Category Archives: Logic

Differential Logic • Comment 3

Posted on December 30, 2017 by Jon Awbrey

In my previous comment on boundaries in object universes and venn diagrams, and always when I’m being careful about their mathematical senses, the definitions of “topology” and “boundary” I have in mind can be found in any standard textbook.  Here are … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Diagrammatic Reasoning, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Differential Logic • Comment 2

Posted on December 28, 2017 by Jon Awbrey

As always, we have to distinguish between the diagram itself, the representation or sign inscribed in some medium, and the formal object it represents under a given interpretation. A venn diagram is an iconic sign we use to represent a … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Diagrammatic Reasoning, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Differential Logic • Comment 1

Posted on December 21, 2017 by Jon Awbrey

Re: Gil Kalai • Pivotal Variables Just a tangential association with respect to logical influence and pivotability.  I have been exploring questions related to pivotal variables (“Differences that Make a Difference” or “Difference In ⟹ Difference Out”) via logical analogues … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Logic, Logical Graphs, Logical Influence, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pivotal Variables, Propositional Calculus, Propositional Equation Reasoning Systems, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Peirce’s 1903 Lowell Lectures • Comment 10

Posted on December 16, 2017 by Jon Awbrey

Re: Peirce List Discussion • John Sowa JFS: In the Lowell Lectures [1903] Peirce defined the Sheet of Assertion as the representation of a universe that was constructed during a discourse between Graphist and Grapheus. But that is just one … 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 • Comment 9

Posted on November 28, 2017 by Jon Awbrey

Re: Peirce List • John Sowa JFS: In 1911, Peirce clarified [the] issues by using two distinct terms:  ‘the universe’ and ‘a sheet of paper’.  The sheet is no longer identified with the universe, and there is no reason why one couldn’t or … 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 • Comment 8

Posted on November 26, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA Re: Laws Of Form Discussion • JB Re: Peirce List Discussion • JA Many aspects of Peirce’s alpha graphs can be clarified by seeing how they relate to the corresponding Venn diagrams. In … 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 • Comment 7

Posted on November 25, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA Re: Peirce List Discussion • JA I’ll go ahead and copy out the first part of the article on Logical Implication, as I find I am still pleased with all I was able … 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 • Comment 6

Posted on November 24, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA Continuing discussion of the conditional form, as expressed in Peirce’s logical graphs under the existential interpretation, incited me to cite one of my own essays on the subject. Re: Peirce List Discussions • … 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

The Difference That Makes A Difference That Peirce Makes • 19

Posted on November 18, 2017 by Jon Awbrey

Re: Peirce List • John Sowa Peirce uses the word “formal” in a sense that gives it normative force.  It is this sense in which he defines logic as formal semiotic. But taking “formal” in a normative sense weighs against John … Continue reading →

Posted in C.S. Peirce, Descriptive Science, Fixation of Belief, Formal Systems, Information, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Normative Science, Pragmatic Maxim, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , | 1 Comment

Peirce’s 1903 Lowell Lectures • Comment 5

Posted on November 16, 2017 by Jon Awbrey

The World of Ā Cf: Laws Of Form Discussion • JA The relationship between classical and non-classical logic is a topic that comes up from time to time in these discussions.  Inquiry into it tends to take a different tack … 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