FD and kid-A,
I attempted once before to demonstrate the distinction through a very clear thought exercise. You guys don't seem interested in anything beyond the tangible, which is the crux of my contention. There is such a thing as an experience that is evidence for me that will NEVER be demonstrable to you.
I agree with Terry, testimonials are not demonstrable evidence. But, for anyone who experienced what the person giving the testamonial experienced, it is further evidence for them.
As I said, I already tried this once and despite the obvious intellectual capacity of the learned atheists and agnostics here none seemed willing to engage in the thought exercise. I will try again. If you need to do so, pretend it is Plato asking your indulgence just after engaging you with the Allegory of the Cave. This thought exercise requires you to imagine a set of circumstances that have not occurred. There never have been a people who only stared at the back wall of a cave and theorized about what the shadows were. Such people would quickly die of starvation and dehydration, and their bodies would have never developed properly due to lack of exercise.
Assume first that no one has ever seen a bee. Assume secondly that no one has EVER been stung by a bee. This is the part where you have to dispense with reality for the thought exercise to work. Just as the Allegory of the Cave is a terrific allegory if you don't analyze it for real world likelihood, this one is a terrific allegory.
One day, you are stung by a bee. You are the only human who has ever been stung by a bee. We will assume—for the sake of argument—that you are not highly allergic and will not go into anaphylactic shock due to the experience. You have a small reddened area on your skin, and a tiny little hole that you can really only see if you know exactly where to look.
You have no demonstrable proof of your experience. But it was real, although you are the only one who knows it was real. At this point you have knowledge that is not possessed by any other human. You have learned that (1) bees exist, (2) can sting, (3) the sting hurts badly, and (4) that the sting can produce a red patch on the skin.
Now, within the parameters this thought exercise try to think through how you would explain the event to someone else.
Let's adjust the parameters. Assume that there is a large percentage of the population that has seen bees. Assume that a smaller percentage of the population has actually been stung by bees. Assume no one has ever captured or studied a bee.
According to what I read from Terry, kid-A, and Funky Derek, it seems that given these parameters you three would not believe in bees unless you had personally seen and/or been stung by a bee.
Which is my point. In this last case, there would be no demonstrable evidence but there would be personal evidence. Personal evidence sufficient to compel belief. And the only sort of explanation that could be offered in such a case would be...testimonial, which is not demonstrable evidence. It is not a valid basis for someone else's belief, but your personal experience is valid basis for your own belief. Even if your personal experience involved a pink unicorn.
Respectfully,
AuldSoul