse? Was the baby hexed? Are the dead (damned) casting a malevolent influence on the living?
6. Past life memories
i) Suppose for argument's sake that reincarnation is true. Suppose someone underwent 100 past lives. In fact, that's a conservative estimate. How would they remember 100 life histories? Wouldn't their recollection be hopelessly scrambled? How would they remember what they did in each life? Who they knew in each life?
Memory has a sense of relative chronology. You remember childhood, adolescence, young adulthood, middle age, &c. You remember that some things happened to you before other things.
But if you underwent 100 past lives, how could you possibly keep the timelines straight? Assuming that some people remember events before they were born, that would actually constitute prima facie evidence that reincarnation is false, since it's hard to see how you could keep all those life histories separate in your mind.
ii) An alternative explanation is that those aren't your memories. You're tapping into someone else's memories. They are invading your mind. That doesn't require all the machinery of reincarnation, so it's a simpler explanation.
iii) To my knowledge, Hinduism has a dualist anthropology while Buddhism has a physicalist anthropology. In Buddhism, humans have no perduring soul. So how is reincarnation even possible? Who's the you that's reincarnated? Weren't you extinguished at the moment of death? A new brain and body won't be you, but a blank slate.
