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Inductive reasoning is coming to a conclusion about something through direct observation of specific examples. For instance, I could observe that 75% of people that go to a certain lake go there to fish. I could also observe my brother arriving at the lake. Through inductive reasoning I could say that there is a 75% chance that my brother is there to fish.
Analogical reasoning is concluding that two things are alike in one respect because they are also alike in another respect. Most frequently this is used to explain one thing that is not well understood by drawing an analogy to something that is better understood. For example, a person might attempt to explain email by saying that it is like mail sent to a post office box. Just as mail is delivered to the PO box and you go to pick it up, email is delivered to your email in box and your software “goes” and picks it up.
Does that make sense?
An analogical argument is an argument in which one concludes that anologies can range very literal