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    The conditional structure 'if X collapses then PH collaps... — Carmelics
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    Challenges→The Polynomial Hierarchy collapses if either the Buss hierarchy of theories collapses at some level or S_2 (or T_2) is finitely axiomatizable

    The conditional structure 'if X collapses then PH collapses' conveys no information about the actual modal status of PH unless the antecedent condition is independently motivated as genuinely possible.

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    Key Terms

    Antecedent(referring to causal conditions that would exist before Plato's decision)
    Something that comes before something else in time; in this case, an earlier event or cause.
    Conditional structure(as used in logic and mathematics)
    A logical setup where one thing depends on or follows from another—like saying 'if X happens, then Y happens.'
    Modal status(as used in metaphysics and logic)
    Whether something is necessary (must be true), possible (could be true), or contingent (just happens to be true). 'Modal' refers to these kinds of distinctions about how things *could be* versus how they actually are.
    convey information(epistemology (theory of knowledge))
    To tell us something meaningful or give us real knowledge about how things are.
    genuinely possible

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    (contrasted with merely conceivable)
    Actually able to happen or exist in reality, not just in imagination or theory.
    independently motivated(describing endorsements that don't need each other to be valid)
    Having reasons or justifications that stand on their own, without needing to rely on other arguments to make sense.

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    The Polynomial Hierarchy collapses if either the Buss hierarchy of theories coll...

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