> 1. No result is 100% reproducible because you can never completely reproduce the conditions of any experiment.
This is why you include the error in your results. We don't care if your two experiments result in 100% the same results. We care about if your results line up within the error of your experiment.
> 2. Even a completely non-reproducible result can be scientifically significant. For example, celestial events are almost never reproducible. Our understanding of celestial mechanics nonetheless rests on solid science.
This is why we share data. That is in essence our observation. A celestial event might be caught by only one instrument, but several people can develop several different models. We wait and watch for similar events though, to check if models are consistent (within error).
> 3. The end-product of science is not truth, it is explanations of observations.
I just wanted to repeat this because it can never be stated enough.
> 4. The statistical tests currently in widespread use as a criterion for publication in peer-reviewed journals guarantee that at least one result in 20 will be due to chance and not because the hypothesis being tested is actually true.
While I don't like p values, because of hacking, (especially 0.05) that's not how stats work. Flipping 10 heads doesn't guarantee 5 tails, not even 1. I wouldn't use as strong as a word as guarantee.
But this is also an argument FOR reproducing. If multiple experiments are consistent with one another (within error) than that strengthens the argument.
TLDR: More brains that look at a problem helps solve the problem.
I will add my own statements about the reproducability problem in science. One is because there is less funding for it. Reproducing an experiment isn't sexy. Another problem just stems from that data isn't always open. It is hard to review work if you don't know everything about the experiment. Data can even have simple mistakes that just weren't caught. But it is also embarrassing to share data.