Animated Logical Graphs • 69

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

“I know what you mean but I say it another way” — it’s a thing I find myself saying often enough, if only under my breath, to rate an acronym for it ☞ IKWYMBISIAW ☜ and not too coincidentally it’s a rubric of relevance to many situations in semiotics where sundry manners of speaking and thinking converge, more or less, on the same patch of pragmata.

We encountered just such a situation in our exploration of the duality between entitative and existential interpretations of logical graphs.  The two interpretations afford distinct but equally adequate ways of reasoning about a shared objective domain.  To cut our teeth on a simple but substantial example of an object domain, we picked the space of boolean functions or propositional forms on two variables.  This brought us to the following Table, highlighting the sign relation L \subseteq O \times S \times I involved in switching between existential and entitative interpretations of logical graphs.

\text{Peirce Duality as Sign Relation}

Peirce Duality as Sign Relation

  • Column 1 shows the object domain O as the set of 16 boolean functions on 2 variables.
  • Column 2 shows the sign domain S as a representative set of logical graphs denoting the objects in O according to the existential interpretation.
  • Column 3 shows the interpretant domain I as the same set of logical graphs denoting the objects in O according to the entitative interpretation.

Resources

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

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Animated Logical Graphs • 69

  1. Pingback: Animated Logical Graphs • 70 | Inquiry Into Inquiry

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