Logical Graphs, Truth Tables, Venn Diagrams • 7

Posted on June 4, 2021 by Jon Awbrey

Re: Logical Graphs, Truth Tables, Venn Diagrams • 6
Re: Amphecks

On the subject of Peirce’s ampheck operators, see the earlier discussion of their duality under entitative and existential interpretations.

The ampheck operators are dual with respect to entitative and existential interpretations:

  • f_{1} = f_{0001} = \text{both not} : \mathbb{B} \times \mathbb{B} \to \mathbb{B}
  • f_{7} = f_{0111} = \text{not both} : \mathbb{B} \times \mathbb{B} \to \mathbb{B}

Under the existential interpretation:

  • f_{1} = f_{0001} = \text{both not} = \texttt{(} x \texttt{)(} y \texttt{)}
  • f_{7} = f_{0111} = \text{not both} = \texttt{(} xy \texttt{)}

Under the entitative interpretation:

  • f_{1} = f_{0001} = \text{both not} = \texttt{(} xy \texttt{)}
  • f_{7} = f_{0111} = \text{not both} = \texttt{(} x \texttt{)(} y \texttt{)}

cc: Cybernetics • Ontolog • Peirce List (1) (2) (3) • Structural Modeling • Systems Science
cc: FB | Logical Graphs • Laws of Form

This entry was posted in Amphecks, Boolean Algebra, Boolean Functions, C.S. Peirce, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Propositional Calculus, Spencer Brown, Truth Tables, Venn Diagrams, Visualization and tagged , , , , , , , , , , , , , , . Bookmark the permalink.

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