Animated Logical Graphs • 18

We had been contemplating the penultimately simple algebraic expression {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime} as a name for a set of arithmetic expressions, namely, \texttt{(} a \texttt{)} = \{ \,\texttt{()}\, , \,\texttt{(())}\, \}, taking the equality sign in the appropriate sense.

Cactus Graph Equation (a) = {(),(())}

Then we asked the corresponding question about the operator {}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime}.  The above selection of arithmetic expressions is what it means to contemplate the absence or presence of the operand {}^{\backprime\backprime} a {}^{\prime\prime} in the algebraic expression {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime}.  But what would it mean to contemplate the absence or presence of the operator {}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime} in the algebraic expression {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime}?

Clearly, a variation between the absence and the presence of the operator {}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime} in the algebraic expression {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime} refers to a variation between the algebraic expressions {}^{\backprime\backprime} a {}^{\prime\prime} and {}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime}, respectively, somewhat as pictured below:

Cactus Graph Equation ¿a? = {a,(a)}

But how shall we signify such variations in a coherent calculus?

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

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 • 18

  1. Pingback: Survey of Animated Logical Graphs • 2 | Inquiry Into Inquiry

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