Category Archives: Graph Theory

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

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

Peirce’s 1903 Lowell Lectures • Comment 4

Posted on November 12, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA A couple of comments in response to questions about the relationship between Spencer Brown’s Laws of Form and the broader scope of Peirce’s Logical Graphs. Re: Peirce List Discussion • HR George Spencer Brown … 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 , , , , , , , , , , , , | 1 Comment

Peirce’s 1903 Lowell Lectures • Comment 3

Posted on November 10, 2017 by Jon Awbrey

Cf: Laws Of Form Discussion • JA Peirce’s use of the “scroll” as a graphical syntax for implication continued to raise many questions at this point in the Peirce List reading.  I think a lot of what bothers people has … 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