If the universal statement were merely definitionally equivalent to its base case and inductive step, induction would add no epistemic content — yet it genuinely extends our knowledge to infinite cases we cannot survey.
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(Offered as the mechanism behind empirical universality.)
The empirical method by which observations are generalized into rules; yields only comparative or assumed universality, not strict universality.
inductive step(as used in mathematical induction)
The part of a mathematical proof where you show that if something is true for one case, it must also be true for the next case—like proving dominoes will keep falling if you knock one down.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.