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Added a recent reference on Peirce’s Gamma graphs for modal logic. This describes his first approach via broken cuts rather than the later tinctured sheet approach. I keep meaning to see if there’s anything in the latter close to LSR 2-category of modes approach.
According to the broken-cut method, possibility is broken cut surrounding solid cut, while necessity is solid cut surrounding broken cut. Since solid cut is negation, broken cut signifies not-necessarily. Easy to see $\Box \neg = \neg \lozenge$ as the same pattern of three cuts, etc.
In the Alpha case, we’re to think of negated propositions as though written elsewhere on another sheet (or the back of the sheet). There seems to be a three-dimensionality to the graphs, e.g., the conditional as like a tube from one sheet to another, Wikipedia. I gather his later ideas on tinctured graphs had this idea of being inscribed on different sheets.
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