Category Archives: Mathematics

Charles Sanders Peirce, George Spencer Brown, and Me

Posted on July 19, 2017 by Jon Awbrey

James Bowery left a comment on my blog and opened a thread in the Yahoo! group devoted to discussing the mathematics of George Spencer Brown’s Laws of Form.  I’ve been meaning to join that discussion as soon as I could work … Continue reading →

Posted in Abstraction, Amphecks, Analogy, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Differential Analytic Turing Automata, Differential Logic, Duality, Form, Graph Theory, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Sign Relations, Spencer Brown, Theorem Proving, Time, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

¿Shifting Paradigms? • 5

Posted on July 16, 2017 by Jon Awbrey

Re: Peter Cameron • Infinity and Foundation We always encounter a multitude of problems whenever we try to rationalize mathematics by reducing it to logic, where logic itself is reduced to a purely deductive style.  A number of thinkers have … 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 , , , , , , , , , , , , , , , | 4 Comments

The Difference That Makes A Difference That Peirce Makes • 17

Posted on June 26, 2017 by Jon Awbrey

Re: Peirce List • JA • GF • JFS • JLRC • JA • JFS • GF A rather amusing, if slightly ominous illustration of the point I am trying to make here has just popped up in the daily … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 16

Posted on June 25, 2017 by Jon Awbrey

Re: Peirce List • JA • JFS JFS: For those of us who are trying to convince modern students to study Peirce, we need to become bilingual.  We need to show how his terminology and notations map to and from … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 15

Posted on June 24, 2017 by Jon Awbrey

Re: Peirce List • JA • GF One could hardly dispute the importance of logical implication relations like   Their set-theoretic analogues are subset relations like which are almost the canonical way of expressing constraint, determination, information, and so on.  … Continue reading →

Posted in Animata, Automata, C.S. Peirce, Category Theory, Chomsky, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 14

Posted on June 24, 2017 by Jon Awbrey

Re: Peirce List • JA • JFS We find ourselves at the thresh‑old of yet another recurring discussion, this time concerning Peirce’s use of the adjectives formal and quasi‑necessary with normative connotations, all of which I think is clear from … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes • 13

Posted on June 22, 2017 by Jon Awbrey

I would like to return to a point where the paths of discussion began to diverge and then bifurcated so chaotically that I could not track them further, namely, here: Re: Peirce List • JA • GF • JA I … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 12

Posted on June 20, 2017 by Jon Awbrey

Re: Peirce List • Kirsti Määttänen I have a sense of what Peirce meant by the “Logic of Science” and what Dewey meant by calling Logic the “Theory of Inquiry”.  If that’s logic in the narrow sense and not Logic … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 11

Posted on June 17, 2017 by Jon Awbrey

Re: Peirce List • Kirsti Määttänen • Jon Awbrey • John Sowa The most important difference between linguistics and logic is that linguistics is descriptive while logic is normative. Yes, some grammarians try to treat grammar as prescriptive, but most … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 10

Posted on June 16, 2017 by Jon Awbrey

Re: Peirce List • Jon Alan Schmidt JA: As I am realizing more and more in recent years, analyzing and classifying signs as a substitute for analyzing and classifying objects is the first slip of a slide into nominalism, namely, … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment