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can be read as a universally quantified variable. Peirce soon lost interest in the entitative graphs when he saw that if conjunction interprets concatenation, then a dot unenclosed by cuts denotes an existentially quantified variable. He worked on the resulting existential graphs from 1896 to the end of his life; his writings on this subject fill more than 100pp of vol. 4 of the CP.
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My completely wild, unfounded intuitive guess is that Pierce stumbled over the distinctions between "boolean-logic or", "exclusive or", and "menu choices" (pick this or this or this). These are clearly quite different things, and of course, Pierce would have clearly understood this, but it is easy to
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Peirce's
Qualitative Logic of 1886, for all its merits, has nothing to do with the entitative graphs. Peirce devised the latter around 1895, in work published in vol. 3 of CP. The entitative graphs are such that disjunction interprets concatenation, and a dot on the blank page, not enclosed by cuts,
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Zeman (1964) showed that the existential graphs are isomorphic to first order logic with identity. Because entitative/existential constitute a dual pair, this isomorphism carries over to the entitative graphs. (A better, but less known, term than "isomorphism" is Tarski's "equipollence".) Peirce
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accidentally intermix these during casual thinking. Try talking about menu-choices with a young student who just learned about boolean logic -- violent argumentation typically ensues. Working with existential graphs avoids this kind of confusion.
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strongly preferred the existential graphs because in his view, they handle quantification more easily. I have yet to encounter any discussion in the secondary literature that does justice to the entitative-existential dichotomy.
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Not only is it incomprehensible, someone has gone through it writing 'why?' on ever claim. Someone has to explain what the hell this stuff is before asking why. Who know why people use mad stuff like this? I certainly
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JA: Peirce was more than familiar with the issues of formal duality all throughout his work, as any person with even a modest mathematical education would have been.
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