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It is not the case that The standard definition of possibility (◇φ ≡ ¬□¬φ) fails under the Gap principle
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1.
Under Gap, in worlds where Bergoglio does not exist, '¬Hb' (Bergoglio is not human) is not statable and hence not true
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2.
Therefore '¬Hb' is not true in any world, so ¬◇¬Hb holds
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3.
But □Hb (Bergoglio is necessarily human) does not follow, because 'Hb' is also not statable in Bergoglio-free worlds and hence not true there either
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