Inquiry Driven Systems

[Jon Awbrey]

Cf: Survey of Inquiry Driven Systems • 2
http://inquiryintoinquiry.com/2020/06/26/survey-of-inquiry-driven-systems-%e2%80%a2-2/

Dear Colleagues,

Here's an update of my Survey ( http://inquiryintoinquiry.com/surveys/ )
of previous blog and wiki posts on Inquiry Driven Systems, fixing many
links that got broken when the InterSciWiki went off the live web.

An “inquiry driven system” is a system having among its state variables
some representing its state of information with respect to various topics
of interest, for example, its own state and the state of any potential
object systems. Thus it has a component of state tracing a trajectory
though an information state space.

Elements
========

• Prospects for Inquiry Driven Systems
https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

• Introduction to Inquiry Driven Systems
https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems

Developments
============

• Functional Logic • Inquiry and Analogy
https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

• Inquiry Driven Systems • Fields Of Inquiry
http://web.archive.org/web/20160616140000/http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems_:_Fields_Of_Inquiry


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

Applications
============

• Interpretation as Action • The Risk of Inquiry
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry

• Exploring Research Data Interactively • Theme One : A Program of Inquiry
https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._Theme_One_A_Program_of_Inquiry

• An Architecture for Inquiry • Building Computer Platforms for Discovery
https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Computer_Platforms_for_Discovery

• Organizations of Learning or Learning Organizations
: The Challenge of Creating Integrative Universities for the Next Century
http://www.iupui.edu/~arisbe/menu/library/aboutcsp/awbrey/integrat.htm

• Conceptual Barriers to Creating Integrative Universities
http://org.sagepub.com/content/8/2/269.abstract

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 Awbrey]

Cf: Inquiry Driven Systems • Comment 6
http://inquiryintoinquiry.com/2020/12/25/inquiry-driven-systems-comment-6/

Re: Peter Cameron
https://cameroncounts.wordpress.com/about/
::: Publication : An Author's View
https://cameroncounts.wordpress.com/2020/12/23/publication-an-authors-view/

Dear Peter,

It's funny you should mention Tennyson's poem in the context of
an author's view of publication since I once laid out a detailed
interpretation of the poem as a metaphor on the poet's quest to
communicate. I know I wrote a shorter, sweeter essay on that
somewhere I can't find right now but here's one of my more
turgid dilatations where I used the poem as an “epitext” —
a connected series of epigraphs — for a discussion of what
I called Ostensibly Recursive Texts (ORTs).

🙞 Inquiry Driven Systems • The Informal Context
https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_2#The_Informal_Context

<EXCERPT>

Tennyson's poem The Lady of Shalott is akin to an ORT, but a bit more remote,
since the name styled as “The Lady of Shalott”, that the author invokes over
the course of the text, is not at first sight the title of a poem, but a title
its character adopts and afterwards adapts as the name of a boat. It is only on
a deeper reading that this text can be related to or transformed into a proper ORT.
Operating on a general principle of interpretation, the reader is entitled to suspect
the author is trying to say something about himself, his life, and his work, and that
he is likely to be exploiting for this purpose the figure of his ostensible character
and the vehicle of his manifest text. If this is an aspect of the author's intention,
whether conscious or unconscious, then the reader has a right to expect several forms
of analogy are key to understanding the full intention of the text.

</EXCERPT>

[Jon Awbrey]

Cf: Survey of Inquiry Driven Systems • 3
http://inquiryintoinquiry.com/2020/12/27/survey-of-inquiry-driven-systems-3/

All,

This updates my Survey ( http://inquiryintoinquiry.com/surveys/ )
of blog and wiki posts on “Inquiry Driven Systems”, repairing in
passing the welter of links broken due to sundry web defunctions.

⁂ ⁂ ⁂

An “inquiry driven system” is a system having among its state variables
some representing its state of information with respect to various topics

of interest, for example, its own state and the states of any potential

object systems. Thus it has a component of state tracing a trajectory
though an information state space.

Elements
========

• Prospects for Inquiry Driven Systems
https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems

• Introduction to Inquiry Driven Systems
https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems

Blog Dialogs
============

• Inquiry Driven Systems • Comments
https://inquiryintoinquiry.com/2018/02/18/inquiry-driven-systems-comment-1/
https://inquiryintoinquiry.com/2018/02/21/inquiry-driven-systems-comment-2/
https://inquiryintoinquiry.com/2018/07/02/inquiry-driven-systems-comment-3/
https://inquiryintoinquiry.com/2018/08/12/inquiry-driven-systems-comment-4/
https://inquiryintoinquiry.com/2018/08/19/inquiry-driven-systems-comment-5/
https://inquiryintoinquiry.com/2020/12/25/inquiry-driven-systems-comment-6/

Developments
============

• Functional Logic • Inquiry and Analogy
https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy

• Inquiry Driven Systems • Fields Of Inquiry

https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Fields_Of_Inquiry

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

Applications
============

• Interpretation as Action • The Risk of Inquiry
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry

• Exploring Research Data Interactively • Theme One : A Program of Inquiry
https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._Theme_One_A_Program_of_Inquiry

• An Architecture for Inquiry • Building Computer Platforms for Discovery
https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Computer_Platforms_for_Discovery

• Organizations of Learning or Learning Organizations
: The Challenge of Creating Integrative Universities for the Next Century

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

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

Cf: Inquiry Driven Systems • Discussion 5
https://inquiryintoinquiry.com/2021/07/25/inquiry-driven-systems-discussion-5/

Re: Laws of Form
https://groups.io/g/lawsofform/topic/inquiry_driven_systems/84227997
::: Leon Conrad
(1) https://groups.io/g/lawsofform/message/513
(2) https://groups.io/g/lawsofform/message/528

<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>

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
em 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.

• Inquiry Into Inquiry • Surveys
( https://inquiryintoinquiry.com/surveys/ )

Best regards,

Jon

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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