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A remark of Marie McGinn inspired these investigations. The idea behind the remark was that perhaps historically given principles relating a priori knowledge and modality in which iterated modalities do not figure are nevertheless sufficient to detemine exactly those principles for iterated modality which are distinctive of S5. That this is so says a lot about the insight of that excellent Kantian, C. I. Lewis.
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Hart, W.D., McGinn, C. Knowledge and necessity. J Philos Logic 5, 205–208 (1976). https://doi.org/10.1007/BF00248729
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DOI: https://doi.org/10.1007/BF00248729