Went to D's, talked with tom7 about modal logic. I still, completely unrelated to my main research project, have this dream that there should exist a workable logic with a countable collection of box-like modalities of increasing "strength" in some sense that is the "grand unification" of classical and intuitionistic propositional logic. This being in a slightly (and perhaps not more than slightly) deeper sense than "oh, just add callcc to intuitionistic and you've got classical". Obviously I would have to figure out a way of expressing that with fewer scare-quotes, but still. The intuition is strong.
Went to D's, talked with tom7 about modal logic. I still, completely unrelated to my main research project, have this dream that there should exist a workable logic with a countable collection of box-like modalities of increasing "strength" in some sense that is the "grand unification" of classical and intuitionistic propositional logic. This being in a slightly (and perhaps not more than slightly) deeper sense than "oh, just add callcc to intuitionistic and you've got classical". Obviously I would have to figure out a way of expressing that with fewer scare-quotes, but still. The intuition is strong.
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