But sometimes ad hoc assumptions are correct. Before magnetism was known, the claim that the object does not fall to the ground because of an additional magnetic force affecting it would have been an ad hoc claim. Popper strives for certainty in his principle of refutation, but in the end even refutation comes as a result of intuition about whether there is some additional ad hoc assumption I do not know, or whether my theory is simply wrong. You have no certain tool for deciding this. Of course, the more refutations there are that force us to invent ad hoc assumptions for them, the weaker the theory becomes, but its refutation will always involve intuition. And if we use intuition in refutation, then why not use it for proof as well, and claim that the intuition behind the principle of induction is also correct? In other words, Popper did not really provide a solution to the problem of uncertainty—he replaced one uncertainty with another.

Indeed, correct. Nobody talks about certainty in science. See the column I just uploaded (588), where I comment on this.

If so, what value is there in Popper’s criterion of refutation?

If I understood you correctly, then the principle of refutation really ought to be formulated like this: “A scientific theory is a theory that can be weakened, to the point that intuition sees it as refuted.”
But the same criterion could also be formulated the other way around—
“A scientific theory is a theory that can be corroborated, until intuition sees it as proven.”

You cannot really prove or refute any theory because of the problem of induction and ad hoc assumptions—you can only weaken and corroborate them, and from there infer incorrectness or correctness.

So why is a scientific theory defined only by the ability to refute (weaken) it and not by the ability to prove (corroborate) it? Both are processes involving intuition, and neither is certain.

What value is there in relating only to refutation? Is there a theory that can be corroborated but cannot be weakened?

Thanks 🙂

All these questions have been discussed ad nauseam in philosophy of science, and some of them already by Popper himself. It is indeed true that there is no way to prove or categorically rule out a theory. There are always possible ad hoc rescue moves. The theory in itself is refutable. An ad hoc rescue is a modification of it. But these are hair-splittings. Science does not deal with certainty, nor with what is definitively refuted. Beyond that, science is not only observation but also includes other components of reason (rationalist ones).
Thomas Kuhn went further. In his view, it is altogether a sociological process and not a philosophical one.

I agree that one can refute its physical realization (if that is what you meant by the theory in itself), but that would not refute the underlying “Platonic” theory or theories.

If science does not deal with what is refuted, then why do people continue to adopt Popper’s definition as a criterion for what counts as a scientific theory?

Is there, in your view, a more precise definition of what a scientific theory is?

Almost nobody today adopts Popper’s definition. It is only a general direction and framework for scientific discussion. There are no precise definitions, nor can there be such definitions. That is exactly why people still speak in Popper’s language.