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    Carmelics

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    Inverse View

    It is not the case that Gödel's platonist position, endorsed in 'What is Cantor's Continuum Problem?', holds that set-theoretic statements like CH possess objective truth values that human axiom systems may simply fail to capture.

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    Reasons For

    1 perspective
    Reason for
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    • 1.We have no epistemological access to abstract objects independent of axiom systems; positing unknowable truths violates parsimony without explanatory gain.
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    • 2.Mathematical truth correlates perfectly with formal derivability in systems we construct; positing mind-independent facts adds no predictive or explanatory power.
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    • 3.Multiple incompatible axiom systems (ZFC, class theory, constructivism) each support internally consistent mathematics, suggesting truth is framework-relative, not absolute.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Mathematical intuition suggests infinite sets have determinate properties independent of our formal systems, similar to how physical objects exist before discovery.
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    • 2.CH's independence from ZFC suggests reality underdetermines our axioms, not that CH lacks truth value—further axioms may resolve it objectively.
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    • 3.Platonism explains why mathematics is unreasonably effective in physics: we discover truths about an objective abstract realm, not merely conventional constructs.
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