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    Carmelics

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    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 If φ is an infinitary sentence, G(¬φ) need not be the strict dual of G(φ), so neither player may possess a winning strategy in either game.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Classical game duality holds structurally regardless of sentence complexity—negation always swaps win conditions symmetrically.
      ?

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    • 2.If G(φ) lacks a winning strategy, logical principles alone guarantee G(¬φ) cannot both lack one—excluding the middle.
      ?

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    • 3.The claim conflates semantic non-determinacy with game-theoretic indeterminacy, which requires separate justification entirely.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Infinitary sentences lack the recursive closure properties finite sentences possess, breaking standard duality assumptions.
      ?

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    • 2.Game trees for infinitary logic can be non-wellfounded, making traditional game-theoretic determinacy proofs inapplicable.
      ?

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    • 3.Neither player can guarantee winning via finite strategies when plays may require infinitely many moves to resolve truth-value.
      ?

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