Tag Archives: Mathematics

Sign Relations, Triadic Relations, Relations • 9

Re: Ontolog Forum • RS Concrete examples are very instructive in this arena, and when it comes to refutations a single counter-example serves to puncture many a fallacious general proposition. Here’s a couple of articles, illustrated with concrete examples of a … Continue reading

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Sign Relations, Triadic Relations, Relations • 8

Re: Ontolog Forum • FK Our thoughts live in natural and artificial languages the way fish swim in natural and artificial bodies of water. One of the lessons most strikingly impressed on me by my first year physics course and … Continue reading

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Sign Relations, Triadic Relations, Relations • 7

Re: Ontolog Forum • JS JS: A binary relation is a set of ordered pairs of the elements of some other set. That is the first definition I learned for binary relations. Slightly more generally, a binary relation is a … Continue reading

Posted in C.S. Peirce, Inquiry Driven Systems, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , | Leave a comment

Theme One Discussion • 3

Re: Ontolog Forum • Systems Science • Structural Modeling Let me step back and talk about the research intention driving this work. In a very real sense everything I’ve been doing along this line of inquiry for the last fifty … Continue reading

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Theme One Discussion • 2

Re: Ontolog Forum • Systems Science • Structural Modeling What I’m doing this summer … Eighteen years living in the same place and we blissfully forgot what it takes to pack up a house and find a new one.  Thankfully … Continue reading

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Spencer Brown, Syntax, Theorem Proving | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Sign Relations, Triadic Relations, Relations • 6

Re: Ontolog Forum • JS Just by way of clarifying and emphasizing a few points — I use the word relation to mean a special type of mathematical object, namely, a designated subset included within a cartesian product of sets. … Continue reading

Posted in C.S. Peirce, Inquiry Driven Systems, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , | Leave a comment

Sign Relations, Triadic Relations, Relations • 5

Re: Ontolog Forum • RS I chose those examples of triadic relations to be as simple as possible without being completely trivial but they already exemplify many features we need to keep in mind in all the more complex cases … Continue reading

Posted in C.S. Peirce, Inquiry Driven Systems, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , | 1 Comment