## Animated Logical Graphs • 18

Last time we contemplated 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. 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 arithmetic constant ${}^{\backprime\backprime} \texttt{(} ~ \texttt{)} {}^{\prime\prime}$ in the place 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 ${}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime}?$

Evidently, 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 expression ${}^{\backprime\backprime} a {}^{\prime\prime}$ and the algebraic expression ${}^{\backprime\backprime} \texttt{(} a \texttt{)} {}^{\prime\prime},$ somewhat as pictured below. But how shall we signify such variations in a coherent calculus?

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

### 8 Responses to Animated Logical Graphs • 18

This site uses Akismet to reduce spam. Learn how your comment data is processed.