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

Logical Graphs • First Impressions 1
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/

Introduction • Moving Pictures of Thought —

A “logical graph” is a graph-theoretic structure in one of the systems of graphical syntax Charles Sanders Peirce developed for logic.

In numerous papers on “qualitative logic”, “entitative graphs”, and “existential graphs”, 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 this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph-theoretic structures. This article examines the common basis of these 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.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistensialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/

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. A couple of beginning pieces are linked below.

Logical Graphs • Introduction
• https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/

I've been thinking about ways to connect the species of logical graphs I've been developing out of Peirce's entitative and existential graphs with the styles of logical graphs envisioned in the RDF Surfaces group.

One thing arising out of those reflections was I began to tease apart two layers of structure, the one involved in conceiving and computing logical formulas and the other employed in displaying the end results.

At any rate, I'll explore that theme further as we go.

For now, the Survey page linked above will provide an overview of work already done.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #PropositionalCalculus #LogicAsSemiotics
#RelationTheory #SignRelations #Semiotics #W3C #RDF #RDFSurfaces

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/

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 link above for the full set of resources.
Here I'll just link to a couple of beginning pieces.

Logical Graphs • Introduction
• https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/

I've been thinking about ways to connect the species of logical graphs
I've been developing out of Peirce's entitative and existential graphs
with the styles of logical graphs envisioned in the RDF Surfaces group.

One thing arising out of those reflections was I began to tease apart
two layers of structure, the one involved in conceiving and computing
logical formulas and the other employed in displaying the end results.

At any rate, I'll be exploring that theme as we go.

For now, the Survey page linked above will provide an overview of work already done.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #PropositionalCalculus #LogicAsSemiotics
#RelationTheory #SignRelations #Semiotics #W3C #RDF #RDFSurfaces

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/

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.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#Boole #BooleanAlgebra #BooleanFunctions #Semiotics #Semeiotics
#SpencerBrown #LawsOfForm #PropositionalCalculus #SignRelations

#LogicalGraphs • 17
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 8 to bring out the dual graphs by themselves affords a view of the first #InitialEquation shown in Figure 9.

Figure 9
• https://oeis.org/w/images/8/85/Logical_Graph_Figure_9_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Turning now to the #InitialEquation or #LogicalAxiom whose text expression is \(\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}\), Figure 8 shows the planar maps and their #DualGraphs superimposed.

Figure 8
• https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 14
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

The procedure just described is called “traversing” the tree and the string read off is called the “#TraversalString” of the tree. The reverse operation of going from the string to the tree is called “parsing” the string and the tree constructed is called the “ParseGraph” of the string.

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 12
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Once we make the connection between one of #Peirce's #AlphaGraphs and its character string expression it's not too big a leap to see how the character string codes up the structure of the topological #DualGraph in the space of #RootedTrees.

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 11
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 4 to bring out the dual graphs by themselves affords a view of the second #InitialEquation shown in Figure 5.

Figure 5
• https://oeis.org/w/images/4/46/Logical_Graph_Figure_5_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 6
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Progenesis

In Lieu of a Beginning —

Consider the #FormalEquations indicated in Figures 1 and 2.

Figure 1
• https://oeis.org/w/images/8/81/Logical_Graph_Figure_1_Visible_Frame.jpg

Figure 2
• https://oeis.org/w/images/6/66/Logical_Graph_Figure_2_Visible_Frame.jpg

For the time being these two forms of transformation may be referred to as axioms or initial equations.

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 5
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Abstract_POV

#AbstractPointOfView (cont.)

In particular, though we may note in passing such historical details as the circumstance that Charles Sanders #Peirce used a #StreamerCross symbol where George #SpencerBrown used a #CarpentersSquare marker, the theme of principal interest at the abstract level of form is neutral with regard to variations of that order.

#Logic #PropositionalCalculus #BooleanFunctions
#LawsOfForm #GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 3
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no

We begin on a low but expansive plateau of #FormalSystems #Peirce mapped out in his system of #AlphaGraphs \((\alpha),\) a platform so abstract in its mathematical forms as to support at least two interpretations for use in the conduct of logical reasoning. Along the way, we incorporate the later contributions of George #SpencerBrown, who revived and augmented Peirce's system in his book #LawsOfForm.

#Logic #GraphTheory #ModelTheory #ProofTheory

Hashtag introduction: #jointspeech #embodiment #deleuze #serres # latour #esoterica #chant #nonduality #kashmirishaivism #rhythm #cognitivescience #lawsofform #ritual #mysticism #alchemy #autopoiesis #enaction #subversiveart #theology #divinemadness #shiva #utterance #mantra #prayer #becominganimal

@thhaase BETEN VERBOTEN. gilt auch für das anbeten von professorenden (so?) https://dissent.is/LoF #LoF #LawsOfForm

#cfp on the #lawsofform conference 2022: https://lof50.com/

If you are interested in the Laws of Form and George Spencer Brown you should watch this video: https://youtu.be/_tcF1YaPhmQ
#systemstheory #lawsofform #logic