Tag Archives: C.S. Peirce

Survey of Precursors Of Category Theory • 1

Posted on May 15, 2015 by Jon Awbrey

A few years ago I began a sketch on the “Precursors of Category Theory”, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of … Continue reading →

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 20 Comments

Survey of Differential Logic • 1

Posted on May 11, 2015 by Jon Awbrey

This is a Survey of blog and wiki posts on Differential Logic, material I plan to develop toward a more compact and systematic account. Elements Differential Logic • Introduction Differential Propositional Calculus • Part 1 • Part 2 Differential Logic … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Animated Logical Graphs • 1

Posted on May 10, 2015 by Jon Awbrey

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading →

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 2 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

Animated Logical Graphs • 6

Posted on March 13, 2015 by Jon Awbrey

Re: Peirce List • 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 all … 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