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Your claims only make sense in your world. They don't make any sense (and thus are non-sensical) to those not in your world.

If you're really interested in this, and also with your logic background, you might want to read Alain Badiou's 'Logic of Worlds' which I think is a nice take on this. Although I don't agree with his finer points, but he does make this point very nicely, I think.

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