Jon, List,
I think I like very much your Cactus Graphs. Meaning that i am in the process of understanding them, and finding it much better not to have to draw circles, but lines. Less easy for me is the differential calculus. Where is the consistency between (x,y,) and (x,y,z) ? (x,y) means, that x and y are not equal, and (x,y,z) means, that one of them is false. Unequality and truth/falsity for me are two concepts so different I cannot think them together or see a consistency between them. What about (w,x,y,z)? Can You give a grammar, like, what does a comma mean, what do brackets mean, what does writing letters following each other with an empty space but no comma mean, and so on? Same with Cactus-Graphs, though I think, they might be self-explaining for me--everything is self-explaining, depending on intellectual capacity, but mine is limited.
Edwina, the book You had recommended me (Harry J. Gensler "Introduction to Logic"), has eventually arrrived. It is very good! Thank you.
Best, Helmut
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
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] .
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
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
_ _ _ _ _ _ _ _ _ _
► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] .
► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
