Well, do we or don’t we? Have we or haven’t we? It actually depends on how you look at it. From the perspective of ultimate truth, which is all there is; all we have is one single eternal moment so the answer is no, because to reincarnate would imply that the past exists, which it doesn’t.
From the perspective of apparent truth, which is what seems to be “all there is” on the surface of things, the answer has to be yes, because people, myself included, have had evidence shown them in one way shape or form, that we do indeed experience many different lives.
However, from the perspective of imagined truth, which is what the mind and ego-self want us to believe, all we have is what we have so the answer is again, no; and we shall live in fear until the day comes when we die and that will be that; goodnight Vienna!
So, the answer to the question of reincarnation; do we or don’t we? Is…
Yes… unless we don’t.
It all depends on the perspective of the thinker at the time!