Category Archives: Logical Graphs

Logical Graphs • First Impressions 5

Posted on September 4, 2024 by Jon Awbrey

Duality : Logical and Topological (cont.) It is easy to see the relation between the parenthetical expressions of Peirce’s logical graphs, showing their contents in order of containment, and the corresponding dual graphs, forming a species of rooted trees to be … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 4

Posted on September 3, 2024 by Jon Awbrey

Duality : Logical and Topological (cont.) Last time we took up the axiom or initial equation shown below. (3) We noted it could be written inline as “( ( ) ) =    ” or set off in the following text display. ( ( ) ) =     When we turn … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 3

Posted on September 1, 2024 by Jon Awbrey

Duality : Logical and Topological In using logical graphs there are two types of duality to consider, logical duality and topological duality. Graphs of the order Peirce considered, those embedded in a continuous manifold like that represented by a plane sheet of … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 2

Posted on August 31, 2024 by Jon Awbrey

Abstract Point of View The bird’s eye view in question is more formally known as the perspective of formal equivalence, from which remove one overlooks many distinctions which appear momentous in more concrete settings.  Expressions inscribed in different formalisms whose … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions 1

Posted on August 30, 2024 by Jon Awbrey

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 … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • First Impressions

Posted on August 26, 2024 by Jon Awbrey

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, Peirce developed several versions of … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • 4

Posted on August 3, 2024 by Jon Awbrey

From Dyadic to Triadic to Sign Relations Peirce’s notation for elementary relatives was illustrated earlier by a dyadic relation from number theory, namely, the relation written for Table 1 shows the first few ordered pairs of the relation on positive … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 3

Posted on August 2, 2024 by Jon Awbrey

Here are two ways of looking at the divisibility relation, a dyadic relation of fundamental importance in number theory. Table 1 shows the first few ordered pairs of the relation on positive integers corresponding to the relative term, “divisor of”.  Thus, … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 2

Posted on August 1, 2024 by Jon Awbrey

What is the relationship between “logical relatives” and “mathematical relations”?  The word relative used as a noun in logic is short for relative term — as such it refers to an item of language used to denote a formal object. … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments

Relations & Their Relatives • 1

Posted on July 31, 2024 by Jon Awbrey

Sign relations are special cases of triadic relations in much the same way binary operations in mathematics are special cases of triadic relations.  It amounts to a minor complication that we participate in sign relations whenever we talk or think … Continue reading →

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 3 Comments