Re: Genus, Species, Pie Charts, Radio Buttons • 1
Re: Laws of Form • William 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 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.

Resources

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

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Minimal Negation Operators • Laws of Form • Peirce List (1) (2) (3)