Author Archives: Jon Awbrey

Systems of Interpretation • 5

Posted on June 11, 2023 by Jon Awbrey

Re: Peirce List • Jerry Chandler An elementary sign relation is an ordered triple   It is called elementary because it is one element of a sign relation where is a set of objects, is a set of signs, and … Continue reading →

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

Systems of Interpretation • 4

Posted on June 10, 2023 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel For its pertinence to the present discussion, here again is what Peirce wrote about the mathematical way of using individual or particular cases to make general hypotheses or suppositions: Mathematical Demonstration … Continue reading →

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

Logic Syllabus • Discussion 2

Posted on June 4, 2023 by Jon Awbrey

Re: Logic Syllabus Re: Laws of Form • John Mingers JM: Is [the “just one true” operator] the same or different to xor?  I have read that xor is true when an odd number of variables are true which would … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 5 Comments

Logic Syllabus • Discussion 1

Posted on June 2, 2023 by Jon Awbrey

Re: Logic Syllabus Re: Laws of Form • John Mingers JM: In a previous post you mentioned the minimal negation operator.  Is there also the converse of this, i.e. an operator which is true when exactly one of its arguments … Continue reading →

Posted in Amphecks, Animata, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Functional Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 5 Comments

Inquiry Into Inquiry • On Initiative 5

Posted on May 22, 2023 by Jon Awbrey

Re: Inquiry Into Inquiry • On Initiative 2 Re: Mathstodon • Joeri Sebrechts JS: That’s not how it works.  The model lacks agency.  It is a machine whose gears are cranked by the user’s prompt.  It can ask questions, but … Continue reading →

Posted in Anthem, Initiative, Inquiry | Tagged , , | 5 Comments

Mathematical Demonstration and the Doctrine of Individuals • 2

Posted on May 16, 2023 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 , , , , , , , , , , | 7 Comments

Mathematical Demonstration and the Doctrine of Individuals • 1

Posted on May 16, 2023 by Jon Awbrey

Selection from C.S. Peirce’s “Logic Of Relatives” (1870) Demonstration of the sort called mathematical is founded on suppositions of particular cases.  The geometrician draws a figure;  the algebraist assumes a letter to signify a single quantity fulfilling the required conditions.  … 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 , , , , , , , , , , | 7 Comments

Inquiry Into Inquiry • On Initiative 4

Posted on May 15, 2023 by Jon Awbrey

Re: Terry Tao • PCAST Working Group on Generative AI Invites Public Input My Comment — I think a lot of people who’ve been working all along on AI, intelligent systems, and computational extensions of human capacities in general are … Continue reading →

Posted in Anthem, Initiative, Inquiry | Tagged , , | 6 Comments

Systems of Interpretation • 3

Posted on May 10, 2023 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel The “triskelion” figure in the previous post shows the bare essentials of an elementary sign relation or individual triple   There’s a less skeletal figure Susan Awbrey and I used in … Continue reading →

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

Systems of Interpretation • 2

Posted on May 7, 2023 by Jon Awbrey

Re: Peirce List • Mike Bergman • Valentine Daniel Let’s start as simply as possible.  The following Figure is typical of many I have used to illustrate sign relations from the time I first began studying Peirce’s theory of signs. … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Interpretive Frameworks, Logic, Logical Graphs, Objective Frameworks, Relation Theory, Semiotics, Sign Relations, Systems of Interpretation, Triadic Relations, Visualization | Tagged , , , , , , , , , , , | 5 Comments