Do you know that homeopathy doesn't work, or do you just lack belief that it does?

[Angrboda]

"Homeopathy works" is a falsifiable hypothesis. "God exists" is not.

You can demonstrate that homeopathy does not work. There is a mountain of evidence that allows us to be certain of this.

Not so with God. So we atheists are going to have to be content with "pretty damn sure" because no amount of evidence will provide complete certainty in the matter.

It does work though. It provides a measurable benefit over no treatment at all.

Of course you and I know it's because of the placebo effect, not because of magic memory water, but many believers would just say the placebo effect is BS, and clearly homeopathy works.

It matters how it is determined that it provides a reasonable benefit. In cases where no putative mechanism for an effect is known, it is perfectly legitimate to demand a higher level of significance in the outcome. Most of these studies already take the placebo effect into account by comparing results to that of a control group. Between those two factors, it becomes clear that homeopathic remedies have not been shown to provide a measurable benefit over any other ineffective remedy. Whether it provides any measurable benefit over no treatment at all depends both on the nature of the problem and its ordinary course of resolution, and how you define benefit. Regardless, in neither case is the null hypothesis supported by the failure to overturn it. Thus we can conclude that homeopathy has not been shown to work, but we cannot conclude that it has been shown that it doesn't work.

So, I think ultimately one can justify a conclusion that homeopathy doesn't work. That doesn't mean we can have absolute certainty that it doesn't work. That's a question about the nature of knowledge as well as about the meaning of scientific theories. As Popper's criterion of falsifiability makes clear, science is not about proving a theory correct, but rather about surviving attempts at falsification. Since such tests don't positively affirm the successful theory, the knowledge gained is in a sense a negative picture. It's more a discarding what doesn't work than it is a choosing that which does. The current dominant theory is simply the last man standing in the battle among theories. And that fact can change at any time.