Das müsste von Sebastian #Plönges mal bei #Twitter gepostet worden sein. Es ging darum, wie sich #Haken aus Laws of Form von George Spencer #Brown über die #Tastatur einfach darstellen lassen.
#Blog #Plönges: https://sebastian-ploenges.com/
#LoF #LawsOfForm #SpencerBrown #Darstellung #Zeichen #Form #Reentry
Charles Sanders Peirce, George Spencer Brown, and Me • 4
• https://inquiryintoinquiry.com/2017/08/06/charles-sanders-peirce-george-spencer-brown-and-me-4/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lh5fsszkmk23
Two things impacting my studies of Peirce and Spencer Brown over the years were my parallel studies in mathematics and computer science. In the overlap between those areas came courses in logic, mathematical linguistics, and the theory of formal languages, grammars, and automata.
My intellectual wanderings over a nine‑year undergraduate career would take me through a cycle of majors from math and physics, to communication, psychology, philosophy, and a cross‑cultural liberal arts program, then back to grad school in mathematics.
The puzzles Peirce and Spencer Brown beset my brain with were a big part of what drove me back to math, since I could see I had no chance of resolving them without learning a lot more algebra, logic, and topology than I had learned till then.
Charles Sanders Peirce, George Spencer Brown, and Me • 1
• https://inquiryintoinquiry.com/2017/07/20/charles-sanders-peirce-george-spencer-brown-and-me-1/
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lgxtd6z3nk2t
It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away.
I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, converting graph-theoretic data structures formed on their ideas to good purpose in the mechanics of its propositional reasoning engine. I thought it might contribute to a number of ongoing discussions if I could articulate what I think I learned from that experience.
Connections: All this RFK fluoridation talk resulted in me starting a re-read of "The Schrodinger's Cat Trilogy." That reminded me I have for decades meant to look into "Laws of Form." Suddenly I am confronted with the enormity of x-squared plus one equals zero and the need for imaginary numbers.
The...NEED...for imaginary numbers. That's as far as I've got:
Logical Graphs • Formal Development 1
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-1-a/
Recap —
A first approach to logical graphs was outlined in the article linked below.
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/
That introduced the initial elements of logical graphs and hopefully supplied the reader with an intuitive sense of their motivation and rationale.
Formal Development —
Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner.
The next order of business is to give the precise axioms used to develop the formal system of logical graphs. The axioms derive from C.S. Peirce's various systems of graphical syntax via the “calculus of indications” described in Spencer Brown's “Laws of Form”. The formal proofs to follow will use a variation of Spencer Brown's annotation scheme to mark each step of the proof according to which axiom is called to license the corresponding step of syntactic transformation, whether it applies to graphs or to strings.
Resources —
Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Logical Graphs • First Impressions 1
• https://inquiryintoinquiry.com/2024/08/30/logical-graphs-first-impressions-1/
Moving Pictures of Thought —
A logical graph is a graph‑theoretic structure in one of the systems of graphical syntax Charles S. Peirce developed for logic.
Introduction —
In numerous papers on qualitative logic, entitative graphs, and existential graphs, C.S. Peirce developed several versions of a graphical formalism, or a graph‑theoretic formal language, designed to be interpreted for logic.
In the century since Peirce initiated their line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph‑theoretic structures. The posts to follow explore the common basis of those formal systems from a bird's eye view, focusing on the aspects of form shared by the entire family of algebras, calculi, or languages, however they happen to be viewed in a given application.
Resources —
Logical Graphs
• https://oeis.org/wiki/Logical_Graphs
Futures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_Graphs
Propositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Charles Sanders Peirce • Bibliography
• https://mywikibiz.com/Charles_Sanders_Peirce
• https://mywikibiz.com/Charles_Sanders_Peirce_%28Bibliography%29
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Transformations of Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/05/22/transformations-of-logical-graphs-discussion-1/
Re: Laws of Form
• https://groups.io/g/lawsofform/topic/transformations_of_logical/105927945
Mauro Bertani
• https://groups.io/g/lawsofform/message/3204
Dear Mauro,
The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/
Additional Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/
Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form
Mathematical Duality in Logical Graphs • Discussion 2.2
• https://inquiryintoinquiry.com/2024/05/04/mathematical-duality-in-logical-graphs-discussion-2/
What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.
Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form
Mathematical Duality in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/05/04/mathematical-duality-in-logical-graphs-discussion-1/
Re: Mathematical Duality in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/
Re: Laws of Form • Lyle Anderson
• https://groups.io/g/lawsofform/message/109
Re: Brading, K., Castellani, E., and Teh, N., (2017), “Symmetry and Symmetry Breaking”, The Stanford Encyclopedia of Philosophy (Winter 2017), Edward N. Zalta (ed.).
• https://plato.stanford.edu/archives/win2017/entries/symmetry-breaking/
Dear Lyle,
Thanks for the link to the article on symmetry and symmetry breaking. I did once take a Master's in Mathematics, specializing in combinatorics, graph theory, and group theory. When it comes to the bearing of symmetry groups on logical graphs and the calculus of indications, it will take careful attention to the details of the relationship between the two interpretations singled out by Peirce and Spencer Brown.
Both Peirce and Spencer Brown recognized the relevant duality, if they differed in what they found most convenient to use in their development and exposition, and most of us will emphasize one interpretation or the other as a matter of facility or taste in a chosen application, so it requires a bit of effort to keep the underlying unity in focus. I recently made another try at taking a more balanced view, drawing up a series of tables in parallel columns the way one commonly does with dual theorems in projective geometry, so I will shortly share more of that work.
Resources —
Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Mathematical Duality in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/
It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.
Resources —
Duality Indicating Unity
• https://inquiryintoinquiry.com/2013/01/31/duality-indicating-unity-1/
C.S. Peirce • Logic of Number
• https://inquiryintoinquiry.com/2012/09/01/c-s-peirce-logic-of-number-ms-229/
C.S. Peirce • Syllabus • Selection 1
• https://inquiryintoinquiry.com/2014/08/24/c-s-peirce-syllabus-selection-1/
References —
• Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.
• Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form
Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/
“All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”
— C.S. Peirce • “Logic of Number”
“A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”
— G. Spencer Brown • “Laws of Form”
The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.
A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.
Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form
Operator Variables in Logical Graphs • Discussion 2
• https://inquiryintoinquiry.com/2024/04/09/operator-variables-in-logical-graphs-discussion-2/
Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/
Re: Cybernetics List • Lou Kauffman
• https://groups.google.com/g/cybcom/c/XKT76QI_OnI/m/3u9P2Ir5AgAJ
LK:
❝I am writing to comment that there are some quite interesting situations that generalize the DeMorgan Duality.
❝One well-known one is this. Let R* denote the real numbers with a formal symbol @, denoting infinity, adjoined so that:
• @ + @ = @
• @ + 0 = @
• @ + x = @ when x is an ordinary real number
• 1 ÷ @ = 0
❝(Of course you cannot do anything with @ or the system collapses. One can easily give the constraints.)
❝Define ¬x = 1/x.
• x + y = usual sum otherwise.
❝Define x ∗ y = xy/(x + y) = 1/((1/x) + (1/y)).
❝Then we have x ∗ y = ¬(¬x + ¬y), so that the system (R*, ¬, +, ∗) satisfies DeMorgan duality and it is a Boolean algebra when restricted to {0, @}.
❝Note also that ¬ fixes 1 and -1. This algebraic system occurs of course in electrical calculations and also in the properties of tangles in knot theory, as you can read in the last part of my included paper “Knot Logic”. I expect there is quite a bit more about this kind of duality in various (categorical) places.❞
Thanks, Lou, there's a lot to think about here, so I'll need to study it a while. Just off hand, the embedding into reals brings up a vague memory of the very curious way Peirce defines negation in his 1870 “Logic of Relatives”. I seem to recall it involving a power series, but it's been a while so I'll have to look it up again.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
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 • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/
Consider De Morgan's rules:
• ¬(A ∧ B) = ¬A ∨ ¬B
• ¬(A ∨ B) = ¬A ∧ ¬B
The common form exhibited by the two rules could be captured in a single formula by taking “o₁” and “o₂” as variable names ranging over a family of logical operators, then asking what substitutions for o₁ and o₂ would satisfy the following equation.
• ¬(A o₁ B) = ¬A o₂ ¬B
We already know two solutions to this “operator equation”, namely, (o₁, o₂) = (∧, ∨) and (o₁, o₂) = (∨, ∧). Wouldn't it be just like Peirce to ask if there are others?
Having broached the subject of “logical operator variables”, I will leave it for now in the same way Peirce himself did:
❝I shall not further enlarge upon this matter at this point, although the conception mentioned opens a wide field; because it cannot be set in its proper light without overstepping the limits of dichotomic mathematics.❞ (Peirce, CP 4.306).
Further exploration of operator variables and operator invariants treads on grounds traditionally known as second intentional logic and “opens a wide field”, as Peirce says. For now, however, I will tend to that corner of the field where our garden variety logical graphs grow, observing the ways in which operative variations and operative themes naturally develop on those grounds.
#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
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/
This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.
Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/
Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_Syllabus
Logical Graphs
• https://oeis.org/wiki/Logical_Graphs
Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator
Propositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems
Examples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_law
Praeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theorema
Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations
Excursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview
Futures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_Graphs
Applications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems
Exploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data
Differential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata
Logical Graphs • Discussion 9
• http://inquiryintoinquiry.com/2023/10/12/logical-graphs-discussion-9/
Re: Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/
Re: Laws of Form • Lyle Anderson
• https://groups.io/g/lawsofform/message/2511
LA:
❝The Gestalt Switch from parenthesis to graphs is stimulating. There are probably things in Laws of Form that we didn't see because we were blinded by the crosses.❞
That has been my experience. Viewing a space of mathematical objects from a new angle and changing the basis of representation can bring out new and surprising aspects of their form and even expand the field of view to novel directions of generalization.
One of the first things I learned in the early years of computing with logical graphs is how essential it is to “slip the surly bonds” of the planar embedding and work with free trees in a space of their own.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Logical Graphs • Discussion 7
• https://inquiryintoinquiry.com/2023/10/01/logical-graphs-discussion-7/
Re: Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-2/
Re: Laws of Form • Alex Shkotin
• https://groups.io/g/lawsofform/message/2461
AS:
❝When we look at undirected graph it is usual, before describing a rules of graph transformation, to describe exactly what kind of graphs we are working with ...❞
Hi Alex,
I am traveling this week, with limited internet. There's a quickie glossary under the heading “Painted And Rooted Cacti” on the following blog page.
Theme One Program • Exposition 2
• https://inquiryintoinquiry.com/2022/06/16/theme-one-program-exposition-2-2/
Regards,
Jon
P.S. Back home now ... with access to books ... will attempt to fill in some of the blanks in last week's sketchy vacation messages. —JA
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Logical Graphs • Formal Development 1
• https://inquiryintoinquiry.com/2023/09/15/logical-graphs-formal-development-1/
Recap —
A first approach to logical graphs can be found in the article linked below.
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
That introduces the initial elements of logical graphs and hopefully supplies the reader with an intuitive sense of their motivation and rationale.
Formal Development —
Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner.
The next order of business is to give the precise axioms used to develop the formal system of logical graphs. The axioms derive from C.S. Peirce's various systems of graphical syntax via the “calculus of indications” described in Spencer Brown's “Laws of Form”. The formal proofs to follow will use a variation of Spencer Brown's annotation scheme to mark each step of the proof according to which axiom is called to license the corresponding step of syntactic transformation, whether it applies to graphs or to strings.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
Logical Graphs • Discussion 6
• https://inquiryintoinquiry.com/2023/08/29/logical-graphs-discussion-6/
Re: Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/
Logical Graphs • Figures 1 and 2
• https://inquiryintoinquiry.files.wordpress.com/2023/08/logical-graph-figures-1-2-framed.png
Re: Academia.edu • Robert Appleton
• https://www.academia.edu/community/lavbw5?c=Q4jlVy
RA:
❝As a professional graphic designer and non-mathematician reading your two diagrams, I need to ask for a simpler statement of their purpose. What do Fig 1 and Fig 2 represent to you? And what insight do they provide us?❞
My Comment —
Figures 1 and 2 are really just a couple of “in medias res” pump‑primers or ice‑breakers. This will all be explained in the above linked blog post, where I'm revising the text and upgrading the graphics of some work I first blogged in 2008 based on work I did even further back. I'll be taking a fresh look at that as I serialize it here.
Those two Figures come from George Spencer Brown's 1969 book Laws of Form, where he called them the Law of Calling and the Law of Crossing. GSB revived and clarified central aspects of Peirce's systems of logical graphs and I find it helpful to integrate his work into my exposition of Peirce. For now you can think of those as exemplifying two core formal principles which go to the root of the mathematical forms underlying logical reasoning.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
