Whenever I see inductive arguments being used, it seems as though they can be redone by simply making certain assumptions and rephrasing the argument as a deduction from those assumptions.
For example, in this Khan Academy video, Sal says that if you're predicting the population of a town in the future based on the past, that's inductive reasoning. However, I believe that you could also frame this as deductive reasoning by adding in the assumption that "If the population of a town followed a particular pattern up until today, then it will continue to follow that pattern past today".
In fact, it seems that any inductive reasoning can be done with deductive reasoning by adding in some assumption that a particular pattern continues to hold.
Is this the case? If so, is there a formal way of determining what assumptions need to be added? If not, can you give an example of a situation with inductive reasoning where deductive reasoning with certain assumptions cannot model the same reasoning and conclusions?