Animated Logical Graphs • 50

Posted on December 5, 2020 by Jon Awbrey

Re: Richard J. Lipton • The Art Of Math
Re: Animated Logical Graphs • (30) (45) (46) (47) (48) (49)

In the last of our six ways of looking at the Peirce duality between entitative and existential interpretations, we consider the previous Table of Logical Graphs and Venn Diagrams sorted in Orbit Order.

Logical Graphs • Entitative and Existential Venn Diagrams • Orbit Order
\text{Logical Graph} \text{Entitative Interpretation} \text{Existential Interpretation}
Cactus Stem
 		 f₁₅(x,y) f₀(x,y)
\texttt{(} ~ \texttt{)}
 		 \text{true}
f_{15}		 \text{false}
f_{0}
Cactus (x)(y)
 		 f₇(x,y) f₁(x,y)
\texttt{(} x \texttt{)(} y \texttt{)}
 		 \lnot x \lor \lnot y
f_{7}		 \lnot x \land \lnot y
f_{1}
Cactus (x)y
 		 f₁₁(x,y) f₂(x,y)
\texttt{(} x \texttt{)} y
 		 x \Rightarrow y
f_{11}		 x \nLeftarrow y
f_{2}
Cactus x(y)
 		 f₁₃(x,y) f₄(x,y)
x \texttt{(} y \texttt{)}
 		 x \Leftarrow y
f_{13}		 x \nRightarrow y
f_{4}
Cactus xy
 		 f₁₄(x,y) f₈(x,y)
x y
 		 x \lor y
f_{14}		 x \land y
f_{8}
Cactus (x)
 		 f₃(x,y) f₃(x,y)
\texttt{(} x \texttt{)}
 		 \lnot x
f_{3}		 \lnot x
f_{3}
Cactus x
 		 f₁₂(x,y) f₁₂(x,y)
x
 		 x
f_{12}		 x
f_{12}
Cactus (x,y)
 		 f₉(x,y) f₆(x,y)
\texttt{(} x \texttt{,} y \texttt{)}
 		 x = y
f_{9}		 x \ne y
f_{6}
Cactus ((x,y))
 		 f₆(x,y) f₉(x,y)
\texttt{((} x \texttt{,} y \texttt{))}
 		 x \ne y
f_{6}		 x = y
f_{9}
Cactus (y)
 		 f₅(x,y) f₅(x,y)
\texttt{(} y \texttt{)}
 		 \lnot y
f_{5}		 \lnot y
f_{5}
Cactus y
 		 f₁₀(x,y) f₁₀(x,y)
y
 		 y
f_{10}		 y
f_{10}
Cactus (xy)
 		 f₁(x,y) f₇(x,y)
\texttt{(} x y \texttt{)}
 		 \lnot (x \lor y)
f_{1}		 \lnot (x \land y)
f_{7}
Cactus (x(y))
 		 f₂(x,y) f₁₁(x,y)
\texttt{(} x \texttt{(} y \texttt{))}
 		 x \nLeftarrow y
f_{2}		 x \Rightarrow y
f_{11}
Cactus ((x)y)
 		 f₄(x,y) f₁₃(x,y)
\texttt{((} x \texttt{)} y \texttt{)}
 		 x \nRightarrow y
f_{4}		 x \Leftarrow y
f_{13}
Cactus ((x)(y))
 		 f₈(x,y) f₁₄(x,y)
\texttt{((} x \texttt{)(} y \texttt{))}
 		 x \land y
f_{8}		 x \lor y
f_{14}
Cactus Root
 		 f₀(x,y) f₁₅(x,y)
 
 		 \text{false}
f_{0}		 \text{true}
f_{15}

Resources

cc: Cybernetics Communications (1) (2) • FB | Logical Graphs • Ontolog Forum (1) (2)
cc: Peirce (1) (2) (3) (4) (5) (6) (7) (8) (9) • Structural Modeling (1) (2) • Systems (1) (2)

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