## Animated Logical Graphs • 72

Re: Richard J. LiptonThe Art Of Math
Re: Animated Logical Graphs • (30)(45)(57)(58)(59)(60)(61)(62)(63)(64)(65)(66)(69)(70)(71)

Turning again to our Table of Orbits let’s see what we can learn about the structure of the sign relational system in view.

We saw in Episode 62 that the transformation group $T = \{ 1, t \}$ partitions the set $X$ of 16 logical graphs and also the set $O$ of 16 boolean functions into 10 orbits:  4 orbits of size 1 each and 6 orbits of size 2 each.

Points in singleton orbits are called fixed points of the transformation group $T : X \to X$ since they are left unchanged, or changed into themselves, by all group actions.  Viewed in the frame of the sign relation $L \subseteq O \times X \times X,$ where the transformations in $T$ are literally translations in the linguistic sense, these $T$-invariant graphs have the same denotations in $O$ for both Existential Interpreters and Entitative Interpreters.

$\text{Peirce Duality as Sign Relation} \stackrel{_\bullet}{} \text{Orbit Order}$

### Resources

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: FB | Logical GraphsLaws of Form

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