Re: Differential Propositional Calculus


 

Cf: Differential Propositional Calculus • Discussion 3
https://inquiryintoinquiry.com/2021/03/15/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

Re: Laws of Form
https://groups.io/g/lawsofform/topic/differential_propositional/81172986
::: Lyle Anderson
(1) https://groups.io/g/lawsofform/message/162
(2) https://groups.io/g/lawsofform/message/163

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 B
to a superset equipped with logical imaginaries, operating on analogy
with the algebraic extension of the real line R to the complex plane 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 some where in that undergrowth the roads converge again …

Resources
=========

Differential Logic • Introduction
https://inquiryintoinquiry.com/2008/07/29/differential-logic/

Differential Propositional Calculus
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1
https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2

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