Category Archives: Form

Survey of Definition and Determination • 3

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from … Continue reading

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Logic, Mathematics, Scientific Method, Semiotics, Sign Relations, Structure | Tagged , , , , , , , , , , , , , , , | Leave a comment

Praeclarum Theorema • 3

Re: Praeclarum Theorema • (1) • (2) The steps of the proof are replayed in the following animation. Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz … Continue reading

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 3 Comments

Praeclarum Theorema • 2

Re: Praeclarum Theorema • 1 And here’s a neat proof of that nice theorem — Reference Leibniz, Gottfried W. (1679–1686?), “Addenda to the Specimen of the Universal Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz : Logical Papers, … Continue reading

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 4 Comments

Praeclarum Theorema • 1

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. This … Continue reading

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 5 Comments

Praeclarum Theorema

Introduction The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus noted and named by G.W. Leibniz, who stated and proved it in the following manner. If a is b and d is c, then ad will be bc. … Continue reading

Posted in Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | 5 Comments

Survey of Definition and Determination • 2

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from … Continue reading

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Semiotics, Structure | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Theme One Program • Motivation 6

Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here. In one of the projects I submitted toward a Master’s in psychology I used the Theme One program to … 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, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Motivation 5

Since I’m working from decades-old memories of first inklings I thought I might peruse the web for current information about Zipf’s Law.  I see there is now something called the Zipf–Mandelbrot (and sometimes –Pareto) Law and that was interesting because … 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, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Motivation 4

From Zipf’s Law and the category of “things that vary inversely with frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient codes. In its first application the … 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, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Theme One Program • Motivation 3

Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s.  Along with its research program the lab … 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, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 Comments