Inquiry Driven Systems


 

Cf: Inquiry Driven Systems • Discussion 1
https://inquiryintoinquiry.com/2021/07/15/inquiry-driven-systems-discussion-1/

Re: Topos Lab ( https://topos.site/ )
::: MathFoldr Project
https://topos.site/blog/2021/07/introducing-the-mathfoldr-project/
Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/the.20MathFoldr.20project/near/245887481
::: Valeria de Paiva
https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/the.20MathFoldr.20project/near/246024979

Dear Brendan and Valeria,

Along those lines, you may wish to look into the model of knowledge development
sketched in my work on Inquiry Driven Systems.

• Inquiry Driven Systems • Inquiry Into Inquiry
( https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview )

• Prospects
( https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems )

• Introduction
( https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems )

• Survey Page
( https://inquiryintoinquiry.com/2020/12/27/survey-of-inquiry-driven-systems-3/ )

I've been a participant∫observer in web-ontology knowledge projects
for a couple of decades and they always give far more attention to
knowledge as a product than due reflection on the dynamics of inquiry
required to develop that provisional knowledge. Many such projects
have come and gone, and it's my guess this bias is one of the reasons.

So I've been working on that …

Jon


 

Cf: Inquiry Driven Systems • Discussion 2
https://inquiryintoinquiry.com/2021/07/18/inquiry-driven-systems-discussion-2/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246318092


All,

Way back in the Summer of Love I met a girl who had just graduated in Chemistry and was thinking about grad school in Education, the hot new field of Instructional Media, we got to talking and dreamed up a vision of using media, at first just shapes in motion, to teach people math from scratch. Long time passing, we got married, she did a dissertation — The Effect of the Hausdorff–Besicovitch Dimension of Figure Boundary Complexity on Hemispheric Functioning ( https://dl.acm.org/doi/book/10.5555/909649 ) — studying the effects of fractal figure complexity on cognitive processing, Mandelbrot gave her permission to use a series of his figures and ranked them by fractal dimension for her, and I pursued an array of parallel lives in math, statistics, computing, philosophy, and psych.

Here is one of our later collaborations aimed toward integrating inquiry learning and information technology into education.

• An Architecture for Inquiry • Building Computer Platforms for Discovery
( https://www.academia.edu/1711266/An_Architecture_for_Inquiry_Building_Computer_Platforms_for_Discovery )

Regards,

Jon


 

Cf: Inquiry Driven Systems • Discussion 3
http://inquiryintoinquiry.com/2021/07/19/inquiry-driven-systems-discussion-3/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children
::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246511511


<QUOTE HS:>
Could one re-invent the whole curriculum from age 5 onwards
built on new [category theoretic] concepts?
</QUOTE>

Henry, All ...

If I were starting from scratch, and I'm always starting from scratch,
I would ease my way up to the pons asinorum of logic and math using
the types of logical graphs laid down by Peirce and Spencer Brown.
That is because I think it's crucial to firm up propositional logic
before taking on quantifiers and to grasp classical logic before
intuitionistic.

The climb from “zeroth order logic” to first order logic is
a lot more interesting and richer in adventure once you have
a truly efficient calculus for propositional logic at the ready.
An approach to categories, combinators, etc. can then be made
via the propositions as types analogy. For the kiddies,
Smullyan's “Mockingbird” would be the primer of choice.

Regards,

Jon


 

Cf: Inquiry Driven Systems • Discussion 4
https://inquiryintoinquiry.com/2021/07/20/inquiry-driven-systems-discussion-4/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children ::: Eduardo Ochs
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246543190


<QUOTE EO:>
Do you have links on how to teach Logical Graphs to children
(and to people like me!) and how to use them as a basis for
learning Propositional Calculus and quantifiers?
</QUOTE>

Dear Eduardo,

There's a lot of stuff I've put on the web over the last
twenty years devoted to CSP and GSB and my own versions of
Logical Graphs — I'm still working at organizing all that in
a step-by-step tutorial fashion. I'll be doing more of that
over time on a number of local streams and topics, e.g.

Logical Graphs • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

Logical Graphs • Semiotics and Semiosis
https://categorytheory.zulipchat.com/#narrow/stream/229179-semiotics-and.20semiosis/topic/logical.20graphs

Differential Logic • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/differential.20logic

Precursors of Category Theory • History of Ideas
https://categorytheory.zulipchat.com/#narrow/stream/232163-learning.3A-history.20of.20ideas/topic/precursors.20of.20category.20theory


C.S. Peirce • Philosophy
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

You might try sampling my Inquiry blog
( https://inquiryintoinquiry.com/ ) for the
daily rushes and discussions or my OEIS user page
( https://oeis.org/wiki/User:Jon_Awbrey ) and OEIS workspace
( https://oeis.org/wiki/User:Jon_Awbrey/WORKSPACE ) to see if
anything engages your interest.

Cheers,
Jon


Leon Conrad
 

Jon - hi
As someone who has worked on, teaches and uses the CoI to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB's work to logical tables, particularly if it does a similar thing.
I tried to access one of the links you provided, but zulip seems to be a closed system.
If you could facilitate access, or email me something, I'd be interested.
Thanks - 
Leon
Application of the CoI to Narrative Analysis - https://www.academia.edu/40470826/The_Unknown_Storyteller


On Tue, 20 Jul 2021 at 19:41, Jon Awbrey <jawbrey@...> wrote:
Cf: Inquiry Driven Systems • Discussion 4
https://inquiryintoinquiry.com/2021/07/20/inquiry-driven-systems-discussion-4/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children :::
Eduardo Ochs
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246543190


<QUOTE EO:>
Do you have links on how to teach Logical Graphs to children
(and to people like me!) and how to use them as a basis for
learning Propositional Calculus and quantifiers?
</QUOTE>

Dear Eduardo,

There's a lot of stuff I've put on the web over the last
twenty years devoted to CSP and GSB and my own versions of
Logical Graphs — I'm still working at organizing all that in
a step-by-step tutorial fashion.  I'll be doing more of that
over time on a number of local streams and topics, e.g.

Logical Graphs • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

Logical Graphs • Semiotics and Semiosis
https://categorytheory.zulipchat.com/#narrow/stream/229179-semiotics-and.20semiosis/topic/logical.20graphs

Differential Logic • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/differential.20logic

Precursors of Category Theory • History of Ideas
https://categorytheory.zulipchat.com/#narrow/stream/232163-learning.3A-history.20of.20ideas/topic/precursors.20of.20category.20theory


C.S. Peirce • Philosophy
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

You might try sampling my Inquiry blog
( https://inquiryintoinquiry.com/ ) for the
daily rushes and discussions or my OEIS user page
( https://oeis.org/wiki/User:Jon_Awbrey ) and OEIS workspace
( https://oeis.org/wiki/User:Jon_Awbrey/WORKSPACE ) to see if
anything engages your interest.

Cheers,
Jon






Lyle Anderson
 

Leon,
Here is the zulipchat invite link Jon provided in another thread: 
https://categorytheory.zulipchat.com/#narrow/stream/229122-general.3A-meta/topic/invite.20link

I will be interested in you comments on the discussions on this forum.

May the Form be with you!
Best regards,
Lyle


bruceschuman@...
 

Dear Leon – thanks for these links.  They appear quite excellent.

 

I thought it was quite interesting that you cite 3 highlighted letters from the cover of the 1979 paperback, forming “AOM”, representing the ancient Hindu mantra or name of God.   I personally find that very appealing and correctly on track – though perhaps I would spell them AUM or OM.

 

 

A currently available edition, as shown on Amazon, has a Moebius Strip on the cover – an idea I am working with closely.

 

https://www.amazon.com/Laws-Form-G-Spencer-Brown/dp/0963989901/ref=monarch_sidesheet

 

 

You mention the mathematician Louis Kaufmann – he has a PDF on LOF that features the Moebius Strip

 

http://homepages.math.uic.edu/~kauffman/KauffSAND.pdf

 

From the Kaufmann PDF

 

 

Bruce Schuman

Santa Barbara CA USA

bruceschuman@... / 805-705-9174

www.origin.org / www.integralontology.net

 

 

 

From: lawsofform@groups.io <lawsofform@groups.io> On Behalf Of Leon Conrad
Sent: Friday, July 23, 2021 1:31 AM
To: lawsofform@groups.io
Subject: Re: [lawsofform] Inquiry Driven Systems

 

Jon - hi

As someone who has worked on, teaches and uses the CoI to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB's work to logical tables, particularly if it does a similar thing.

I tried to access one of the links you provided, but zulip seems to be a closed system.

If you could facilitate access, or email me something, I'd be interested.

Thanks - 

Leon

Application of the CoI to Narrative Analysis - https://www.academia.edu/40470826/The_Unknown_Storyteller

 

On Tue, 20 Jul 2021 at 19:41, Jon Awbrey <jawbrey@...> wrote:

Cf: Inquiry Driven Systems • Discussion 4
https://inquiryintoinquiry.com/2021/07/20/inquiry-driven-systems-discussion-4/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children :::
Eduardo Ochs
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246543190


<QUOTE EO:>
Do you have links on how to teach Logical Graphs to children
(and to people like me!) and how to use them as a basis for
learning Propositional Calculus and quantifiers?
</QUOTE>

Dear Eduardo,

There's a lot of stuff I've put on the web over the last
twenty years devoted to CSP and GSB and my own versions of
Logical Graphs — I'm still working at organizing all that in
a step-by-step tutorial fashion.  I'll be doing more of that
over time on a number of local streams and topics, e.g.

Logical Graphs • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

Logical Graphs • Semiotics and Semiosis
https://categorytheory.zulipchat.com/#narrow/stream/229179-semiotics-and.20semiosis/topic/logical.20graphs

Differential Logic • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/differential.20logic

Precursors of Category Theory • History of Ideas
https://categorytheory.zulipchat.com/#narrow/stream/232163-learning.3A-history.20of.20ideas/topic/precursors.20of.20category.20theory


C.S. Peirce • Philosophy
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

You might try sampling my Inquiry blog
( https://inquiryintoinquiry.com/ ) for the
daily rushes and discussions or my OEIS user page
( https://oeis.org/wiki/User:Jon_Awbrey ) and OEIS workspace
( https://oeis.org/wiki/User:Jon_Awbrey/WORKSPACE ) to see if
anything engages your interest.

Cheers,
Jon





Leon Conrad
 

Thanks, Bruce - 
The note re the Möbius strip on the cover is interesting - Rappaport has taken this into 3D with Klein bottles -
The picture has intrigued me - is there 1 twist, or 3?
Personally, I've stayed away from the 're-entrant' forms, as they don't really speak to me as immediately as the simpler form of the CoI does - I imagine two 'marks' starting at opposite sides of the strip, going in opposite directions around the strip - they'll pass each other on the same side, then on the opposite side in turn, but they will always be in contact with the strip and the space it's in - this, to me, is just semantics - we're just applying the 'marked'/'unmarked' states to the presence or absence of the strip between them, but the strip itself is a mark in space. For me, I prefer the cleanliness of the single mark as an idea in the mind - that emerges in and of the mind, but that's just me. 
As long as people are clear about what is 'marked' and what is 'unmarked' when they apply LoF to 3D forms (or anything else, for that matter), and the ideas can be seen to correlate to GSB's, I'm fine.
Leon

On Fri, 23 Jul 2021 at 18:34, <bruceschuman@...> wrote:

Dear Leon – thanks for these links.  They appear quite excellent.

 

I thought it was quite interesting that you cite 3 highlighted letters from the cover of the 1979 paperback, forming “AOM”, representing the ancient Hindu mantra or name of God.   I personally find that very appealing and correctly on track – though perhaps I would spell them AUM or OM.

 

 

A currently available edition, as shown on Amazon, has a Moebius Strip on the cover – an idea I am working with closely.

 

https://www.amazon.com/Laws-Form-G-Spencer-Brown/dp/0963989901/ref=monarch_sidesheet

 

 

You mention the mathematician Louis Kaufmann – he has a PDF on LOF that features the Moebius Strip

 

http://homepages.math.uic.edu/~kauffman/KauffSAND.pdf

 

From the Kaufmann PDF

 

 

Bruce Schuman

Santa Barbara CA USA

bruceschuman@... / 805-705-9174

www.origin.org / www.integralontology.net

 

 

 

From: lawsofform@groups.io <lawsofform@groups.io> On Behalf Of Leon Conrad
Sent: Friday, July 23, 2021 1:31 AM
To: lawsofform@groups.io
Subject: Re: [lawsofform] Inquiry Driven Systems

 

Jon - hi

As someone who has worked on, teaches and uses the CoI to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB's work to logical tables, particularly if it does a similar thing.

I tried to access one of the links you provided, but zulip seems to be a closed system.

If you could facilitate access, or email me something, I'd be interested.

Thanks - 

Leon

Application of the CoI to Narrative Analysis - https://www.academia.edu/40470826/The_Unknown_Storyteller

 

On Tue, 20 Jul 2021 at 19:41, Jon Awbrey <jawbrey@...> wrote:

Cf: Inquiry Driven Systems • Discussion 4
https://inquiryintoinquiry.com/2021/07/20/inquiry-driven-systems-discussion-4/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children :::
Eduardo Ochs
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246543190


<QUOTE EO:>
Do you have links on how to teach Logical Graphs to children
(and to people like me!) and how to use them as a basis for
learning Propositional Calculus and quantifiers?
</QUOTE>

Dear Eduardo,

There's a lot of stuff I've put on the web over the last
twenty years devoted to CSP and GSB and my own versions of
Logical Graphs — I'm still working at organizing all that in
a step-by-step tutorial fashion.  I'll be doing more of that
over time on a number of local streams and topics, e.g.

Logical Graphs • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/logical.20graphs

Logical Graphs • Semiotics and Semiosis
https://categorytheory.zulipchat.com/#narrow/stream/229179-semiotics-and.20semiosis/topic/logical.20graphs

Differential Logic • Theory of Logic
https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/differential.20logic

Precursors of Category Theory • History of Ideas
https://categorytheory.zulipchat.com/#narrow/stream/232163-learning.3A-history.20of.20ideas/topic/precursors.20of.20category.20theory


C.S. Peirce • Philosophy
https://categorytheory.zulipchat.com/#narrow/stream/229134-philosophy/topic/Peirce

You might try sampling my Inquiry blog
( https://inquiryintoinquiry.com/ ) for the
daily rushes and discussions or my OEIS user page
( https://oeis.org/wiki/User:Jon_Awbrey ) and OEIS workspace
( https://oeis.org/wiki/User:Jon_Awbrey/WORKSPACE ) to see if
anything engages your interest.

Cheers,
Jon





Lyle Anderson
 

On Fri, Jul 23, 2021 at 11:43 PM, Leon Conrad wrote:
Personally, I've stayed away from the 're-entrant' forms, as they don't really speak to me as immediately as the simpler form of the CoI does
Leon,
Try thinking of 're-entrant' forms as the transition from forms used for calculation by an observer to forms that can calculate and observe.  It gets us to the finite state machine, the with either Turing's or Bruce's tape gets us to entities that can adapt to their surroundings. 

May the Form be with you!
Best regards,
Lyle


Leon Conrad
 

Thanks Lyle - 
Tried to access Zulip via the link you provided - this is all I get ...
image.png
Can someone facilitate access to the logic and category files, please? Both are of interest to me.
Thanks - 
Leon

On Fri, 23 Jul 2021 at 17:57, Lyle Anderson <LylePhone@...> wrote:
Leon,
Here is the zulipchat invite link Jon provided in another thread: 
https://categorytheory.zulipchat.com/#narrow/stream/229122-general.3A-meta/topic/invite.20link

I will be interested in you comments on the discussions on this forum.

May the Form be with you!
Best regards,
Lyle


Lyle Anderson
 

Jon,
I can't figure out how to invite people to zulipchat, and the link you gave me has expired.  Would you please help Leon get on board? 
Thanks, Lyle


 

here's the last invite link I see ... fresh just yesterday ...

https://categorytheory.zulipchat.com/join/tnshth3vujiclcfnefe72cui/

kind of a silly system ...

sorry i may be out of the loop till the middle of next week ...
trying to re-connect with some work backlogged a year ago ...
i have to take my car into the shop on monday
and myself into the dentist on tuesday
so we'll see ...

jon


Leon Conrad
 

Thanks, Jon - 
Interesting work - strange looking at an 'upside down' version of notation I'm familiar with - I find GSB's notation far more visually intuitive, though.
I'm wondering whether the forms can be reduced to fewer levels by doing what I propose in my paper and distinguishing between negation and distribution.
Musement is in progress.
Leon


On Sat, 24 Jul 2021 at 19:25, Jon Awbrey <jawbrey@...> wrote:
here's the last invite link I see ... fresh just yesterday ...

https://categorytheory.zulipchat.com/join/tnshth3vujiclcfnefe72cui/

kind of a silly system ...

sorry i may be out of the loop till the middle of next week ...
trying to re-connect with some work backlogged a year ago ...
i have to take my car into the shop on monday
and myself into the dentist on tuesday
so we'll see ...

jon






 

On 7/25/2021 3:31 AM, Leon Conrad wrote:
Thanks, Jon -
Interesting work - strange looking at an 'upside down
< https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1#Cactus_Language_for_Propositional_Logic >'
version of notation I'm familiar with - I find GSB's notation far more
visually intuitive, though.
I'm wondering whether the forms can be reduced to fewer levels by doing
what I propose in my paper and distinguishing between negation and
distribution.
Musement is in progress.
Leon
Ahoy Leon! welcome aboard, a-synchronicity being what it is,
it may be september before i get both my hands back on this
deck myself as i've got a bunch of long-procrastinated home
and garden and auto and health-related matters to deal with.

If you're an old time web surfer like we all used to be way
back when i could leave you with a link or two to follow up
on your own recognizance -- i know, i know, these days it's
more like you can link a horse to whatev but you can't make
him click it.

I will try to write something more coherent later today but
failing that here's a link to an omnibus Survey page for my
blog, where you can find what's been occupying my trains of
thought for the past half-century. The last-numbered links
under each topic include and update all the earlier entries.

https://inquiryintoinquiry.com/surveys/

best regards,

jon


 

Cf: Inquiry Driven Systems • Discussion 6
https://inquiryintoinquiry.com/2021/07/25/inquiry-driven-systems-discussion-6/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children ::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246941350


<QUOTE HS:>
If one were to think about maths and children's education one would need to look at the needs of other subjects too. It should be easy for people here to work out how cats ties in with physics and biology — having a maths of open systems could help a lot there. But one would also want to help maths tie in with the humanities. In France children sometime after 13 or so read Voltaire's Candide published 1759, where Voltaire makes fun of Leibniz' idea that we live in the best possible world, by having Candide go around the world and witness all the suffering known at the time. It would be good if the maths department then also gave some introduction to fragments of contemporary modal logic, so that the children could see that the “best possible world” idea is abandoned by contemporary modal logics.
</QUOTE>

Dear Henry,

I've never found much use for modal logic in mathematics proper since mathematics is all about possible existence, in the sense of what is not inconsistent with a given set of premisses. Of course, one can entertain modal logic as an endeavor to construct mathematical models of natural language intuitions about possibility, contingency, necessity, etc. but that is an application of mathematics to an empirical domain.

As far as best possibilities go we certainly do a lot of work on optimization in math and its applications to the special sciences and engineering. For instance, a lot of physics begins with skiers on snowy slopes and their contemplation of gradients. That very sort of thinking by Leibniz led to his personal discovery of differential calculus.

• Leibniz • The Present Is Big With The Future
https://inquiryintoinquiry.com/2013/04/01/the-present-is-big-with-the-future/

Regards,

Jon


 

Cf: Inquiry Driven Systems • Discussion 7
https://inquiryintoinquiry.com/2021/07/26/inquiry-driven-systems-discussion-7/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children ::: Henry Story
https://categorytheory.zulipchat.com/#narrow/stream/233322-practice.3A-communication/topic/teaching.20children/near/246973853


<QUOTE HS:>
I place Logic within Mathematics and modal logic is a field of Logic,
and so of mathematics. You will find that modal logics comes up a lot
working with machines, programs, and all state based systems.
</QUOTE>

Dear Henry,

Just by way of personal orientation, I tend to follow Peirce and
assorted classical sources in viewing logic as a normative science
whereas mathematics is a hypothetical descriptive science. That
gives a picture of their relationship like the one I drew in the
following post.

Definition and Determination • 4
https://inquiryintoinquiry.com/2012/05/31/definition-and-determination-4/

Peirce Syllabus
http://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg

“Normative science rests largely on phenomenology and on mathematics;
metaphysics on phenomenology and on normative science.”

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)
http://web.archive.org/web/20111105121054/http://www.princeton.edu/~batke/peirce/cl_o_sci_03.htm

The way I see it, then, logic is more an application of mathematics than a subfield of it.

Regards,

Jon


 

Cf: Inquiry Driven Systems • Discussion 8
https://inquiryintoinquiry.com/2021/07/26/inquiry-driven-systems-discussion-8/

Re: Category Theory
https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/category.20theory.20in.20human.20psychology
::: Simon Burton
https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/category.20theory.20in.20human.20psychology/near/247135634


<QUOTE SB:>
From what I've noticed there are two kinds of mathematical thinking:
manipulating abstract syntax, versus direct experience/perception of
concrete mathematics. These two are intertwined in various ways, but
in my experience people generally excel in one of these two styles of
thinking and not the other. I think that many famous collaborations
between two mathematicians are divided along these lines.
</QUOTE>

Dear Simon.

Susan Awbrey ( https://scholar.google.com/citations?user=CguW_vwAAAAJ )
and I have worked a lot and written a little on a variety of “two-culture”
and “cognitive style” questions from a broadly pragmatic perspective
informed by the work of C.S. Peirce, John Dewey, and like-minded thinkers.
The three dimensional spaces of Peirce's triadic sign relations afford
a perspective on the ways diverse thinkers can specialize their thought
to different planes or facets of a sign relation's full volume. Various
issues along these lines are discussed in the following paper.

• Conceptual Barriers to Creating Integrative Universities
https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

Regards,

Jon


bruceschuman@...
 

Jon -- Interesting article and theme --  "Conceptual barriers to integrative universities" -- and "the two cultures".

 

Both of these ideas have been highly motivating for me, and do tend to drive my interest in "the structure of knowledge"

 

https://en.wikipedia.org/wiki/The_Two_Cultures

 

"The Two Cultures" is the first part of an influential 1959 Rede Lecture by British scientist and novelist C. P. Snow which were published in book form as The Two Cultures and the Scientific Revolution the same year. Its thesis was that science and the humanities which represented "the intellectual life of the whole of western society" had become split into "two cultures" and that this division was a major handicap to both in solving the world's problems.

 

Perhaps over-simplistically, I tend to view the relationship between the two cultures ("deep intuition versus empiricism " -- or perhaps "humanities versus science") as essentially involving levels of abstraction (and generalization) – and I called that idea “the bridge across consciousness”

 

And I saw a basic beak in the definition chain as happening or emerging somewhere along a common spectrum that should be connecting these levels – but for various reasons, including those you cite, is not actually working in practice, except maybe in rarified or experimental cutting-edge integral or new-age kinds of environments.

 

My sense is – this is the biggest epistemological/ontological/philosophical challenge of our moment in history.  We need to figure this out and build a bridge that works.

 

 

 

PS – I like this too:

 

> The way I see it, then, logic is more an application of mathematics than a subfield of it.

 

Bruce Schuman

Santa Barbara CA USA

bruceschuman@... / 805-705-9174

www.origin.org / www.integralontology.net

 

 

 

-----Original Message-----
From: lawsofform@groups.io <lawsofform@groups.io> On Behalf Of Jon Awbrey
Sent: Monday, July 26, 2021 8:20 AM
To: Cybernetic Communications <cybcom@...>; Laws of Form <lawsofform@groups.io>; Ontolog Forum <ontolog-forum@...>; Peirce List <peirce-l@...>; Structural Modeling <structural-modeling@...>; SysSciWG <syssciwg@...>
Subject: Re: [lawsofform] Inquiry Driven Systems

 

Cf: Inquiry Driven Systems • Discussion 8 https://inquiryintoinquiry.com/2021/07/26/inquiry-driven-systems-discussion-8/

 

Re: Category Theory

https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/category.20theory.20in.20human.20psychology

::: Simon Burton

https://categorytheory.zulipchat.com/#narrow/stream/229111-general/topic/category.20theory.20in.20human.20psychology/near/247135634

 

 

<QUOTE SB:>

From what I've noticed there are two kinds of mathematical thinking:

manipulating abstract syntax, versus direct experience/perception of concrete mathematics.  These two are intertwined in various ways, but in my experience people generally excel in one of these two styles of thinking and not the other.  I think that many famous collaborations between two mathematicians are divided along these lines.

</QUOTE>

 

Dear Simon.

 

Susan Awbrey ( https://scholar.google.com/citations?user=CguW_vwAAAAJ ) and I have worked a lot and written a little on a variety of “two-culture”

and “cognitive style” questions from a broadly pragmatic perspective informed by the work of C.S. Peirce, John Dewey, and like-minded thinkers.

The three dimensional spaces of Peirce's triadic sign relations afford a perspective on the ways diverse thinkers can specialize their thought to different planes or facets of a sign relation's full volume. Various issues along these lines are discussed in the following paper.

 

• Conceptual Barriers to Creating Integrative Universities https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

 

Regards,

 

Jon

 

 

 


Lyle Anderson
 

On Mon, Jul 26, 2021 at 02:06 AM, Jon Awbrey wrote:
“Normative science rests largely on phenomenology and on mathematics;
metaphysics on phenomenology and on normative science.”

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)
http://web.archive.org/web/20111105121054/http://www.princeton.edu/~batke/peirce/cl_o_sci_03.htm
Jon,
Why would anyone want to do Normative Science? "a scientific technique regarding mandating norms or common or favored values for behaviorschooling, wellness, or other social or cultural facets. In comparison to descriptive science, which tries to describe actions and other phenomena as they actually are, efforts to establish what they ought to be in effort to fulfill several varied standards."
https://psychologydictionary.org/normative-science/

Or: "a science that tests or evaluates and not merely describes or generalizes facts
specifically the group comprising logic, ethics, and aesthetics"
https://www.merriam-webster.com/dictionary/normative%20science

We can now see why you "gave Pierce as chance" and stuck with it.  http://www.commens.org/dictionary/term/normative-science

My father, remember he was a Chaplin at a Mental Hospital, used to say that there were two kinds of marriages: 1. Problem solving or 2. Problem perpetuating.  Both are stable as long as one of the partners does not want to change mode.  My corollary to this is that there are two kinds of academics: 1. Those who are looking for the answer or 2. Those who want to impose their answer.  People who practice "descriptive science" are in the former group, and those who practice "normative science" are in the latter group.  George Spencer-Brown was obviously in the former group, and Charles Sanders Pierce was in the latter.

Here is George Spencer-Brown on the state of education "today":  Laws, 1972, pg 109 ff.
Note 2. Sheffer explicitly assumes the restriction of his operator to a binary scope, and also, implicitly, assumes the relevance of the order in which the variables under operation appear. Each of these assumptions is in fact less central to mathematics than is commonly supposed, and neither is necessary at this stage. Sheffer was therefore forced to design his initial equations so ingeniously as to contradict them both. The latter he can contradict explicitly, without the disorder becoming too apparent, by allowing a l b = b l a as a consequence, but he cannot explicitly contradict the former without obviously denying a rule already recorded, and this would appear foolish, although it is, in fact, now the best way out of the deep trouble that such an ill-considered rule brings in its train. By allowing it to stand, Sheffer's description is rendered practically useless as a calculus.

To understand why Sheffer did not see this, let us take the unusual course of considering his position in the light of the social forces at work around him.

Discoveries of any great moment in mathematics and other disciplines, once they are discovered, are seen to be extremely simple and obvious, and make everybody, including their discoverer, appear foolish for not having discovered them before. It is all too often forgotten that the ancient symbol for the renascence of the world* is a fool, and that foolishness, being a divine state, is not a condition to he either proud or ashamed of.

Unfortunately we find systems of education today which have departed so far from the plain truth, that they now teach us to be proud of what we know and ashamed of ignorance. This is doubly corrupt. It is corrupt not only because pride is in itself a mortal sin, but also because to teach pride in knowledge is to put up an effective barrier against any advance upon what is already known, since it makes one ashamed to look beyond the bonds imposed by one's ignorance.

To any person prepared to enter with respect into the realm of his great and universal ignorance, the secrets of being will eventually unfold, and they will do so in a measure according to his freedom from natural and indoctrinated shame in his respect of their revelation.

In the face of the strong, and indeed violent, social pressures against it, few people have been prepared to take this simple and satisfying course towards sanity. And in a society where a prominent psychiatrist can advertise that, given the chance, he would have treated Newton to electric shock therapy, who can blame any person for being afraid to do so?

To arrive at the simplest truth, as Newton knew and practiced, requires years of contemplation. Not activity. Not reasoning. Not calculating. Not busy behavior of any kind. Not reading. Not talking. Not making an effort. Not thinking. Simply bearing in mind what it is one needs to know. And yet those with the courage to tread this path to real discovery are not only offered practically no guidance on how to do so, they are actively discouraged and have to set about it in secret, pretending meanwhile to be diligently engaged in the frantic diversions and to conform with the deadening personal opinions which are being continually thrust upon them.

In these circumstances, the discoveries that any person is able to undertake represent the places where, in the face of induced psychosis, he has, by his own faltering and unaided efforts, returned to sanity. Painfully, and even dangerously, maybe. But nonetheless returned, however furtively.

We may note in this connection that Peirce [13], who discovered, some thirty years ahead of Sheffer, that the logic of propositions could be done with one constant, did not publish this discovery, although its importance must have been evident to him; that Stamm, who himself discovered and published [17] this fact two years before Sheffer, omits, in his paper, to make a simple and obvious substitution which would have put his claim beyond doubt; and that Sheffer [3], who ignores Stamm's paper, is currently credited with the major discovery recorded in it. 

* wer = man, ald = age, old. The world may be taken to be the manifest properties of the all, its identity with the age of man being evident through the fact that man is a primary animal with a hand (`manifest' coming from manus = hand, festus = struck). Thus the world is considerably less than the all, which includes the unmanifest, but considerably greater than 'the' universe (more correctly, than any universe), which is merely the formal appearance of one of the possible manifestations which make up the world. 
- - - -
Emphasis added.

It is perhaps a good thing that the Creator took George Spencer-Brown when He did.  With his opinion of education as of 1972 above, one can only imagine his reaction to the teaching of "2+2=5" and "mathematics is inherently racist" that we are currently having imposed on us by the "educational establishment."

As I think I have noted before, one of the benefits of growing up among state-certified crazy people is that I am quite comfortable around them, and will continue to care about their eventual return to sanity.  I would also note that Georg Cantor did die in an Insane Asylum as a consequence of his insane notions about infinities.  

I truly wish that the Form will be with you!
Trust the Form!
Best regards,
Lyle


 

Cf: Inquiry Driven Systems • Discussion 9
https://inquiryintoinquiry.com/2021/07/26/inquiry-driven-systems-discussion-9/

Re: Laws of Form
https://groups.io/g/lawsofform/topic/inquiry_driven_systems/84227997
::: Leon Conrad ( https://groups.io/g/lawsofform/message/513 )

<QUOTE LC:>
As someone who has worked on, teaches, and uses the CoI [Calculus of Indications] to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB's work to logical tables, particularly if it does a similar thing.
</QUOTE>

Dear Leon,

Gauging the gap between entry-level formal systems like propositional calculi and calculi qualified to handle quantified predicates, functions, combinators, etc. is one of my oldest research pursuits and still very much a work in progress. When I point people to the live edges of my understanding, the places where I break off in my searches I usually end up numbering those episodes of risk-taking under the heading of “Failures to Communicate” — but it doesn't stop me from trying. So I'll take a chance and post a few links along those lines in a little while but it may avert a measure of misunderstanding if I mention the main forces setting me on my present path.

I had already been studying Peirce's Collected Papers from my first couple of years in college, especially fascinated by his approach to logic, his amphecks, his logical graphs, both entitative and existential, his overall visual and visionary way of doing mathematics. And then a friend pointed me to the entry for Spencer Brown's Laws of Form in the first Whole Earth Catalog and I sent off for a copy right away. My computer courses and self-directed programming play rounded out the triple of primary impacts on the way I would understand and develop logical graphs from that point on.

To be continued …

Regards,

Jon