Category Archives: Relation Theory

Survey of Semiotics, Semiosis, Sign Relations • 6

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands … Continue reading

Posted in C.S. Peirce, Icon Index Symbol, Inquiry, Logic, Logic of Relatives, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , | 26 Comments

Survey of Relation Theory • 9

In the present Survey of blog and wiki resources for Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set‑theoretic constructions, many … Continue reading

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Formal Languages, Foundations of Mathematics, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Model Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Survey of Precursors Of Category Theory • 6

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

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Foundations of Mathematics, Hilbert, Hypostatic Abstraction, Kant, Logic, Mathematics, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Pragmatic Semiotic Information • 9

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character but this line of inquiry is more open‑ended than most.  The question … Continue reading

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Survey of Cybernetics • 5

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? — Plato … Continue reading

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Higher Order Sign Relations • 1

Higher Order Sign Relations • Introduction When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections.  They need signs referring to sign relations, signs referring to elements and components of … Continue reading

Posted in C.S. Peirce, Higher Order Sign Relations, Inquiry, Inquiry Into Inquiry, Logic, Mathematics, Recursion, Reflection, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Type Theory | Tagged , , , , , , , , , , , , | 6 Comments

Interpreter and Interpretant • Selection 10

Transfer Returning to the scene of Dewey’s “Sign of Rain” example, let’s continue examining how the transfer of knowledge through the analogy of experience works in that case. By way of a recap, we began by considering a fragment of … Continue reading

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 9

Transfer Let’s examine how the transfer of knowledge through the analogy of experience works in the case of Dewey’s “Sign of Rain” example. For concreteness, consider a fragment of the reasoner’s knowledge base which is logically equivalent to a conjunction … Continue reading

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 8

Transfer What exactly gives the acquisition of a knowledge base its distinctively inductive character?  It is evidently the “analogy of experience” involved in applying what we’ve learned in the past to what confronts us in the present. Whenever we find … Continue reading

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments

Interpreter and Interpretant • Selection 7

Learning Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference.  For example, consider a proposition of the following form. Such a proposition is usually induced from a consideration of … Continue reading

Posted in C.S. Peirce, Hermeneutics, Interpretation, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 4 Comments