I understand that mathematical induction is deductive reasoning (but why doesn't

I understand that mathematical induction is deductive reasoning (but why doesn't

I understand that mathematical induction is deductive reasoning (but why doesn't it have another name?!). But I wonder if there can be true induction based only on reason. Here is an example: I may think about a possible practical problem and think what I would do in many variants of it. I can also ask other people to imagine other variants and I can ask them help about what to do in all those variants. After all this thinking, it is possible that one notices a general rule about what to do with that problem, and come to believe that that rule would be good for every variant of it, even for those variants we didn't check. Wouldn't that be an inductive conclusion? And do you think that this conclusion would be less acceptable than inductive conclusions in the natural sciences?

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