how does induction relate to falsifiability, and when does one trump
the other?
Why Karl Popper wanted to say that the criteria of falsifiability is better than induction?
Popper wanted to say that induction is not justifiable. That a theory has been corroborated in the past "says nothing whatever about future performance." Popper wanted to say that it is possible to avoid assuming that the future will, or probably will, be like the past, and this is why he has claimed to have solved the problem of induction. We do not have to make the assumption, he tells us, if we proceed by formulating conjectures and attempting to falsify them. He says that, as a basis for action, we should prefer "the best-tested theory." This can only mean the theory that has survived refutation in the past; but why, since Popper says that past corroboration has nothing to do with future performance, is it rational to prefer this?
Without the inductive assumption, the fact that a theory was refuted yesterday is quite irrelevant to its truth-status today. So demising the inductive assumption makes nonsense of Popper's own theory of the growth of scientific knowledge. The more often a conjecture passes efforts to falsify it, Popper maintained, the greater becomes its "corroboration", although corroboration is also uncertain and can never be quantified by degree of probability. "Corroboration" is a form of induction, and Popper has simply sneaked induction in through a back door by giving it a new name.
Every falsification of a conjecture is simultaneously a confirmation of an opposite conjecture, and every conforming instance of a conjecture is a falsification of an opposite conjecture. If Popper bet on a certain horse to win a race, and the horse won, you would not expect him to shout, "Great! My horse failed to lose!" Astronomers look for signs of water on Mars. They do not think they are making efforts to falsify the conjecture that Mars never had water. For Popper, what Carnap called a "degree of confirmation", a logical relation between a conjecture and all relevant evidence, is a useless concept. Instead, the more tests for falsification a theory passes, the more it gains in "corroboration”. It's not so much that Popper disagreed with inductivists as that he restated their views in a bizarre and cumbersome terminology. Why scratch your left ear with your right hand?
