This is the problem: While a few skeptics by their own admission can’t accept reincarnation regardless of what evidence is presented to them (see Impossible To Prove), most agree that some form of anomalous information access should be considered evidence. Great as that sounds, the quotes in the Anomalous Information section reveal that a reconciliation of the far ends of the spectrum is painfully remote.
That’s not a problem. It is a solution. Also, you are misrepresenting the quotes.
The quotes about “Impossible To Prove” are quotes about why reincarnation (or, more precisely, past-life memory) as “impossible”, not quotes about “Impossible To Prove”. These are two different things. Past-life is not possible within our understanding of how things work (and we have a very good understanding of how things work).
It should be obvious that “anomalous information access” would be the proof of past life memory? What else would you expect?
There is the old saying “exceptional claims require exception evidence”. If past-life memory were proven, it would require a radical change of our knowledge. Without any practical or logical mechanism, the possibility for past-life memory is relegated to the realm of what we generally refer to as “impossible” (which actually means very, very, very, etc, improbable).
In order for any evidence supporting past-life memory to become accepted, it must be more plausible than the “impossible” evidence that we currently have. If a three-year-old saying a 20-character code that ends up being a Swiss bank account number to some treasure, the plausibility must be measured.
All of our knowledge, everything that we know, trust, believe and have faith in, is measured in our brains on a scale. Nothing is absolutely true or false. We routinely scale things based on many factors. These factors may result in either true of false beliefs. If we really want to know the truth of something (as best as possible), we use two methods: the logic method and the scientific method.
The logical method allows us to make evaluations (scale of belief) without empirical evidence. In the case of past-life memory, a logical evaluation puts the belief very much in the false category, to the extent that it would be grouped with other beliefs categorized as “impossible”.
The scientific method is an empirical test, ideally where conditions are controlled so that the only possible results are a proof that a belief is either true or false. In many cases, these ideal conditions cannot be achieved. Therefore, the scale of belief is established based on the evidence available from tests based on how uncontrolled the conditions are (how many other plausible competing beliefs exist and their scale value) and in comparison to the scale of belief established by the logical method.
In order for a belief to become accepted, the “scale of belief” for the belief must overcome these. That is, the empirical evidence must be sufficient to outweigh the conclusions reached by the logical method. This means that if the logical method results in a very false conclusion, the empirical evidence must be very strong to over come this as the accepted belief.
The empirical evidence can only overcome a belief based on the logical method, and other evidence, by becoming unquestionable. The only method to make evidence unquestionable, is by using the scientific method to establish a test that decreases (or preferably, eliminates) the possibility of any other belief.
THEREFORE:
Using the logical method, past-life memory is false because it has no logical basis and would contradict current knowledge. So it is not unreasonable that some poster’s would characterize past-life memory as “impossible”.
Using the scientific method, past-life memory is false because it there is not sufficient evidence to overcome the conclusions derived from the logical method. It is actually much more than that. There is not the evidence that we would expect if reincarnation and past-life memory were true (which would be common cases of accurate and verifiable memories of a past life from most, or at least a decent percentage of, the 6 billion people alive on Earth)
Because past-life memory is false by logic and by our expected empirical experience, the evidence that would be required to overcome this belief would be categorized as “extraordinary”, or, as you put it, “painfully remote”.
Proof is possible, but it must be to the extent that it overcomes our current belief, which is well founded in false. Therefore, there must be proof that proves that our logical conclusions are false, that our expected experience if the belief were true are miscalculated, and that the evidence presented has no other more plausible explanation.
A single case would cause us to question the belief. Several cases might lead us to accept the belief as possibly true. Replication of the evidence on demand would result in us believing the belief, but with some uncertainty. We would only really accept the belief as true with overwhelming evidence or a provable, logical explanation that results in information that allows us to make accurate predictions.