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?

It's not clear to me how your example counts as "induction based only on reason." As I understand it, the process you imagine involves asking other people to think about the problem and then share with you their advice. Even if you stick entirely to your own thoughts about the problem, they'll no doubt be informed by your experience with practical problems of a similar kind. Either of those methods is at least partly empirical rather than "based only on reason." You would indeed be drawing conclusions inductively rather than (purely) deductively. As for the reliability of the results, I prefer a method in which various possible solutions to a type of practical problem are actually tried out rather than merely thought about. As anyone who's tried DIY renovations can tell you, there's a world of difference between thinking about how a practical problem should be solved and seeing how it actually gets solved once you put your thoughts into practice!

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