Genus, Species, Pie Charts, Radio Buttons • Discussion 3

Re: Genus, Species, Pie Charts, Radio Buttons • 1
Re: Laws of FormWilliam Bricken

Last time I alluded to the general problem of relating a variety of formal languages to a shared domain of formal objects, taking six notations for the boolean functions on two variables as a simple but critical illustration of the larger task.  This time we’ll take up a subtler example of cross-calculus communication, where the same syntactic forms bear different logical interpretations.

In each of the Tables below —

  • Column 1 shows a conventional name f_{i} and a venn diagram for each of the sixteen boolean functions on two variables.
  • Column 2 shows the logical graph canonically representing the boolean function in Column 1 under the entitative interpretation.  This is the interpretation C.S. Peirce used in his earlier work on entitative graphs and the one Spencer Brown used in his book Laws of Form.
  • Column 3 shows the logical graph canonically representing the boolean function in Column 1 under the existential interpretation.  This is the interpretation C.S. Peirce used in his later work on existential graphs.

\text{Boolean Functions and Logical Graphs on Two Variables} \stackrel{_\bullet}{} \text{Index Order}

Boolean Functions and Logical Graphs on Two Variables

\text{Boolean Functions and Logical Graphs on Two Variables} \stackrel{_\bullet}{} \text{Orbit Order}

Boolean Functions and Logical Graphs on Two Variables

Resources

  • Logical Graphs, Iconicity, Interpretation • (1)(2)
  • Minimal Negation Operators • (1)(2)(3)(4)

cc: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Minimal Negation OperatorsLaws of Form • Peirce List (1) (2) (3)

This entry was 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 and tagged , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Genus, Species, Pie Charts, Radio Buttons • Discussion 3

  1. Pingback: Survey of Animated Logical Graphs • 4 | Inquiry Into Inquiry

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