I would like to know what is the difference between deduction and induction. Mathematical induction I know well, but now I would like to look at these from a philosophical point of view.
All help is appreciated.
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Mathematical induction is a form of deduction and is, in my opinion, poorly named. As far as I know, 'philosophical' induction is reasoning based on shear probability, i.e. 'There is so-and-so evidence to believe that...' For instance, most court cases are decided based on (overall) inductive reasoning.
The reason mathematical induction is a form of deduction is that the logic is clearly enunciated. See here for more.