Tag Archives: Propositional Calculus

Fourier Transforms of Boolean Functions • 1

Posted on May 30, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Twin Primes Are Useful The problem is concretely about Boolean functions of variables, and seems not to involve prime numbers at all. For any subset of the coordinate [indices], the corresponding Fourier coefficient … Continue reading →

Posted in Boolean Functions, Computational Complexity, Fourier Transforms, Harmonic Analysis, Logic, Mathematics, Propositional Calculus | Tagged , , , , , , | 1 Comment

Finding a Needle in a Cactus Patch

Posted on April 30, 2013 by Jon Awbrey

Re: R.J. Lipton • Sex, Lies, And Quantum Computers Don’t know much about quantum computation, but my ventures in graphical syntaxes for propositional calculus did turn up a logical operator whose evaluation process reminded me a little of the themes … Continue reading →

Posted in Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Quantum Computing, Semiotics | Tagged , , , , , , , , , , , , | 4 Comments

Indicator Functions • 1

Posted on March 13, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? One of the things it helps to understand about 19th Century mathematicians, and those who built the bridge to the 20th, is that they were capable of high abstraction … Continue reading →

Posted in Abstraction, Boole, Boolean Functions, C.S. Peirce, Category Theory, Characteristic Functions, Euler, Indicator Functions, John Venn, Logic, Mathematics, Peirce, Propositional Calculus, Set Theory, Venn Diagrams, Visualization | Tagged , , , , , , , , , , , , , , , | Leave a comment

I Wonder, Wonder Who

Posted on February 25, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Who Invented Boolean Functions? The question recalls recent discussions of discovery and invention in the mathematical field, bringing back to mind questions I’ve wondered about for as long as I can remember. Speaking … Continue reading →

Posted in Anamnesis, Aristotle, Boole, Boolean Functions, C.S. Peirce, Discovery, Invention, Learning, Logic, Mathematics, Meno, Model Theory, Peirce, Plato, Propositional Calculus, Recollection, Semiotics, Socrates, Teaching | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s Law

Posted on October 6, 2008 by Jon Awbrey

Peirce’s law is a logical proposition that states a non-obvious truth of classical logic and affords a novel way of defining classical propositional calculus. Continue reading →

Posted in C.S. Peirce, Equational Inference, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce's Law, Proof Theory, Propositional Calculus, Propositions As Types Analogy, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , | 15 Comments

Praeclarum Theorema

Posted on October 5, 2008 by Jon Awbrey

The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus that was noted and named by G.W. Leibniz. Continue reading →

Posted in Abstraction, Animata, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Form, Graph Theory, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , | 17 Comments

Logical Graphs • Formal Development

Posted on September 19, 2008 by Jon Awbrey

Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner. Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 41 Comments

Logical Graphs • Introduction

Posted on July 29, 2008 by Jon Awbrey

A logical graph is a graph-theoretic structure in one of the styles of graphical syntax that Charles Sanders Peirce developed for logic. Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Diagrammatic Reasoning, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , | 43 Comments