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Ideas for 'A Puzzle about Belief', 'Fact, Fiction and Forecast (4th ed)' and 'Necessary Beings'

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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The two Barcan principles are easily proved in fairly basic modal logic [Hale]
With a negative free logic, we can dispense with the Barcan formulae [Hale]