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

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.

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

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

### Resources

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

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