Tag Archives: Mathematics

Pragmatic Traction • 7

Posted on November 8, 2017 by Jon Awbrey

Re: Peirce List • John Sowa It’s good to remember that observation, perception itself, has an abductive character in Peirce’s analysis and induction for him is more a final testing than initial conception stage.  Yes, it’s wheels upon wheels but … Continue reading →

Posted in Abduction, Action, C.S. Peirce, Control, Cybernetics, Deduction, Definition, Determination, Fixation of Belief, Induction, Inference, Information, Inquiry, Inquiry Driven Systems, Learning, Learning Theory, Logic, Logic of Science, Mathematics, Metaphysics, Normative Science, Observation, Peirce, Peirce's Categories, Perception, Phenomenology, Philosophy, Pragmatic Maxim, Pragmatism, Recursion, Scientific Method, Semiotics, Volition | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s 1903 Lowell Lectures • Comment 1

Posted on November 6, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA A question arose concerning one of Peirce’s ways of explaining logical negation. Re: Peirce List Discussion • GF I commented as follows. One way of saying “not x” or “x is false” is … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , | Leave a comment

Peirce’s 1903 Lowell Lectures • Preliminaries

Posted on November 1, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA Re: Peirce List Discussion • GF In September the Peirce List began a reading of Peirce’s 1903 Lowell Lectures (“Some Topics of Logic Bearing on Questions Now Vexed”).  I’ve had opportunities for only … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , | Leave a comment

Ask Meno Questions • Discussion 4

Posted on October 19, 2017 by Jon Awbrey

Re: FB | Foundations of Mathematics • Oguzhan Kosar The questions raised under the heading of “Foundations of Mathematics” are generally considered to fall under the “Philosophy of Mathematics”, in particular, critical reflection on the possibility of mathematical knowledge and … Continue reading →

Posted in Anamnesis, Arete, C.S. Peirce, Descartes, Education, Epistemology, Eternal Return, Foundations of Mathematics, Infinity, Innate Idea, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Knowledge, Learning, Locke, Logic, Mathematics, Medium = Message, Meno, Peirce, Philosophy of Mathematics, Plato, Pragmata, Pragmatism, Pythagoras, Recollection, Semiotics, Sign Relations, Socrates, Tabula Rasa, Teaching, Triadic Relations, Turing Test, Virtue | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

¿Shifting Paradigms? • 6

Posted on October 17, 2017 by Jon Awbrey

Re: Peter Cameron • Infinity and Foundation C.S. Peirce is one who recognized the constitutional independence of mathematical inquiry, finding at its core a mode of operation tantamount to observation and more primitive than logic itself.  Here is one place … Continue reading →

Posted in Algorithms, Boole, C.S. Peirce, Combinatorics, Computation, Foundations of Mathematics, Inquiry, Laws of Form, Leibniz, Logic, Mathematics, Model Theory, Paradigms, Peirce, Proof Theory, Spencer Brown | Tagged , , , , , , , , , , , , , , , | Leave a comment

Pragmatic Traction • 6

Posted on October 15, 2017 by Jon Awbrey

Re: Peirce List Discussion • GF • JFS When it comes to the relative contributions of phenomenology and mathematics to logic, I always find myself returning to the picture I drew once before from Peirce’s Syllabus, on the relationship of phenomenology and … Continue reading →

Posted in C.S. Peirce, Control, Cybernetics, Definition, Determination, Fixation of Belief, Information, Inquiry, Inquiry Driven Systems, Logic, Logic of Science, Mathematics, Metaphysics, Normative Science, Peirce, Peirce's Categories, Phenomenology, Philosophy, Pragmatic Maxim, Pragmatism, Scientific Method, Semiotics, Volition | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Sign Relational Manifolds • Discussion 1

Posted on October 10, 2017 by Jon Awbrey

Semiotic Orbits, Manifolds, Arcs The arc of the semiotic universe is long but it bends towards universal harmony. Re: FB | Semiotics, Books, Links, News • What’s at the End of a Chain of Interpretants? Semiotic manifolds, like physical and … Continue reading →

Posted in C.S. Peirce, Cybernetics, Differential Geometry, Differential Logic, Geometry, Interoperability, Logic, Manifolds, Mathematics, Riemann, Semiotics, Sign Relational Manifolds, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , | Leave a comment

Minimal Negation Operators • 4

Posted on September 1, 2017 by Jon Awbrey

Note.  I’m including a more detailed definition of minimal negation operators in terms of conventional logical operations largely because readers of particular tastes have asked for it in the past.  But it can easily be skipped until one has a … 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 , , , , , , , , , , , , , , , , , , , | 10 Comments

Minimal Negation Operators • 3

Posted on August 30, 2017 by Jon Awbrey

It will take a few more rounds of stage-setting before we are able to entertain concrete examples of applications but the following may indicate the direction of generalization embodied in minimal negation operators. To begin, let’s observe two ways of … 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 , , , , , , , , , , , , , , , , , , , | 11 Comments

Minimal Negation Operators • 2

Posted on August 30, 2017 by Jon Awbrey

Re: Minimal Negation Operators • 1 The brief description of minimal negation operators given in the previous post is enough to convey the rule of their construction.  For future reference, a more formal definition is given below. Initial Definition The … 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 , , , , , , , , , , , , , , , , , , , | 11 Comments