Tag Archives: Relation Theory

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.4

Posted on April 24, 2015 by Jon Awbrey

Dyadic relations enjoy yet another form of graph-theoretic representation as labeled bipartite graphs or labeled bigraphs.  I’ll just call them bigraphs here, letting the labels be understood in this logical context. The figure below shows the bigraphs of the 16 … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 9 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.3

Posted on April 23, 2015 by Jon Awbrey

Dyadic relations have graph-theoretic representations as labeled directed graphs with loops, also known as labeled pseudo-digraphs in some schools of graph theory.  I’ll just call them digraphs here, letting the labels and loops be understood in this logical context. The … Continue reading →

Posted in Dyadic Relations, Graph Theory, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , | 10 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2

Posted on April 19, 2015 by Jon Awbrey

Because it can sometimes be difficult to reconnect abstractions with their concrete instances, especially after the abstract types have become autonomous and taken on a life of their own, let us resort to a simple concrete case and examine the … Continue reading →

Posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Matrix Theory, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , | 11 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.1

Posted on April 13, 2015 by Jon Awbrey

I wanted to call attention to a very important statement from Selection 7 (CP 3.225–226).  Peirce enumerates the fundamental forms of individual dual relatives in the following terms: 225.   Individual relatives are of one or other of the two forms … Continue reading →

Posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , | 9 Comments

Objective Frameworks • Properties and Instances 1

Posted on April 9, 2015 by Jon Awbrey

Dealing with sign relations containing many types of signs — icons, indices, symbols, and more complex varieties — calls for a flexible and powerful organizational framework, one with the ability to grow and develop over time.  This is one of … Continue reading →

Posted in C.S. Peirce, Icon Index Symbol, Inquiry, Interpretive Frameworks, Logic, Logic of Relatives, Mathematics, Objective Frameworks, Peirce, Relation Theory, Relative Membership, Semiotics, Set Theory, Sign Relations | Tagged , , , , , , , , , , , , , | 2 Comments

Relations & Their Relatives • Discussion 5

Posted on March 22, 2015 by Jon Awbrey

Re: Peirce List • Howard Pattee At this point we can distinguish two forms of decomposability or reducibility — along with their corresponding negations, indecomposability or irreducibility – that commonly arise. Reducibility under relational composition All triadic relations are irreducible … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 15 Comments

Relations & Their Relatives • Discussion 4

Posted on March 19, 2015 by Jon Awbrey

Re: Peirce List Discussion • Howard Pattee We use this or that species of diagrams to represent a fraction of the properties, hardly ever all the properties, of the objects in an object domain.  The diagrams that Peirce developed to … Continue reading →

Posted in Diagrammatic Reasoning, Diagrams, Logic, Logic of Relatives, Mathematics, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , | 12 Comments

Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 8

Posted on March 12, 2015 by Jon Awbrey

Chapter 3. The Logic of Relatives (cont.) §4. Classification of Relatives (cont.) 227.   These different classes have the following relations.  Every negative of a concurrent and every alio-relative is both an opponent and the negative of a self-relative.  Every … Continue reading →

Posted in Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , | 9 Comments

Relations & Their Relatives • Discussion 3

Posted on March 5, 2015 by Jon Awbrey

Re: Peirce List • Edwina Taborsky • Howard Pattee In the best mathematical terms, a triadic relation is a cartesian product of three sets together with a specified subset of that cartesian product. Alternatively, one may think of a triadic … Continue reading →

Posted in C.S. Peirce, Cartesian Product, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce's Categories, Relation Theory, Rheme, Semiotics, Set Theory, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 13 Comments

Relations & Their Relatives • Discussion 2

Posted on March 4, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien In systems theory and engineering there is a well-recognized duality or complementarity between the dimensions of Control and Information, frequently cast in terms of action and perception, actuators and detectors, effectors and sensors, and … Continue reading →

Posted in C.S. Peirce, Category Theory, Control, Cybernetics, Dyadic Relations, Information, Inquiry, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiosis, Semiotics, Sign Relations, Systems Theory, Triadic Relations | Tagged , , , , , , , , , , , , , , , , | 14 Comments