This seems to contradict the very tools we use to perform the scientific method. Immediately after performing any experiment, the measurement becomes a historical event, and this says that we cannot say that any historical event has actually occurred. Thus, I cannot actually say that I performed an experiment and obtained a measurement....and if you cannot obtain concrete evidence, then you cannot prove scientific theories! In fact, if you cannot say that any past event has actually occurred, then you cannot use logic to describe the universe, because in logic a statement is true or false but cannot be "true with some probability"...and mathematics is derived from logic, so mathematics also breaks down!

Events are probabilistic in the sense that our experiments repeat probabilistically. That is, try as we might to do the exact same thing every time we still get variations. The distribution of the variations is repeatable, so the experiment is repeatable in that sense.

Once a measurement is made then probability drops out of the picture. A measurement is a measurement. We use these measurements to get a probability distribution.

So I guess an "event" would be a measurement that has not yet actually been made.

You must have abbreviated your argument, missing out some essential premises that would make it comprehensible.

For instance on the face of it, more plausible than "we cannot say that any historical event has actually occurred" seems that we cannot say anything else about the physical world. Almost.

Also what you present as an objection to quantum mechanics, or maybe a particular formulation or interpretation of it, seems to apply to all Science.

Roger Penrose in THE ROAD TO REALITY, pages 666-669 discusses interpretations of Feynman's path integral/sum over histories approach...in a general way....a continuous infinity of classical alternatives, infinite dimensional configuration space, etc, but beginning on page 670 discusses DIVERGENT PATH INTEGRALS: FEYNMAN'S RESPONSE where Penrose discusses the Feynman propagator and some mathematical properties associated with his approach....I'm not qualified to really understand the math he references.

I have no issue with summing over all possible paths in order to compute the probability of measuring a particular outcome in an experiment...this prevents us from making exact predictions about what the outcome will be, but it does not prevent us from making definitive statements such as "I performed an experiment."

The issue with summing over all possible histories from the origin of the big bang singularity is that there are some histories in which we do not even exist and never performed an experiment. If this is the case then we cannot actually say "I performed an event" or "I exist" we can only say "With some probability, I exist.." but then this confuses the very notion of probability, which is a description of the odds of making some measurement under the assumption that definitive measurements can be made.