This is a classic case of overthinking. Induction should not yield new knowledge because nothing new is discovered, but it does. Deduction likewise also cannot establish new knowledge, yet it does. Empirical science is flawed on extremely many levels but it works because on average, over time, many converging observations can build refined and accurate causal theories. It’s a matter of practicality that things cannot be proven fully. Judging from the state of modern medicine, engineering and the sciences, the system works ok regardless