Differential Propositional Calculus • Discussion 1

The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time.

W. Ross Ashby • An Introduction to Cybernetics

Re: Cybernetics CommunicationsKlaus Krippendorff

KK:
To me, differences are the result of drawing distinctions.  They don’t exist unless you actively draw them.  So, the act of drawing distinctions is more fundamental than the differences thereby created.

I often return to that line from Ashby.  This time I thought it made an apt segue from the scene of propositional calculus, where universes of discourse are ruled by collections of distinctive features, to the differential extension of propositional calculus, which enables us to describe trajectories within and transformations between our logical universes.

So I agree with Klaus Krippendorff about “which came first”, the distinctions drawn or the states distinguished in space or time.  The primitive character of distinctions is especially salient in this setting since our formalism for propositional calculus is built on the forms of distinction pioneered by C.S. Peirce and augmented by George Spencer Brown.

Resources

cc: CyberneticsOntolog • Peirce List (1) (2)Structural ModelingSystems Science

This entry was posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

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