Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/

Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/

Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1Rxy

SD:
❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞

Stephen,

“Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …

As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.

Resources —

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Semeiotic
• https://oeis.org/wiki/Semeiotic

Sign Relations
• https://oeis.org/wiki/Sign_relation

Triadic Relations
• https://oeis.org/wiki/Triadic_relation

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/

In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.

I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables