For me, reincarnation is a fact. I have absolutely no recollection of past lives, but I have decided to accept this idea as fact, for two reasons.
First, my master says it is real; he has also written a book describing a few of his past lives. I don’t think my master lies, specially in matters like this.
Second, there is more than half a century of painstaking work done in this field by the researchers of the DOPS (Division Of Perceptual Studies) of the University of Virginia, School of Medicine in the US. These researchers are scholars in neurology, medicine, psychology or other scientific disciplines, with advanced degrees. They are not personally from cultures which believe in reincarnation. They publish their findings in refereed journals and conference proceedings. They have gathered a few thousand case studies of near-death experiences, past-life recollections, etc, and have investigated many of them in detail to rule out common biases or fraud. What remains is a collection of case studies for which modern science has absolutely no explanation, which means that modern science pretends that the DOPS UVA does not exist.
But as a student of vedanta, I am forced to ask what reincarnation really means to me. The simplistic way we see reincarnation is to say that I had many lives in the past, and will have many lives in future. Looking at this from a vedantic perspective, I am forced to ask who this “I” is. Is the “I” from the previous life the same as the “I” from the current one? Given the tiny amount of content which gets carried forward from lifetime to lifetime, are we justified in saying that the two lives are being lived by the same person? If I accept the details of the reincarnation process offered by vedanta, there is probably less carried forward from lifetime to lifetime than is transmitted from parent to child via our DNA. If we are allowed to say that “I” live multiple lives, are we then also permitted to say that our progeny’s lives are our lives? So, one has to be a bit careful about subscribing to reincarnation, I feel.
The evidence from UVA DOPS makes it clear that reincarnation happens, and has happened thousands of times. But it does not indicate that every person reincarnates after death. One has to be a bit careful.