Animated Logical Graphs • 17

To get a clearer view of the relation between primary arithmetic and primary algebra consider the following extremely simple algebraic expression:

Cactus Graph (a)

In this expression the variable name {}^{\backprime\backprime} a {}^{\prime\prime} appears as an operand name.  In functional terms, {}^{\backprime\backprime} a {}^{\prime\prime} is called an argument name, but it’s best to avoid the potentially confusing connotations of the word argument here, since it also refers in logical discussions to a more or less specific pattern of reasoning.

As we discussed, the algebraic variable name indicates the contemplated absence or presence of any arithmetic expression taking its place in the surrounding template, which expression is proxied well enough by its formal value, and of which values we know but two.  Thus, the given algebraic expression varies between these two choices:

Cactus Graph Set (),(())

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}?

That is the question I’ll take up next.

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 • 17

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

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