Category Archives: C.S. Peirce

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

Animated Logical Graphs • 6

Posted on March 13, 2015 by Jon Awbrey

Re: Peirce List Discussion • Jim Willgoose At root we are dealing with a genre of very abstract formal systems.  They have grammars that determine their well-formed expressions and rules that determine the permissible transformations among expressions, but they lack … Continue reading →

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Graph Theory, Iconicity, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 12 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

Relations & Their Relatives • Discussion 1

Posted on February 27, 2015 by Jon Awbrey

Re: Peirce List • Helmut Raulien The divisor of relation signified by is a dyadic relation on the set of positive integers and thus may be understood as a subset of the cartesian product   It is an example 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 , , , , , , , , , , , , , , , | 15 Comments

Mathematical Demonstration and the Doctrine of Individuals • 2

Posted on February 23, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) In reference to the doctrine of individuals, two distinctions should be borne in mind.  The logical atom, or term not capable of logical division, must be one of which every predicate may … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 6 Comments

Mathematical Demonstration and the Doctrine of Individuals • 1

Posted on February 22, 2015 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) Demonstration of the sort called mathematical is founded on suppositions of particular cases.  The geometrician draws a figure;  the algebraist assumes a letter to signify a single quantity fulfilling the required conditions.  … Continue reading →

Posted in C.S. Peirce, Deduction, Doctrine of Individuals, Foundations of Mathematics, Identity, Information = Comprehension × Extension, Logic, Logic of Relatives, Mathematical Demonstration, Mathematics, Relation Theory | Tagged , , , , , , , , , , | 5 Comments

Relations & Their Relatives • 3

Posted on February 18, 2015 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”.  … 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 , , , , , , , , , , , , , , , | 12 Comments

Relations & Their Relatives • 2

Posted on February 17, 2015 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 , , , , , , , , , , , , , , , | 10 Comments

Relations & Their Relatives • 1

Posted on February 17, 2015 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 , , , , , , , , , , , , , , , | 10 Comments