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    Carmelics

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    Made withinDC&Austin
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that It is currently an open problem whether the second machine class properly extends the first machine class

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The 'openness' of a mathematical problem is an epistemic fact about human knowledge, not an ontological fact about machine class relations.
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    • 2.Epistemic uncertainty about whether P≠NP does not entail metaphysical indeterminacy in the extensional relationship between the classes.
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    • 3.Therefore, the claim conflates our ignorance of the answer with the answer itself being genuinely unsettled in reality.
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    Reason for 2 of 2
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    • 1.Lakatos's philosophy of mathematics shows that 'open problems' exist within fallible proof-practices, not as brute features of mathematical reality.
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    • 2.If the second machine class in fact properly extends the first, the problem is not open but merely unsolved by current methods.
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    • 3.Characterizing the separation problem as 'open' smuggles a verificationist assumption—that truth tracks proof availability—into a realist mathematical domain.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Formally demonstrating that second machine class models are unrealistic would require proving complexity class separation results
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    • 2.The relevant complexity class separation results are currently unresolved
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