Author Archives: Jon Awbrey

Semiotics, Semiosis, Sign Relations • Discussion 7

Posted on August 13, 2021 by Jon Awbrey

Re: Category Theory • Morgan Rogers MR: Okay, this is hard to parse, but I’ve looked at it a few times now framed with discussion from a few different sources, and it seems that if we fix some sets of signs, … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Semiotics, Semiosis, Sign Relations • Comment 3

Posted on August 12, 2021 by Jon Awbrey

It helps me to compare sign relations with my other favorite class of triadic relations, namely, groups.  Applications of mathematical groups came up just recently in the Laws of Form discussion group, so it will save a little formatting time to adapt … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Semiotics, Semiosis, Sign Relations • Comment 2

Posted on August 10, 2021 by Jon Awbrey

Re: Semiotics, Semiosis, Sign Relations • Comment 1 Definitions tend to call on other terms in need of their own definitions, and so on till the process terminates at the level of primitive terms.  The main two concepts requiring supplementation in … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Semiotics, Semiosis, Sign Relations • Comment 1

Posted on August 9, 2021 by Jon Awbrey

I opened a topic on Sign Relations in the Logic stream of Category Theory Zulipchat to work on Peirce’s theory of triadic sign relations in a category-theoretic framework. I had been reading Peirce for a decade or more before I found … Continue reading →

Posted in C.S. Peirce, Category Theory, Logic, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 8 Comments

Relations & Their Relatives • Comment 3

Posted on August 6, 2021 by Jon Awbrey

Here’s a couple of selections from Peirce’s 1870 Logic of Relatives bearing on the proper use of individuals in mathematics, and thus on the choice between nominal thinking and real thinking. 😸 Mathematical Demonstration & the Doctrine of Individuals • … 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 , , , , , , , , , , , , , , , | 9 Comments

Relations & Their Relatives • Comment 2

Posted on August 5, 2021 by Jon Awbrey

Before I forget how I got myself into this particular briar patch — I mean the immediate occasion, not the long ago straying from the beaten path — it was largely in discussions with Henry Story where he speaks of … 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 , , , , , , , , , , , , , , , | 9 Comments

Descriptive and Normative • Discussion 1

Posted on August 4, 2021 by Jon Awbrey

Re: Logical Graphs • Discussion 3 Re: Laws of Form • John Mingers JM: I hesitate to enter into this debate but I would want to draw different distinctions to normative/descriptive. I would distinguish (following philosopher Roy Bhaskar) between the … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Relations & Their Relatives • Comment 1

Posted on August 2, 2021 by Jon Awbrey

I opened a topic on Relation Theory in the Logic stream of Category Theory Zulipchat to discuss the logic of relative terms and the mathematics of relations as they develop from Peirce’s first breakthroughs (1865–1870). As I have mentioned on … 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 , , , , , , , , , , , , , , , | 9 Comments

Logical Graphs • Discussion 4

Posted on August 1, 2021 by Jon Awbrey

Re: Category Theory • Henry Story HS: Evan Patterson’s “Knowledge Representation in Bicategories of Relations” is also drawn up in terms of string diagrams, as a way of explaining the W3C RDF and OWL standards.  So it looks like we … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Notes On Categories • 2

Posted on July 31, 2021 by Jon Awbrey

Re: Category Theory • Joe Moeller JM: In category theory, we have this perspective that we should focus attention on maps, on the relationships between objects, rather than on the objects themselves.  What’s your favorite examples of people giving a … Continue reading →

Posted in Abstraction, Category Theory, Computing, Graph Theory, Logic, Mathematics, Relation Theory, Type Theory | Tagged , , , , , , , | 2 Comments