Quick Tour of the Neighborhood

This much preparation allows us to take up the founding axioms or initial equations which determine the entire system of logical graphs.

Primary Arithmetic as Semiotic System

Though it may not seem too exciting, logically speaking, there are many reasons to make oneself at home with the system of forms represented indifferently, topologically speaking, by rooted trees, balanced strings of parentheses, and finite sets of non‑intersecting simple closed curves in the plane.

• For one thing it gives us a non‑trivial example of a sign domain on which to cut our semiotic teeth, non‑trivial in the sense that it contains a countable infinity of signs.
• In addition it allows us to study a simple form of computation recognizable as a species of semiosis or sign‑transforming process.

This space of forms, along with the pair of axioms which divide it into two formal equivalence classes, is what Spencer Brown called the primary arithmetic.

Resources

• Logical Graphs
• Survey of Animated Logical Graphs

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