The problem of induction is a classic theme in the philosophy of science. Traditionally it was considered (e.g., Francis Bacon) that if one could collect enough data one would be able to infer the patterns tht occur in nature (laws, etc.) – by a process of induction. The problem of induction was how can one percieve patterns that one is not yet aware of? There seemed to be a logical 'gap' in this process. (This might be seen as akin to the so-called learning paradox.) It was often both accepted that there was a problem of induction, but assumed induction must occur.
Karl Popper suggested that science did not proceed through induction at all, but rather there were always conjectures about what might be found before data was collected and analysed – and so science proceedes deductively, but examining data to see if it matched predicted patterns (hypotheses about what would be found under certain conditions, informed by conjectured principles, etc.). This closed the logical gap, as now scientists always knew what they were looking for to support a conjecture – but at the cost of a model of science that proceeded by logically rejecting alternatives that are refuted when hypothesised patterns are not found.
