## Differential Propositional Calculus • Discussion 3

That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea.  But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can.  Here the story is traced from the beginning.

G. Spencer Brown • Laws of Form

Dear Lyle,

Charles S. Peirce, with his x-ray vision, revealed for the first time in graphic detail the mathematical forms structuring our logical organon.  Spencer Brown broadened that perspective in two directions, tracing more clearly than Peirce’s bare foreshadowings the infrastructure of primary arithmetic and hypothesizing the existence of imaginary logical values in a larger algebraic superstructure.

Spencer Brown explored the algebraic extension of the boolean domain $\mathbb{B}$ to a superset equipped with logical imaginaries, operating on analogy with the algebraic extension of the real line $\mathbb{R}$ to the complex plane $\mathbb{C}.$  Seeing as how complex variables are frequently used to model time domains in physics and engineering, that will continue to be a likely and natural direction of exploration.

My own work, however, led me in a different direction.  There are many different ways of fruitfully extending a given domain.  Aside from the above class of algebraic extensions there is a class of differential extensions and when that proverbial road diverged I took the differential one.

Who knows? maybe on through that undergrowth the roads converge again …

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