Category Archives: Mathematical Models

Objects, Models, Theories • 2

Posted on September 12, 2026 by Jon Awbrey

Re: Gödel’s Lost Letter • The Graph Of Math GLL: Kurt Gödel is said to have been a latecomer to appreciating the power of Model Theory.  He was of course the greatest architect of Proof Theory, which stands in contrast … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Objects, Models, Theories • 1

Posted on September 10, 2026 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839 I return once more to a recurring subject. Re: Artem Kaznatcheev • Three Types of Mathematical Models In speaking of models one tends to find denizens of different disciplines talking at … Continue reading →

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Propositional Calculus • Discussion 9

Posted on January 21, 2024 by Jon Awbrey

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have.  Then, your conception of those effects is the whole of your conception of the object. — C.S. Peirce • The Maxim of … Continue reading →

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Differential Propositional Calculus • 37

Posted on January 1, 2024 by Jon Awbrey

Foreshadowing Transformations • Extensions and Projections of Discourse And, despite the care which she took to look behind her at every moment, she failed to see a shadow which followed her like her own shadow, which stopped when she stopped, … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Differential Propositional Calculus • 36

Posted on December 31, 2023 by Jon Awbrey

Transformations of Discourse It is understandable that an engineer should be completely absorbed in his speciality, instead of pouring himself out into the freedom and vastness of the world of thought, even though his machines are being sent off to … Continue reading →

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Differential Propositional Calculus • Discussion 8

Posted on December 30, 2023 by Jon Awbrey

Re: Drives and Their Vicissitudes • Fourth Gear Orbits Re: Laws of Form • Lyle Anderson LA: Some of your diagrams, specifically Figure 16. A Couple of Fourth Gear Orbits, are beginning to look like Heim’s sketches for the structure … Continue reading →

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Differential Propositional Calculus • 35

Posted on December 29, 2023 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (concl.) Applied to the example of ‑gear curves, the indexing scheme results in the data of the next two Tables, showing one period for each orbit. The states in each orbit are listed as … Continue reading →

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Differential Propositional Calculus • 34

Posted on December 28, 2023 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (cont.) With a little thought it is possible to devise a canonical indexing scheme for the states in differential logical systems.  A scheme of that order allows for comparing changes of state in universes … Continue reading →

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Differential Propositional Calculus • 33

Posted on December 27, 2023 by Jon Awbrey

Example 2. Drives and Their Vicissitudes (cont.) Expressed in terms of drives and gears our next Example may be described as the family of ‑gear curves in the fourth extension   Those are the trajectories generated subject to the dynamic … Continue reading →

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Differential Propositional Calculus • 32

Posted on December 26, 2023 by Jon Awbrey

I open my scuttle at night and see the far‑sprinkled systems, And all I see, multiplied as high as I can cipher, edge but      the rim of the farther systems. — Walt Whitman • Leaves of Grass Example 2. Drives … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments