Tag Archives: Proof Theory

¿Shifting Paradigms? • 6

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

Charles Sanders Peirce, George Spencer Brown, and Me • 10

Re: Laws Of Form Discussion With any formal system it is easy to spend a long time roughing out primitives and reviewing first principles before getting on to practical applications, and logical graphs are no different in that respect.  But … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 9

Re: Laws Of Form Discussion • Boundary Logic • RS A wider field of investigation opens up at this point, having to do with the diversity of interactions among the languages we use, and systems of signs in general, to … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 8

Re: Laws Of Form Discussion • Boundary Logic • JW For me, the heart of the matter is what is the purpose of logic and what is the purpose of math and what is their relationship? There are semiotic situations … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Charles Sanders Peirce, George Spencer Brown, and Me • 7

Re: Laws Of Form Discussion • Boundary Logic • CB A statement that implies both and is called a false statement, and anyone can prove anything at all from a false statement, as we all too frequently observe on the … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 6

Re: Laws Of Form Discussion • Peirce’s Law • AM • AM The formal system of logical graphs is defined by a foursome of formal equations, called initials when regarded purely formally, in abstraction from potential interpretations, called axioms when … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Charles Sanders Peirce, George Spencer Brown, and Me • 5

Re: Laws Of Form Discussion • Peirce’s Law Here are blog and wiki versions of an article I wrote on Peirce’s Law, an axiom or theorem (depending on your choice of logical basis) that distinguishes classical from intuitionistic propositional calculus.  … Continue reading

Posted in Abstraction, Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Deduction, Diagrammatic Reasoning, Differential Logic, Duality, Form, Graph Theory, Iconicity, Information Theory, Inquiry, Laws of Form, Logic, Logical Graphs, Mathematics, Model Theory, Painted Cacti, Peirce, Peirce's Law, Pragmatic Maxim, Proof Theory, Propositional Calculus, Semiotics, Sign Relational Manifolds, Spencer Brown, Symbolism, Systems Theory, Theorem Proving, Topology, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment