A note to a friend regarding the problem of induction and Karl Popper.
"Regarding the problem of induction, when analysed in the context of Popper's critical rationalism, where rationality concerns critical preference and not justification, the problem does not arise. In other words, critical rationalists do not presuppose any principle, such as that of induction, or the uniformity of nature. Instead, critical rationalists propose uniformity in nature through theories, and do not presuppose it to justify theories.
In other words, critical rationalists do not presuppose, or commit to, any principle of induction, or uniformity of nature. It may be true, that for scientific investigation to bear fruit, nature must be uniform, but there is no need to presuppose it, since it is entirely possible that there is no uniformity. The purpose of scientific investigation is the search for laws that express regularities, though science cannot promise that there is anything to find.
That there may be no scientific laws to find is a possibility, but not one that a critical rationalist is eager to accept, and thus makes a methodological decision: to search tirelessly for laws and regularities wherever they may be, to conjecture and experiment. Ironically, we arrive at the view that there is uniformity in nature, by trying our best to find disorder, to bring every theory which proposes order, to the severest tests and criticism.
The problem of induction originally arose because it was supposed that synthetic statements must be justified by sense experience i.e. derivable from sense-data, or singular statements. That the principle of induction, or the uniformity of nature, are obviously synthetic statements, yet also irreducible to sense-data, or singular statements, caused the problem. It seemed that we could have no rational justification for any statement about the future.
It is because critical rationalism employs sense experience as a means of criticism, rather than justification, that the problem of induction does not arise. In other words, the critical rationalist does not try to derive theories from sense experience, but tries to contradict theories with sense experience. The method is reversed, and the problem of induction dissolved."