Second edition: I was wrong. I have written about it before, but I forgot: induction doesn't exist. The number of possible theories for any set of observations are infinite. Brett Hall showed me the right path forward. We don't use induction to find knowledge. Instead we use a fundamental theory: There are regularities in the world. We use this theory to quickly draw conclusions from a few examples, also when the perceived regularity requires complicated transformations to be extracted from the experience. We hold on to the knowledge until we find a convincing counterexample, either through thinking or by observation.
Is it even possible to form a theory of an irregularity? Yes, I think so. We can use chaos theory and no-go theorems as examples. These theories can't be used to make predictions. It is more like a warning sign. Don't spend energy looking for regularities here, there are none.
First edition: Hume showed us that induction is not the mechanism we use to create knowledge but couldn't find an alternative explanation. Popper solved the problem using conjectures and refutations. We guess how the world works and our guesses can be falsified by things we already know and by cleverly constructed experiments when we lack convincing reasons to choose between competing theories.
But Popper does not tell us how we come up with conjectures. For this, induction is very useful. It lets us find patterns, regularities and causal relations that works surprisingly well as first guesses. If you believe that the sun will rise tomorrow because it has done so all days that came before, it will serve you well for billions of years. Only if you fail, with more time, to figure out how the solar system actually works - which will falsify your initial inductive guess - it will threaten your survival.
