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Is it possible for there to be a world that logic does not apply? That is, can't a "married bachelor" actually exist in some world that there is no logic or that there is a different logic that applies? And if so, then isn't it the case that we merely assume the first principles of logic (noncontradiction, identity, excluded middle, etc...) because we observe them in our actual world, which is 1 of many possible worlds? And if it is mere assumption, then can't we be wrong about them when we say they can/should apply to other possible worlds?

I don't think this question can be answered. I think no one -- including the questioner -- understands the question being asked. In asking "Is it possible for there to be a world where logic doesn't apply?" is the questioner asking (a) "Is it possible for there to be a world where logic doesn't apply?" or (b) "Is it possible for there to be a world where logic does and doesn't apply?" or (c) "Is it possible for there to be a world where logic neither applies nor doesn't apply?" or (d) "Is it possible for there to be a world where logic does apply?" If logic doesn't apply in a world, then...then what? In a world where logic doesn't apply, does logic also apply? If not, why not? Unless logic applies in every world, how can we tell which, if any, of (a)-(d) is the question that the questioner is asking?

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