Monthly Archives: August 2024

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

Peircean Semiotics and Triadic Sign Relations • 3

Posted on August 23, 2024 by Jon Awbrey

Having labored mightily to bring out a new edition of my primer on sign relations, including material on the pivotal concept of semiotic equivalence relations, I thought it worth the candle to post a notice of the new version here. Sign … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Logic of Relatives, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 4 Comments

Peircean Semiotics and Triadic Sign Relations • 2

Posted on August 22, 2024 by Jon Awbrey

When I returned to graduate school for the third time around, this time in systems engineering, I had in mind integrating my long‑standing projects investigating the dynamics of information, inquiry, learning, and reasoning, viewing each as a process whose trajectory evolves … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Logic of Relatives, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 4 Comments

Peircean Semiotics and Triadic Sign Relations • 1

Posted on August 20, 2024 by Jon Awbrey

As a “guide for the perplexed”, at least when it comes to semiotics, I’ll use this thread to collect a budget of resources I think have served to clarify the topic in the past. By way of a first offering, … Continue reading →

Posted in C.S. Peirce, Inquiry, Logic, Logic of Relatives, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 4 Comments

Logic of Relatives

Posted on August 5, 2024 by Jon Awbrey

The logic of relatives, more precisely, the logic of relative terms, is the study of relations as represented in symbolic forms known as “rhemes”, “rhemata”, or “relative terms”. Continue reading →

Posted in C.S. Peirce, Logic, Logic of Relatives, Mathematical Logic, Mathematics, Relation Theory, Semiotics | Tagged , , , , , , | 3 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