Peirce’s 1870 “Logic Of Relatives” • Discussion 1

Posted on September 30, 2019 by Jon Awbrey

Re: Ontolog Forum • John Bottoms
Re: History View Blog • A Yukaghir Girl Writes A Love Letter
Re: Peirce’s 1870 “Logic Of Relatives” • Proto-Graphical Syntax

John Bottoms, writing in the Ontolog Forum, compared the graphic I drew for one of Peirce’s relational formulas to a pictographic image he had been studying.

Peirce introduced the compound term “giver of a horse to a lover of a woman” in Selection 7 to illustrate his use of marks of reference to identify the corresponding correlates of component terms.  The symbolic form of this compound term is shown below.

\mathfrak{g}_{\dagger\ddagger} {}^\dagger\mathit{l}_\parallel {}^\parallel\mathrm{w} {}^\ddagger\mathrm{h}

In my comment on Proto-Graphical Syntax I drew lines of identity to connect the corresponding marks of reference, as shown in the following Figure.

Giver of a Horse to a Lover of a Woman

John tells us what he sees in this Figure in the following words:

One of my interests is in the intersection between images and prose.  The note [on Proto-Graphical Syntax] is prescient.  It echoes a semasiographic image that has been discussed recently on the web.  The image below shows two houses, and the tree shapes represent people.

In the image a girl complains to her ex-lover that his new relationship is not useful, and he is missing an opportunity to have children with her.  This image was created by a Yukaghir girl for a local game similar to Pictionary.

Geoffery Sampson • A Yukaghir Girl Writes A Love Letter

I started a draft in the middle of the night to draw out the analogies and disanalogies of these two Figures but the clear light of day showed me I would need to deal with a host of preliminary issues before moving on.  So I will turn to that task next.

cc: Systems Science • Structural Modeling • Ontolog Forum • Laws of Form • Cybernetics

This entry was posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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