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    If φ is an infinitary sentence, G(¬φ) need not be the str... — Carmelics
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    Challenges→Player ∃ has a winning strategy in G(¬φ) if and only if player ∃ does not have a winning strategy in G(φ).

    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.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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    Connections

    2 topics

    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Classical game duality holds structurally regardless of sentence complexity—nega...Game trees for infinitary logic can be non-wellfounded, making traditional game-...If G(φ) lacks a winning strategy, logical principles alone guarantee G(¬φ) canno...Infinitary sentences lack the recursive closure properties finite sentences poss...
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    Neither player can guarantee winning via finite strategies when plays may requir...Player ∃ has a winning strategy in G(¬φ) if and only if player ∃ does not have a...The claim conflates semantic non-determinacy with game-theoretic indeterminacy, ...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit