Category Archives: Mathematics

Differential Logic • The Logic of Change and Difference

Posted on August 22, 2023 by Jon Awbrey

Differential logic is the logic of variation — the logic of change and difference. Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes … Continue reading →

Posted in Animata, Boolean Difference Calculus, Boolean Functions, C.S. Peirce, Differential Logic, Differential Propositions, Discrete Dynamical Systems, Leibniz, Logic, Logical Graphs, Minimal Negation Operators, Visualization | Tagged , , , , , , , , , , , | 6 Comments

Inquiry Into Inquiry • Discussion 9

Posted on August 19, 2023 by Jon Awbrey

Re: Pragmatic Maxim Re: Academia.edu • Milo Gardner MG: Do you agree that Peirce was limited to bivalent logic? Taking classical logic as a basis for reasoning is no more limiting than taking Dedekind cuts as a basis for constructing … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Compositionality, Formal Languages, Inference, Information, Information Fusion, Initiative, Inquiry, Logic, Relation Theory, Semiotics, Triadic Relation Irreducibility, Visualization | Tagged , , , , , , , , , , , , , , | 5 Comments

Inquiry Into Inquiry • Discussion 8

Posted on August 18, 2023 by Jon Awbrey

Re: Inquiry Into Inquiry • Discussion 7 Re: Academia.edu • Milo Gardner MG: Peirce sensed that bivalent syntax was superceded by trivalent syntax, but never resolved that nagging question. The main thing is not a question of syntax but a … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Compositionality, Formal Languages, Inference, Information, Information Fusion, Initiative, Inquiry, Logic, Relation Theory, Semiotics, Triadic Relation Irreducibility, Visualization | Tagged , , , , , , , , , , , , , , | 5 Comments

Inquiry Into Inquiry • Discussion 7

Posted on August 17, 2023 by Jon Awbrey

Dan Everett has prompted a number of discussions on Facebook recently which touch on core issues in Peirce’s thought — but threads ravel on and fray so quickly in that medium one rarely gets a chance to fill out the … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Compositionality, Formal Languages, Inference, Information, Information Fusion, Initiative, Inquiry, Logic, Relation Theory, Semiotics, Triadic Relation Irreducibility, Visualization | Tagged , , , , , , , , , , , , , , | 5 Comments

Survey of Precursors Of Category Theory • 4

Posted on August 1, 2023 by Jon Awbrey

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, Diagrams, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Survey of Relation Theory • 7

Posted on July 26, 2023 by Jon Awbrey

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, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Pragmatic Semiotic Information • 7

Posted on July 23, 2023 by Jon Awbrey

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, 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Functional Logic • Inquiry and Analogy • 21

Posted on July 19, 2023 by Jon Awbrey

Inquiry and Analogy • Generalized Umpire Operators To get a better handle on the space of higher order propositions and continue developing our functional approach to quantification theory, we’ll need a number of specialized tools.  To begin, we define a … Continue reading →

Posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Pragmatic Semiotic Information, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotics, Sign Relations, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Functional Logic • Inquiry and Analogy • 20

Posted on July 18, 2023 by Jon Awbrey

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Table 21 provides a thumbnail sketch of the relationships discussed in this section. Resources Logic Syllabus Boolean Function Boolean-Valued Function Logical Conjunction Minimal Negation Operator Introduction to Inquiry … Continue reading →

Posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Pragmatic Semiotic Information, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotics, Sign Relations, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Functional Logic • Inquiry and Analogy • 19

Posted on July 17, 2023 by Jon Awbrey

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Reflection is turning a topic over in various aspects and in various lights so that nothing significant about it shall be overlooked — almost as one might turn … Continue reading →

Posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Pragmatic Semiotic Information, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotics, Sign Relations, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments