Tag Archives: Boolean Algebra

Frankl, My Dear • 1

Posted on September 7, 2014 by Jon Awbrey

Re: Dick Lipton and Ken Regan • (1) • (2) I need to think a little about the context Lipton and Regan have wrapped around the Frankl Conjecture, if not exactly about the problem itself.  This will be a scratch-worky … Continue reading →

Posted in Boolean Algebra, Boolean Functions, Computational Complexity, Differential Logic, Frankl Conjecture, Logic, Logical Graphs, Mathematics, Péter Frankl | Tagged , , , , , , , , | 11 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 9.4

Posted on February 27, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.4 Boole rationalizes the properties of what we now call boolean multiplication, roughly equivalent to logical conjunction, by means of his concept of selective operations.  Peirce, in his turn, taking a radical step … Continue reading →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 10 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 9.3

Posted on February 26, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.3 An idempotent element in an algebraic system is one which obeys the idempotent law, that is, it satisfies the equation   Under most circumstances it is usual to write this as If … Continue reading →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 11 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 9.2

Posted on February 26, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.2 In setting up his discussion of selective operations and their corresponding selective symbols, Boole writes the following. The operation which we really perform is one of selection according to a prescribed principle … Continue reading →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 11 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 9.1

Posted on February 24, 2014 by Jon Awbrey

Peirce’s 1870 “Logic of Relatives” • Comment 9.1 Perspective on Peirce’s use of the comma operator at CP 3.73 and CP 3.74 can be gained by dropping back a few years and seeing how George Boole explained his twin conceptions of selective … Continue reading →

Posted in Boole, Boolean Algebra, C.S. Peirce, Logic, Logic of Relatives, Mathematics, Relation Theory, Visualization | Tagged , , , , , , , | 10 Comments

All Process, No Paradox • 6

Posted on January 22, 2014 by Jon Awbrey

Re: R.J. Lipton • Anti-Social Networks Re: Lou Kauffman • Iterants, Imaginaries, Matrices Comments I made elsewhere about computer science and (anti-)social networks have a connection with the work in progress on this thread, so it may steal a march … Continue reading →

Posted in Algorithms, Amphecks, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Differential Logic, Graph Theory, Laws of Form, Logic, Logical Graphs, Lou Kauffman, Mathematics, Minimal Negation Operators, Painted Cacti, Paradox, Peirce, Process Thinking, Propositional Calculus, Spencer Brown, Systems, Time | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

“What we’ve got here is (a) failure to communicate” • 6

Posted on November 15, 2013 by Jon Awbrey

Excerpt from Warren S. McCulloch, “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?” (1960) Please remember that we are not now concerned with the physics and chemistry, the anatomy … Continue reading →

Posted in Abduction, Amphecks, Aristotle, Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Combinatorics, Deduction, Duns Scotus, Induction, Leibniz, Logic, Logic of Relatives, Mathematics, Neural Models, Ockham, Peirce, Propositional Logic, Psychons, Relation Theory, Sources, Triadic Relations, Warren S. McCulloch, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Lambda Point • 1

Posted on August 1, 2013 by Jon Awbrey

A note on the title.  From long ago discussions with Harvey Davis, one of my math professors at Michigan State.  I remember telling him of my interest in the place where algebra, geometry, and logic meet, and he quipped, “Ah … Continue reading →

Posted in Algebra, Amphecks, Boolean Algebra, C.S. Peirce, Cactus Graphs, Geometry, Graph Theory, Lambda Point, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Peirce, Propositional Calculus, Topology | Tagged , , , , , , , , , , , , , , | Leave a comment

How To Succeed In Proof Business Without Really Trying

Posted on July 15, 2013 by Jon Awbrey

Re: R.J. Lipton • Surely You Are Joking? Comment 1 Even at the mailroom entry point of propositional calculus, there is a qualitative difference between insight proofs and routine proofs.  Human beings can do either sort, as a rule, but … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Automatic Theorem Proving, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Graph Theory, Logic, Logical Graphs, Minimal Negation Operators, Model Theory, Peirce, Praeclarum Theorema, Proof Theory, Propositional Calculus, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 7 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