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Would modern medicine be falsifiable according to Popper? What about alternative medicine, such as homeopathy?
My problem with this, is that I imagine such falsification depends on double blind studies. However, those results are not enough to conclude anything from, since they are just statistics. The medicine tested might just be "having a bad day" as it were. Is something that depends so heavily on chance enough for falsification?
Why are you postulating that medicines might "have a bad day" as it were? The whole point of statistics is to avoid being fooled by chance circumstances. (You might still be fooled by unexpected correlations.)
Anyway, yes, medicine is falsifiable. It's hard, because it's difficult to adequately control conditions, and it is tempting to use statistics that are easy to calculate instead of those that better capture the underlying distributions. But people do it all the time: just look at any issue of e.g. the New England Journal of Medicine.
(Whether we should always wait until medicine has passed attempted falsifications is a different issue; there is some reason to think that we might have different standards for what we think is "likely a good approximation to the truth" vs. what we think is "worth trying in such-and-so circumstances".)
Your example assumes that "medicine" is making some absolute claim of doing something, but that is not what medicine claims. If "medicine" is the general population's understanding of medicine, then you may have a point. However, to medical researchers, medical practitioners, and other medical agencies (FDA, etc), "medicine" describes our knowledge of chemicals acting on the body and everyone in those groups understand the limits of our knowledge on the topics. That's why you will always hear them qualify claims like "results may vary", "may not be appropriate for everyone", "side effects include...", etc.
So, in a medical journal where they are being technically precise with their words, they will say things like "the p-value was 0.0076 with an alpha of 0.01, so the null hypothesis _____ can be statistically rejected." They will not say (unless they are being lazy) things like "this drug cures _____ ." It is always qualified. A number without a confidence interval is not useful information.
So in that sense, medicine is what it is - simply measurements of experiments and statistics. It's hard to say that's wrong (unless someone is being lazy our fraudulent, which isn't the point).
"Medicine" could also mean our practical application of our observations, and in that case it's proven wrong all the time. And "wrong" here means that the statistics of a thing are no longer probable at a given confidence level. This is different from the claim that something always our never happens.
