Differential Logic • Discussion 9

Re: Laws of FormLyle Anderson

All I am asking is what is your definition of \mathrm{d}p in relation to p‌.  So far I have \mathrm{d}p is what one has to do to get from p to \texttt{(} p \texttt{)} or from \texttt{(} p \texttt{)} to p‌.  Is that all there is to it?  If that is the case, then what you are really dealing with is some flavor of Lattice Theory.

Dear Lyle,

Standing back for a moment to take in the Big Picture, what we’re doing here is taking all the things we would normally do in a “calculus of many variables” setting with spaces like:

\begin{matrix}  \mathbb{R}, &   \mathbb{R}^{j}, &   \mathbb{R}^{j} \to \mathbb{R}, &   \mathbb{R}^{j} \to \mathbb{R}^{k}, &   \ldots \end{matrix}

and functoring that whole business over to \mathbb{B}, in other words, cranking the analogies as far as we can push them to spaces like:

\begin{matrix}  \mathbb{B}, &   \mathbb{B}^{j}, &   \mathbb{B}^{j} \to \mathbb{B}, &   \mathbb{B}^{j} \to \mathbb{B}^{k}, &   \ldots \end{matrix}

A few analogies are bound to break in transit through the Real-Bool barrier, once familiar constructions morph into new-fangled configurations, and other distinctions collapse or “condense” as Spencer Brown called it.  Still enough structure gets preserved overall to reckon the result a kindred subject.

To be continued …

cc: Category TheoryCyberneticsOntologStructural ModelingSystems Science
cc: FB | Differential LogicLaws of Form

This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Equational Inference, Frankl Conjecture, Functional Logic, Gradient Descent, Graph Theory, Hologrammautomaton, Indicator Functions, Inquiry Driven Systems, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Surveys, Time, Topology, Visualization, Zeroth Order Logic and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

4 Responses to Differential Logic • Discussion 9

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