Talk:Entitative graph

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Additional information: Related task forces (core areas): Logic

[edit] Notes & Queries

Jon Awbrey 15:32, 12 January 2006 (UTC)

[edit] Qualitative logic

[edit] This entry is mistaken

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, 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.

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 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.202.36.179.65 16:23, 14 February 2006 (UTC)

• 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. Jon Awbrey 16:54, 14 February 2006 (UTC)