Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that A theorem whose premises invoke physically unrealizable models yields conclusions whose modal force is limited to mathematical, not computational, necessity.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Unrealizable premises can still yield conclusions with computational force if they abstract stable properties shared by all physically realizable implementations.
      ?

      Think about whether this reason is strong or weak

    • 2.The distinction between mathematical and computational necessity may be artificial—computation just *is* mathematics applied to physical substrates, not a separate modality.
      ?

      Think about whether this reason is strong or weak

    • 3.Many productive theorems (P vs NP, halting problem) use idealized models yet restrict computational claims appropriately without invoking the unrealizability objection.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Physically unrealizable models (e.g., infinite memory, zero noise) lack empirical grounding, so their theorems cannot guarantee real-world computational behavior.
      ?

      Think about whether this reason is strong or weak

    • 2.Mathematical necessity concerns logical possibility; computational necessity requires physical instantiation. These are distinct modal categories with different scopes.
      ?

      Think about whether this reason is strong or weak

    • 3.Theorems from idealized models (Turing machines, frictionless planes) traditionally yield only bounded claims about actual systems, not absolute guarantees.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.