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Sep 11, 2019, 2:36:15 PM9/11/19

to SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications

Cf: Differential Logic and Dynamic Systems : Overview

At: https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-%e2%80%a2-overview/

In modeling intelligent systems, whether we are trying to understand

a natural system or engineer an artificial system, there has long been

a tension or trade-off between dynamic paradigms and symbolic paradigms.

Dynamic models take their cue from physics, using quantitative measures

and differential equations to model the evolution of a system's state

through time. Symbolic models use logical methods to describe systems

and their agents in qualitative terms, deriving logical consequences of

a system's description or an agent's state of information. Logic-based

systems have tended to be static in character, largely because we have

lacked a proper logical analogue of differential calculus. The line of

work laid out in this series of posts is intended to address that lack.

Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1

Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2

Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3

Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4

Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appendices

References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References

Doc History : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Document_History

Note: This is work I carried out under the auspices of a Systems Engineering program

at Oakland University. I will spend the next few weeks revising the text, redrawing

the graphics, and reformatting the LaTeX, as the ravages of time and the innovations

of MediaWiki developers oblivious to the civilities of upward compatibility have not

been kind. Meanwhile, I'll also experiment with serializing the content to my blog.

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

At: https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-%e2%80%a2-overview/

In modeling intelligent systems, whether we are trying to understand

a natural system or engineer an artificial system, there has long been

a tension or trade-off between dynamic paradigms and symbolic paradigms.

Dynamic models take their cue from physics, using quantitative measures

and differential equations to model the evolution of a system's state

through time. Symbolic models use logical methods to describe systems

and their agents in qualitative terms, deriving logical consequences of

a system's description or an agent's state of information. Logic-based

systems have tended to be static in character, largely because we have

lacked a proper logical analogue of differential calculus. The line of

work laid out in this series of posts is intended to address that lack.

Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1

Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2

Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3

Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4

Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appendices

References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References

Doc History : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Document_History

Note: This is work I carried out under the auspices of a Systems Engineering program

at Oakland University. I will spend the next few weeks revising the text, redrawing

the graphics, and reformatting the LaTeX, as the ravages of time and the innovations

of MediaWiki developers oblivious to the civilities of upward compatibility have not

been kind. Meanwhile, I'll also experiment with serializing the content to my blog.

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

isw: http://intersci.ss.uci.edu/wiki/index.php/JLA

facebook page: https://www.facebook.com/JonnyCache

May 18, 2021, 11:45:25 AM5/18/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 1

http://inquiryintoinquiry.com/2021/05/18/differential-logic-and-dynamic-systems-discussion-1/

❝It is understandable that an engineer should be completely

absorbed in his speciality, instead of pouring himself out

into the freedom and vastness of the world of thought, even

though his machines are being sent off to the ends of the

earth; for he no more needs to be capable of applying to

his own personal soul what is daring and new in the soul of

his subject than a machine is in fact capable of applying

to itself the differential calculus on which it is based.

The same thing cannot, however, be said about mathematics;

for here we have the new method of thought, pure intellect,

the very well-spring of the times, the fons et origo of an

unfathomable transformation.❞

❧ Robert Musil • The Man Without Qualities

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#Transformations_of_Discourse

Re: Michael Harris • Does Mathematics “Progress”?

https://mathematicswithoutapologies.wordpress.com/2021/05/05/does-mathematics-progress/

All,

Just off-hand, by way of getting grounded and oriented,

there are a few questions I'd have to ask first.

• Is mathematics a science, or a form of scientific inquiry?

• If so, what is the place of mathematics within the sciences?

• Does science progress?

•• (I mean progress in the sense of progress toward a goal,

not necessarily progressive jazz or progressions in music

generally.)

• If so, what is the goal of science?

• If science has a goal, does mathematics serve it?

• If so, how?

By “science” or “scientific inquiry” I meant to focus on species

of goal-directed activity with the specific goal of “knowledge”

and to ask whether mathematical arts and crafts and rites fall

within that ballpark. We come back to the antic Socratic question

of whether we put another quarter in the machine for the sake of

an external gain or simply to continue the play for its own sake.

<QUOTE MH:>

In this post I was less concerned with philosophy than with philology —

which, by the way, is another example of a term that was once seen as

hopelessly antiquated and musty but that has been revived recently.

But when you introduce “knowledge” you have to grapple with “truth” and

“objective reality”. Philosophy has been so unsuccessful at pinning those

down that some would prefer to give up on them altogether. We can choose

to call what mathematics generates “knowledge” but that just leads to the

(philological) question of what this has to do with what other practices

call “knowledge”.

</QUOTE>

Not that I don't love wisdom and words, however often their stars may cross,

but I invoked Musil rather for the way he syzygied the way of the engineer,

the way of the mathematician, and the recursive point where their ways diverge.

It's in this frame I think of the word “entelechy”, which I got from readings

in Aristotle, Goethe, and Peirce and promptly gave a personal gloss as “end

in itself”, partly on the influence of Conway's game theory.

And that's where I remember all those two-bit pieces I gave up to pinball

machines in the early 70s and the critical point in my own trajectory when

I realized I would never beat those machines, not that way, not ever, and

I turned to the more collaboratory ends of teaching machines how to learn

and reason.

♩ On A Related Note ♪ The Music Of The Primes ♫

( https://oeis.org/wiki/Riffs_and_Rotes )

Now there's a progression of progressions I could enjoy, musically speaking,

ad infinitum, and yet this pilgrim would consider it progress, mathematically

speaking, if he could understand why the sequentiae should be sequenced as

they are. Would that understanding add to my enjoyment? On jugera …

Resources

=========

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

Regards,

Jon

http://inquiryintoinquiry.com/2021/05/18/differential-logic-and-dynamic-systems-discussion-1/

❝It is understandable that an engineer should be completely

absorbed in his speciality, instead of pouring himself out

into the freedom and vastness of the world of thought, even

though his machines are being sent off to the ends of the

earth; for he no more needs to be capable of applying to

his own personal soul what is daring and new in the soul of

his subject than a machine is in fact capable of applying

to itself the differential calculus on which it is based.

The same thing cannot, however, be said about mathematics;

for here we have the new method of thought, pure intellect,

the very well-spring of the times, the fons et origo of an

unfathomable transformation.❞

❧ Robert Musil • The Man Without Qualities

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3#Transformations_of_Discourse

Re: Michael Harris • Does Mathematics “Progress”?

https://mathematicswithoutapologies.wordpress.com/2021/05/05/does-mathematics-progress/

All,

Just off-hand, by way of getting grounded and oriented,

there are a few questions I'd have to ask first.

• Is mathematics a science, or a form of scientific inquiry?

• If so, what is the place of mathematics within the sciences?

• Does science progress?

•• (I mean progress in the sense of progress toward a goal,

not necessarily progressive jazz or progressions in music

generally.)

• If so, what is the goal of science?

• If science has a goal, does mathematics serve it?

• If so, how?

By “science” or “scientific inquiry” I meant to focus on species

of goal-directed activity with the specific goal of “knowledge”

and to ask whether mathematical arts and crafts and rites fall

within that ballpark. We come back to the antic Socratic question

of whether we put another quarter in the machine for the sake of

an external gain or simply to continue the play for its own sake.

<QUOTE MH:>

In this post I was less concerned with philosophy than with philology —

which, by the way, is another example of a term that was once seen as

hopelessly antiquated and musty but that has been revived recently.

But when you introduce “knowledge” you have to grapple with “truth” and

“objective reality”. Philosophy has been so unsuccessful at pinning those

down that some would prefer to give up on them altogether. We can choose

to call what mathematics generates “knowledge” but that just leads to the

(philological) question of what this has to do with what other practices

call “knowledge”.

</QUOTE>

Not that I don't love wisdom and words, however often their stars may cross,

but I invoked Musil rather for the way he syzygied the way of the engineer,

the way of the mathematician, and the recursive point where their ways diverge.

It's in this frame I think of the word “entelechy”, which I got from readings

in Aristotle, Goethe, and Peirce and promptly gave a personal gloss as “end

in itself”, partly on the influence of Conway's game theory.

And that's where I remember all those two-bit pieces I gave up to pinball

machines in the early 70s and the critical point in my own trajectory when

I realized I would never beat those machines, not that way, not ever, and

I turned to the more collaboratory ends of teaching machines how to learn

and reason.

♩ On A Related Note ♪ The Music Of The Primes ♫

( https://oeis.org/wiki/Riffs_and_Rotes )

Now there's a progression of progressions I could enjoy, musically speaking,

ad infinitum, and yet this pilgrim would consider it progress, mathematically

speaking, if he could understand why the sequentiae should be sequenced as

they are. Would that understanding add to my enjoyment? On jugera …

Resources

=========

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

Regards,

Jon

May 19, 2021, 9:48:22 AM5/19/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

All,

Here's an update of the anchor post on this subject.

In modeling intelligent systems, whether we are trying to understand

a natural system or engineer an artificial system, there has long been

a tension or trade-off between dynamic paradigms and symbolic paradigms.

Dynamic models take their cue from physics, using quantitative measures

and differential equations to model the evolution of a system's state

through time. Symbolic models use logical methods to describe systems

and their agents in qualitative terms, deriving logical consequences of

a system's description or an agent's state of information. Logic-based

systems have tended to be static in character, largely because we have

lacked a proper logical analogue of differential calculus. The work

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

All,

Here's an update of the anchor post on this subject.

In modeling intelligent systems, whether we are trying to understand

a natural system or engineer an artificial system, there has long been

a tension or trade-off between dynamic paradigms and symbolic paradigms.

Dynamic models take their cue from physics, using quantitative measures

and differential equations to model the evolution of a system's state

through time. Symbolic models use logical methods to describe systems

and their agents in qualitative terms, deriving logical consequences of

a system's description or an agent's state of information. Logic-based

systems have tended to be static in character, largely because we have

laid out in this series of posts is intended to address that lack.

Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1

Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2

Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3

Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4

Part 5 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5
Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1

Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2

Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3

Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4

Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appendices

References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References

References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_References

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

facebook page: https://www.facebook.com/JonnyCache
Jon

inquiry into inquiry: https://inquiryintoinquiry.com/

academia: https://independent.academia.edu/JonAwbrey

oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey

May 20, 2021, 10:45:12 AM5/20/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 2

http://inquiryintoinquiry.com/2021/05/20/differential-logic-and-dynamic-systems-discussion-2/

Re: Michael Harris • Does Mathematics “Progress”? • Comment

https://mathematicswithoutapologies.wordpress.com/2021/05/05/does-mathematics-progress/#comment-21380

All,

In several places I can't find right now I described formalization as an arrow. A related idea occurs in a paper by

Susan Awbrey and myself where we discussed “a dimension of increasing formalization in our mental models of the world”

as an obstacle to integrating knowledge across various styles of inquiry. An excerpt follows.

<QUOTE>

Conceptual Barriers to Creating Integrative Universities

========================================================

https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

The Trivializing of Integration

===============================

From reviewing its philosophical sources, we can see that the trivialization of integration hypothesis presents

barriers to creating an integrated learning environment. Below we focus on three closely interrelated problematics and

the bearing that the triviality of integration hypothesis has on them.

Problematic 1 is the tension that arises along a dimension of increasing formalization in our mental models of the

world, between what we may call the ‘informal context’ of real-world practice and the ‘formal context’ of specialized study.

Problematic 2 is the difficulty in communication that is created by differing mental models of the world, in other

words, by the tendency among groups of specialists to form internally coherent but externally disparate systems of

mental images.

Problematic 3 is a special type of communication difficulty that commonly arises between the ‘Two Cultures’ of the

scientific and the humanistic disciplines. A significant part of the problem derives from the differential emphasis

that each group places on its use of symbolic and conceptual systems, limiting itself to either the denotative or the

connotative planes of variation, but seldom integrating the two.

</QUOTE>

References

==========

• Awbrey, S.M., and Awbrey, J.L. (May 2001), “Conceptual Barriers to Creating Integrative Universities”, Organization :

The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.

Abstract ( https://org.sagepub.com/cgi/content/abstract/8/2/269 ) . Online (

https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities ) .

• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge

of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal

‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st

Century, University of Massachusetts, Amherst, MA. Online (

https://arisbe.sitehost.iu.edu//menu/library/aboutcsp/awbrey/integrat.htm ) .

Resources

=========

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

http://inquiryintoinquiry.com/2021/05/20/differential-logic-and-dynamic-systems-discussion-2/

Re: Michael Harris • Does Mathematics “Progress”? • Comment

https://mathematicswithoutapologies.wordpress.com/2021/05/05/does-mathematics-progress/#comment-21380

All,

In several places I can't find right now I described formalization as an arrow. A related idea occurs in a paper by

Susan Awbrey and myself where we discussed “a dimension of increasing formalization in our mental models of the world”

as an obstacle to integrating knowledge across various styles of inquiry. An excerpt follows.

<QUOTE>

Conceptual Barriers to Creating Integrative Universities

========================================================

https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

The Trivializing of Integration

===============================

From reviewing its philosophical sources, we can see that the trivialization of integration hypothesis presents

barriers to creating an integrated learning environment. Below we focus on three closely interrelated problematics and

the bearing that the triviality of integration hypothesis has on them.

Problematic 1 is the tension that arises along a dimension of increasing formalization in our mental models of the

world, between what we may call the ‘informal context’ of real-world practice and the ‘formal context’ of specialized study.

Problematic 2 is the difficulty in communication that is created by differing mental models of the world, in other

words, by the tendency among groups of specialists to form internally coherent but externally disparate systems of

mental images.

Problematic 3 is a special type of communication difficulty that commonly arises between the ‘Two Cultures’ of the

scientific and the humanistic disciplines. A significant part of the problem derives from the differential emphasis

that each group places on its use of symbolic and conceptual systems, limiting itself to either the denotative or the

connotative planes of variation, but seldom integrating the two.

</QUOTE>

References

==========

• Awbrey, S.M., and Awbrey, J.L. (May 2001), “Conceptual Barriers to Creating Integrative Universities”, Organization :

The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.

Abstract ( https://org.sagepub.com/cgi/content/abstract/8/2/269 ) . Online (

https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities ) .

• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge

of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal

‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st

Century, University of Massachusetts, Amherst, MA. Online (

https://arisbe.sitehost.iu.edu//menu/library/aboutcsp/awbrey/integrat.htm ) .

Resources

=========

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

May 21, 2021, 9:00:10 AM5/21/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 3

https://inquiryintoinquiry.com/2021/05/21/differential-logic-and-dynamic-systems-discussion-3/

Re: FB | Differential Logic

https://www.facebook.com/DifferentialLogic/

::: Rajib Hossain Pavel

https://www.facebook.com/JonnyCache/posts/10223983051737669?comment_id=10223983444667492

<QUOTE RHP:>

How can Differential Logic find Optimal Condition in a Game setting for an

Individual Player (Individual Choice) and Overall System (Social Welfare)?

</QUOTE>

Dear Rajib,

Differential logic is a general framework for analyzing aspects of change

and difference in systems amenable to qualitative description, for example,

processes taking place in a universe of discourse or transformations mapping

a source universe to a target universe. To apply its concepts and methods to

a concrete case one has to define the state space and the objective function

one desires to optimize. This may indeed be the hardest part of the problem.

It helps to break ground if one can think up a simple example from the class

of systems one has in mind.

Resources

=========

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Regards,

Jon

https://inquiryintoinquiry.com/2021/05/21/differential-logic-and-dynamic-systems-discussion-3/

Re: FB | Differential Logic

https://www.facebook.com/DifferentialLogic/

::: Rajib Hossain Pavel

https://www.facebook.com/JonnyCache/posts/10223983051737669?comment_id=10223983444667492

<QUOTE RHP:>

How can Differential Logic find Optimal Condition in a Game setting for an

Individual Player (Individual Choice) and Overall System (Social Welfare)?

</QUOTE>

Dear Rajib,

Differential logic is a general framework for analyzing aspects of change

and difference in systems amenable to qualitative description, for example,

processes taking place in a universe of discourse or transformations mapping

a source universe to a target universe. To apply its concepts and methods to

a concrete case one has to define the state space and the objective function

one desires to optimize. This may indeed be the hardest part of the problem.

It helps to break ground if one can think up a simple example from the class

of systems one has in mind.

Resources

=========

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

• Differential Logic and Dynamic Systems • Overview

https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-systems-overview/

Jon

May 26, 2021, 1:15:45 PM5/26/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 4

https://inquiryintoinquiry.com/2021/05/26/differential-logic-and-dynamic-systems-discussion-4/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_propositional/81172986

::: Lyle Anderson

https://groups.io/g/lawsofform/message/162

https://groups.io/g/lawsofform/message/163

Dear Lyle,

I've been meaning to get back to your comments linked above — the connections you observed to finite difference

calculus, ordinary and partial differential equations, and differential geometry are very apt — but preparing the ground

for a smooth transition to differential logic takes time, plus I needed to deal with the details of the En ↔ Ex logical

graph duality I've been wanting to give their due for decades.

The flat out fastest key to the highway of differential logic is still the “Casual Introduction” I wrote for

“Differential Propositional Calculus”. It affords direct access to the basic intuitions and motivations of the

subject but stops short of the syntactic mechanics needed to really take off.

The jump from this point to the more aggressive approaches of “Differential Logic” and “Differential Logic and Dynamic

Systems” has long been a challenge. I went looking for materials to bridge the gap and was pleased to find a few old

writings I had almost forgotten but wrote when I myself was passing through a similar transition. Perhaps one of these

will help the intrepid reader hit the ground running in this field.

I'll take up one of those pieces next time.

To be continued …

Resources

=========

Differential Propositional Calculus • Part 1

https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1

Casual Introduction

https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1#Casual_Introduction

Differential Logic

https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview

Differential Logic and Dynamic Systems

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

Regards,

Jon

https://inquiryintoinquiry.com/2021/05/26/differential-logic-and-dynamic-systems-discussion-4/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_propositional/81172986

::: Lyle Anderson

https://groups.io/g/lawsofform/message/162

https://groups.io/g/lawsofform/message/163

Dear Lyle,

I've been meaning to get back to your comments linked above — the connections you observed to finite difference

calculus, ordinary and partial differential equations, and differential geometry are very apt — but preparing the ground

for a smooth transition to differential logic takes time, plus I needed to deal with the details of the En ↔ Ex logical

graph duality I've been wanting to give their due for decades.

The flat out fastest key to the highway of differential logic is still the “Casual Introduction” I wrote for

“Differential Propositional Calculus”. It affords direct access to the basic intuitions and motivations of the

subject but stops short of the syntactic mechanics needed to really take off.

The jump from this point to the more aggressive approaches of “Differential Logic” and “Differential Logic and Dynamic

Systems” has long been a challenge. I went looking for materials to bridge the gap and was pleased to find a few old

writings I had almost forgotten but wrote when I myself was passing through a similar transition. Perhaps one of these

will help the intrepid reader hit the ground running in this field.

I'll take up one of those pieces next time.

To be continued …

Resources

=========

Differential Propositional Calculus • Part 1

https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1

Casual Introduction

https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1#Casual_Introduction

Differential Logic

https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview

Differential Logic and Dynamic Systems

Regards,

Jon

Jun 13, 2021, 1:40:39 PM6/13/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 5

https://inquiryintoinquiry.com/2021/06/13/differential-logic-and-dynamic-systems-discussion-5/

Re: Differential Logic and Dynamic Systems • Discussion 4

All,

Last time I mentioned a few old writings I thought might serve to smooth the

transition between “Differential Propositional Calculus” [1] and the steeper

climbs of “Differential Logic” [2] & “Differential Logic and Dynamic Systems” [3].

[1] https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview

[2] https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview

[3] https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

I was pleased to discover LibreOffice made nice PDFs of my ancient Word Docs,

so I can make a first installment on my promissory note by linking to a couple

of those documents below.

❧ Theme One • A Program Of Inquiry

https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview

❧ Introduction • Program Overview and User Guide (pdf)

https://inquiryintoinquiry.files.wordpress.com/2021/05/theme-one-guide.pdf

❧ Linear Topics • Differential Theory of Qualitative Equations (pdf)

https://inquiryintoinquiry.files.wordpress.com/2021/05/theme-one-guide-e280a2-linear-topics.pdf

Those are samples of the documentation I wrote for the Theme One Program

I developed all through the 1980s and eventually submitted in fulfillment

of the thesis requirement for my Master’s in Psychology at Michigan State (1989).

In time I’ll upgrade the formatting and serialize the relevant parts to my blog.

Resources

=========

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

• Survey of Theme One Program

https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/

Regards,

Jon

https://inquiryintoinquiry.com/2021/06/13/differential-logic-and-dynamic-systems-discussion-5/

Re: Differential Logic and Dynamic Systems • Discussion 4

https://inquiryintoinquiry.com/2021/05/26/differential-logic-and-dynamic-systems-discussion-4/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_propositional/81172986

::: Lyle Anderson ( https://groups.io/g/lawsofform/message/163 )
Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_propositional/81172986

All,

Last time I mentioned a few old writings I thought might serve to smooth the

transition between “Differential Propositional Calculus” [1] and the steeper

climbs of “Differential Logic” [2] & “Differential Logic and Dynamic Systems” [3].

[1] https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview

[2] https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview

[3] https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview

I was pleased to discover LibreOffice made nice PDFs of my ancient Word Docs,

so I can make a first installment on my promissory note by linking to a couple

of those documents below.

❧ Theme One • A Program Of Inquiry

https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview

❧ Introduction • Program Overview and User Guide (pdf)

https://inquiryintoinquiry.files.wordpress.com/2021/05/theme-one-guide.pdf

❧ Linear Topics • Differential Theory of Qualitative Equations (pdf)

https://inquiryintoinquiry.files.wordpress.com/2021/05/theme-one-guide-e280a2-linear-topics.pdf

Those are samples of the documentation I wrote for the Theme One Program

I developed all through the 1980s and eventually submitted in fulfillment

of the thesis requirement for my Master’s in Psychology at Michigan State (1989).

In time I’ll upgrade the formatting and serialize the relevant parts to my blog.

Resources

=========

• Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

https://inquiryintoinquiry.com/2020/08/28/survey-of-theme-one-program-3/

Regards,

Jon

Jun 14, 2021, 1:25:57 PM6/14/21

Cf: Differential Logic and Dynamic Systems • Discussion 6

http://inquiryintoinquiry.com/2021/06/14/differential-logic-and-dynamic-systems-discussion-6/

Re: Differential Logic and Dynamic Systems • Discussions

https://inquiryintoinquiry.com/2021/05/26/differential-logic-and-dynamic-systems-discussion-4/

https://inquiryintoinquiry.com/2021/06/13/differential-logic-and-dynamic-systems-discussion-5/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_logic_and/82914915

::: Lyle Anderson ( https://groups.io/g/lawsofform/message/316 )

<QUOTE LA:>

Have you ever done any statistical analysis of data, or any of the statistical sciences such as The theory of Error,

Experimental Psychology, Thermodynamics, Quantum Theory? These handle what you are calling differential logic using

probability distribution functions of various types over various knowledge domains. If you are heading toward logic

based on vague or imprecise statements, then there is the well established science and application of Fuzzy Logic.

</QUOTE>

Dear Lyle,

Yes, been there done that. On top of the usual theory courses

in Probability and Statistics, Measure Theory, etc. contributing

to a master's in math (1980) and the canonical year of “Advanced

Psychometrics”, really a quaint legacy term for what had long since

morphed into statistical methods for experimental design and analysis,

sine qua non for a master's in psych (1989), there was a raft of short

courses on statistical computing packages which always seemed to get me a

lot more bucks for the head-banging than anything else as the years wore on.

Regards,

Jon

http://inquiryintoinquiry.com/2021/06/14/differential-logic-and-dynamic-systems-discussion-6/

Re: Differential Logic and Dynamic Systems • Discussions

https://inquiryintoinquiry.com/2021/05/26/differential-logic-and-dynamic-systems-discussion-4/

https://inquiryintoinquiry.com/2021/06/13/differential-logic-and-dynamic-systems-discussion-5/

Re: Laws of Form

https://groups.io/g/lawsofform/topic/differential_logic_and/82914915

::: Lyle Anderson ( https://groups.io/g/lawsofform/message/316 )

<QUOTE LA:>

Have you ever done any statistical analysis of data, or any of the statistical sciences such as The theory of Error,

Experimental Psychology, Thermodynamics, Quantum Theory? These handle what you are calling differential logic using

probability distribution functions of various types over various knowledge domains. If you are heading toward logic

based on vague or imprecise statements, then there is the well established science and application of Fuzzy Logic.

</QUOTE>

Dear Lyle,

Yes, been there done that. On top of the usual theory courses

in Probability and Statistics, Measure Theory, etc. contributing

to a master's in math (1980) and the canonical year of “Advanced

Psychometrics”, really a quaint legacy term for what had long since

morphed into statistical methods for experimental design and analysis,

sine qua non for a master's in psych (1989), there was a raft of short

courses on statistical computing packages which always seemed to get me a

lot more bucks for the head-banging than anything else as the years wore on.

Regards,

Jon

Feb 9, 2022, 1:48:22 PM2/9/22

to Conceptual Graphs, Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Differential Logic and Dynamic Systems • Discussion 7

http://inquiryintoinquiry.com/2022/02/09/differential-logic-and-dynamic-systems-discussion-7/

Re: Differential Logic and Dynamic Systems

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1

::: Intentional Propositions

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1#Intentional_Propositions

Re: FB | Differential Logic

https://www.facebook.com/DifferentialLogic/posts/2868375713219794

::: Marius V. Constantin

https://www.facebook.com/JonnyCache/posts/10225410016490896?comment_id=10225410104973108

All,

Marius Constantin asks about the logical value of intentions which are not carried out.

<QUOTE MVC:>

I have in my intention to give like, but I didn't.

What is the value (logic) of this proposition?

</QUOTE>

Dear Marius,

A difference between an expected state and an observed state

is called a Surprise. A surprise calls for an explanation.

A difference between an intended state and an observed state

is called a Problem. A problem calls for a plan of action.

There's more discussion in the following essay and section.

Prospects for Inquiry Driven Systems

https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

Topos : Rudiments and Immediate Resources

https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Topos_:_Rudiments_and_Immediate_Resources

Resources

=========

Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

Survey of Inquiry Driven Systems

https://inquiryintoinquiry.com/2020/12/27/survey-of-inquiry-driven-systems-3/

Regards,

Jon

http://inquiryintoinquiry.com/2022/02/09/differential-logic-and-dynamic-systems-discussion-7/

Re: Differential Logic and Dynamic Systems

::: Intentional Propositions

https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1#Intentional_Propositions

Re: FB | Differential Logic

https://www.facebook.com/DifferentialLogic/posts/2868375713219794

::: Marius V. Constantin

https://www.facebook.com/JonnyCache/posts/10225410016490896?comment_id=10225410104973108

All,

Marius Constantin asks about the logical value of intentions which are not carried out.

<QUOTE MVC:>

I have in my intention to give like, but I didn't.

What is the value (logic) of this proposition?

</QUOTE>

Dear Marius,

A difference between an expected state and an observed state

is called a Surprise. A surprise calls for an explanation.

A difference between an intended state and an observed state

is called a Problem. A problem calls for a plan of action.

There's more discussion in the following essay and section.

Prospects for Inquiry Driven Systems

https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

Topos : Rudiments and Immediate Resources

https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems#Topos_:_Rudiments_and_Immediate_Resources

Resources

=========

Survey of Differential Logic

https://inquiryintoinquiry.com/2021/05/15/survey-of-differential-logic-3/

https://inquiryintoinquiry.com/2020/12/27/survey-of-inquiry-driven-systems-3/

Regards,

Jon

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