## Differential Propositional Calculus • Discussion 4

It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be.

HR:
1. I think I like very much your Cactus Graphs.  Meaning that I am in the process of understanding them, and finding it much better not to have to draw circles, but lines.
2. Less easy for me is the differential calculus.  Where is the consistency between $\texttt{(} x \texttt{,} y \texttt{)}$ and $\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}?$  $\texttt{(} x \texttt{,} y \texttt{)}$ means that $x$ and $y$ are not equal and $\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}$ means that one of them is false.  Unequality and truth/falsity for me are two concepts so different I cannot think them together or see a consistency between them.
3. What about $\texttt{(} w \texttt{,} x \texttt{,} y \texttt{,} z \texttt{)}?$
4. Can you give a grammar, like, what does a comma mean, what do brackets mean, what does writing letters following each other with an empty space but no comma mean, and so on?
5. Same with Cactus Graphs, though I think, they might be self-explaining for me — everything is self-explaining, depending on intellectual capacity, but mine is limited.

Dear Helmut,

Many thanks for your detailed comments and questions.  They help me see the places where more detailed explanation is needed.  I added numbers to your points above for ease of reference and possible future reference in case I can’t get to them all in one pass.

I’m glad you found the cactus graphs to your liking.  It was a critical transition for me when I passed from trees to cacti in my graphing and programming and it came about by recursively applying a trick of thought I learned from Peirce himself.  These days I call it a “Meta-Peircean Move” to apply one of Peirce’s heuristics of choice or standard operating procedures to the state of development resulting from previous applications.  All that makes for a longer story I made a start at telling in the following series of posts.

Well, the clock in the hall struck time for lunch some time ago, so I think I’ll heed its call and continue later …

Regards,

Jon

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