Category Archives: Category Theory

Differential Logic, Dynamic Systems, Tangent Functors • 1

People interested in category theory as applied to systems may wish to check out the following article, reporting work I carried out while engaged in a systems engineering program at Oakland University. The problem addressed is a longstanding one, that … Continue reading

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Definition and Determination : 17

Re: Ontolog Forum Discussion • Richard McCullough RM:  We clearly have some differences in the “definition” of “definition”. I suppose it all depends on the sorts of things one wants to define, something we might call the context of application.  … Continue reading

Posted in C.S. Peirce, Category Theory, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Relatives, Logical Graphs, Mathematics, Ontology, Peirce, Relation Theory, Semiotics, Sign Relations, Structure, Theorem Proving, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Definition and Determination : 16

Re: Ontolog Forum Discussion • Richard McCullough RM:  What is your view of definitions? A recurring question, always worth some thought, so I added my earlier comment to a long-running series on my blog concerned with Definition and Determination. Definition and … Continue reading

Posted in C.S. Peirce, Category Theory, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Relatives, Logical Graphs, Mathematics, Ontology, Peirce, Relation Theory, Semiotics, Sign Relations, Structure, Theorem Proving, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Definition and Determination : 15

Re: Ontolog Forum Discussion In some early math course I learned a fourfold scheme of Primitives (undefined terms), Definitions, Axioms, and Inference Rules.  But later excursions tended to run the axioms and definitions together, speaking for example of mathematical objects … Continue reading

Posted in C.S. Peirce, Category Theory, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Relatives, Logical Graphs, Mathematics, Ontology, Peirce, Relation Theory, Semiotics, Sign Relations, Structure, Theorem Proving, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes : 18

Re: Peter Smith • Which Is The Quantifier? From a functional point of view it was a step backward when we passed from Peirce’s and to the current convention of and for logical quantifiers.  There’s a rough indication of what … Continue reading

Posted in C.S. Peirce, Category Theory, Complementarity, Duality, Formal Languages, Higher Order Propositions, Indicator Functions, Inquiry, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Pragmatism, Predicate Calculus, Propositional Calculus, Propositions, Quantifiers, Relation Theory, Semiotics, Type Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes : 17

Re: Peirce List Discussion • JA • GF • JFS • JLRC • JA • JFS • GF A rather amusing, if slightly ominous illustration of the point I am trying to make here has just popped up in the … Continue reading

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes : 16

Re: Peirce List Discussion • JA • JFS JFS: For those of us who are trying to convince modern students to study Peirce, we need to become bilingual.  We need to show how his terminology and notations map to and … Continue reading

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment