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    If the universal statement were merely definitionally equ... — Carmelics
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    Challenges→Mathematical induction does not function as an inference that derives a universal conclusion from two premises

    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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    Key Terms

    Definitionally equivalent(logic and language)
    Two things that mean exactly the same thing by their definitions, with no additional information added beyond what's already contained in the definitions.
    Epistemic content(epistemology (the study of knowledge))
    The amount of new knowledge or information something adds — how much it tells us that we didn't already know.
    Universal statement(logic and mathematics)
    A claim that applies to all cases in a category, not just specific examples — like saying 'all triangles have three sides' rather than 'this triangle has three sides.'
    base case(as used in mathematical induction)
    The starting point in a mathematical proof, where you show that something is true for the first step (usually the simplest or smallest example).
    induction

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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.

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    Mathematical induction does not function as an inference that derives a universa...

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