In the Way of Inquiry

[Jon Awbrey]

Cf: In the Way of Inquiry • Recircus
http://inquiryintoinquiry.com/2023/01/06/in-the-way-of-inquiry-recircus-2/

“I must lie down where all the ladders start
In the foul rag and bone shop of the heart.”

— W.B. Yeats
https://web.archive.org/web/20200402124816/https://www.web-books.com/Classics/Poetry/Anthology/Yeats/Circus.htm

All,

I was never on Twitter but many people whose writings I follow
here and there on the web often reshared their posts from there.
So when a horde of them began migrating to Fediverse locales like
Mastodon and especially Mathstodon (where they have LaTeX) I took
a chance on tagging along. I don't know whether micro-blooging is
really my medium yet but the diversity of readings from others has
been pretty interesting so far. It's also serving as a beneficial
exercise trying to quantize my macro-bloggings down to micro scale,
so I'll keep working at that for the time being and see how it goes.

For now I have in mind circling back to a point in my project on
Inquiry Driven Systems, namely, the chapter addressing various
Obstacles to the Project.

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

Inquiry Driven Systems • Obstacles
https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_5#Obstacles

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Obstacles
https://inquiryintoinquiry.com/2023/01/07/in-the-way-of-inquiry-obstacles-2/
https://mathstodon.xyz/@Inquiry/109604792996683677

“Upon this first, and in one sense this sole, rule of reason, that in order
to learn you must desire to learn, and in so desiring not be satisfied with
what you already incline to think, there follows one corollary which itself
deserves to be inscribed upon every wall of the city of philosophy:

“Do not block the way of inquiry.”

C.S. Peirce, Collected Papers, CP 1.135–136
From an unpaginated ms. “F.R.L.”, c. 1899.

All,

Often the biggest obstacle to learning more is the need to feel
one already knows. And yet there are some things a person knows,
at least, in comparison to other things, and it makes sense to use
what one already knows best in order to learn what one needs to know
better. The question is, how does one know which is which? What test
can tell what is known so well it can be trusted in learning what is not?

One way to test a supposed knowledge is to try to formulate it in such a way
that it can be taught to other people. A related test, harder in some ways
but easier in others, is to try to formalize it so completely that even a
computer could go through the motions that are supposed to be definitive
of its practice.

Both ways of testing a supposition of knowledge depend on putting knowledge
in forms which can be communicated or transported from one medium or system
of interpretation to another. Knowledge already in a concrete form takes
no more than a simple reformation or transformation, otherwise it takes
a more radical metamorphosis, from a wholly disorganized condition to
the first inklings of a portable or sharable form.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Initial Unpleasantness
http://inquiryintoinquiry.com/2023/01/08/in-the-way-of-inquiry-initial-unpleasantness-2/

Clouds and thunder:
The image of Difficulty at the Beginning.
Thus the superior man
Brings order out of confusion.

— I Ching ䷂ Hexagram 3

All,

Inquiry begins in doubt, a debit of certainty and a drought of information,
never a pleasant condition to acknowledge, and one of the primary obstacles to
inquiry may be reckoned as owing to the onus one naturally feels on owning up to
that debt. Human nature far prefers to revel in the positive features of whatever
scientific knowledge it already possesses and the mind defers as long as possible the
revolt it feels arising on facing the uncertainties that still persist, the “nots” and
“not yets” it cannot as yet and ought not deny.

Reference

The I Ching, or Book of Changes, R. Wilhelm and C.F. Baynes (trans.),
Foreword by C.G. Jung, Bollingen Series 19, Princeton University Press,
Princeton, NJ. 1st edition 1950, 2nd edition 1961, 3rd edition 1967.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Justification Trap
https://inquiryintoinquiry.com/2023/01/10/in-the-way-of-inquiry-justification-trap-2/

All,

There is a particular type of “justification trap” a person can fall into,
of trying to prove the scientific method by solely deductive means, that is,
of trying to show the scientific method is a good method by starting from the
simplest possible axioms, principles everyone would accept, about what is good.

Often this happens, in spite of the fact one really knows better, simply in
the process of arranging one's thoughts in a rational order, say, from the
most elementary and independent to the most complex and derivative, as if
for the sake of a logical and summary exposition. But when does this
rearrangement cease to be a rational reconstruction and start to become
a destructive rationalization, a distortion of the genuine article, and
a falsification of the authentic inquiry it attempts to recount?

Sometimes people express their recognition of this trap and their appreciation
of the factor it takes to escape it by saying there is really no such thing as
the scientific method, that the very term “scientific method” is a misnomer and
does not refer to any kind of method at all, in sum, the development of knowledge
cannot be reduced to any fixed method because it involves in an essential way such
a large component of non-methodical activities. If one's idea of what counts as
method is fixed on the ideal of a deductive procedure then it's no surprise one
draws that conclusion.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Formal Apology
http://inquiryintoinquiry.com/2023/01/12/in-the-way-of-inquiry-formal-apology-2/

Part 1
======

Using “form” in the sense of “abstract structure”, the focus of my
interest in this investigation is limited to the formal properties
of the inquiry process. Among its chief constituents are numbered
all the thinking and unthinking processes supporting the ability to
learn and to reason.

This formal apology, the apologetics of declaring a decidedly formal intent,
will be used on numerous occasions to beg off a host of material difficulties
and thus avoid the perceived necessity of meeting a multitude of conventional
controversies.

Category Double-Takes

The first use of the formal apology is to rehabilitate certain classes
of associations between concepts otherwise marked as category mistakes.
The conversion is achieved by flipping from one side of the concept's
dual aspect to the other as the context demands. Thus it is possible
in selected cases to reform the characters of category mistakes in the
manner of categorical “retakes” or “double-takes”.

Conceptual Extensions

The second use of the formal apology is to permit the tentative extension of
concepts to novel areas, giving them experimental trial beyond the cases and
domains where their use is already established in the precedents of accustomed
habit and successful application.

This works to dispel the “in principle” objection that any category distinction
puts a prior constraint on the recognition of similar structure between materially
dissimilar domains. It leaves the issue a matter to be settled by post hoc judgment,
a matter of what fits best “in practice”.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Formal Apology

https://inquiryintoinquiry.com/2023/01/12/in-the-way-of-inquiry-formal-apology-2/

Part 2
======

Explosional Recombinations

Another obstacle to inquiry is posed by the combinatorial explosion
of questions arising in complex cases. The embarrassment of riches
found here is deceptively deadly to the ends of inquiry in the very
measure it appears so productive at first. An eye to form provides
a way to manage the wealth of material diversity by identifying formal
similarities among materially distinct domains. It allows the same
formal answer to unify a host of concrete questions under a single roof,
overall reducing the number of distinct topics that need to be covered.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Formal Apology
https://inquiryintoinquiry.com/2023/01/12/in-the-way-of-inquiry-formal-apology-2/

Part 3
======

Interpretive Frameworks

Iterations of the recombinatorial process generate alternative hierarchies of
categories for controlling the explosion of parts in the domain under inquiry.
If by some piece of luck an alternative framework is uniquely suited to the
natural ontology of the domain in question, it becomes advisable to reorganize
the inquiry along the lines of the new topic headings.

But a complex domain seldom falls out that neatly. The new interpretive framework
will not preserve all the information in the object domain but typically capture
only another aspect of it. To take the maximal advantage of all the different
frameworks that might be devised it is best to quit depending on any one of them
exclusively. Thus, a rigid reliance on a single hierarchy to define the ontology
of a given domain passes over into a flexible application of interpretive frameworks
to make contact with particular aspects of one’s object domain.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

[Jon Awbrey]

Cf: In the Way of Inquiry • Material Exigency
http://inquiryintoinquiry.com/2023/01/20/in-the-way-of-inquiry-material-exigency-2/

Part 1
======

Our survey of obstacles to inquiry has dealt at length with blocks arising
from its formal aspects. On the other hand, I have cast this project as
an empirical inquiry, proposing to represent experimental hypotheses in
the form of computer programs. At the heart of that empirical attitude
is a feeling all formal theories should arise from and bear on experience.

Every season of growth in empirical knowledge begins with a rush to
the sources of experience. Every fresh-thinking reed of intellect is
raised to pipe up and chime in with the still-viable canons of inquiry
in one glorious paean to the personal encounter with natural experience.

But real progress in the community of inquiry depends on observers being
able to orient themselves to objects of common experience — the uncontrolled
exaltation of individual phenomenologies leads as a rule to the disappointment
and disillusionment which befalls the lot of unshared enthusiasms and fragmented
impressions.

Look again at the end of the season and see it faltering to a close, with
every novice scribe rapped on the knuckles for departing from that uninspired
identification with impersonal authority which expresses itself in third-person
passive accounts of one’s own experience.

Regards,

Jon
https://mathstodon.xyz/@Inquiry

[Jon Awbrey]

Cf: In the Way of Inquiry • Material Exigency

https://inquiryintoinquiry.com/2023/01/20/in-the-way-of-inquiry-material-exigency-2/

Part 2
======

A turn of events so persistent must have a cause, a force of
reason to explain the dynamics of its recurring moment in the
history of ideas. The nub of it's not born on the sleeve of
its first and last stages, where the initial explosion and the
final collapse march along their stubborn course in lockstep
fashion, but is embodied more naturally in the middle of the
above narrative.

Experience exposes and explodes expectations. How can experiences impact
expectations unless the two types of entities are both reflected in one
medium, for instance and perhaps without loss of generality, in the form
of representation constituting the domain of signs?

However complex its world may be, internal or external to itself or on
the boundaries of its being, a finite creature’s description of it rests
in a finite number of finite terms or a finite sketch of finite lines.
Finite terms and lines are signs. What they indicate need not be finite
but what they are, must be.

Regards,

Jon
https://mathstodon.xyz/@Inquiry

[Jon Awbrey]

Cf: In the Way of Inquiry • Reconciling Accounts
https://inquiryintoinquiry.com/2023/01/24/in-the-way-of-inquiry-reconciling-accounts-2/

All,

The Reader may share with the Author a feeling of discontent
at this point, attempting to reconcile the formal intentions
of this inquiry with the cardinal contentions of experience.
Let me try to express the difficulty in the form of a question:

What is the bond between form and content in experience,
between the abstract formal categories and the concrete
material contents residing in experience?

Once toward the end of my undergrad years a professor asked me
how I'd personally define mathematics and I told him I saw it as
“the form of experience and the experience of form”. This is not
the place to argue for the virtues of that formulation but it does
afford me one of the handles I have on the bond between form and
content in experience.

I have no more than a tentative way of approaching the question.
I take there to be a primitive category of “form‑in‑experience” —
I don't have a handy name for it yet but it looks to have a flexible
nature which from the standpoint of a given agent easily passes from
the “structure of experience” to the “experience of structure”.

Regards,

Jon
https://mathstodon.xyz/@Inquiry

[kall...@gmail.com]

While abstraction seems hierarchically ordered, the objects structured by ordering in (FigAbstractionChainComplex) are mutually meta-coupled - mapped onto - (FigFrameworkOfScientificWorlds-Lloyd). The mathematical theories exist in the Platonic World, and 'expressed' by the language of Mathematics in the World of Intelligence (which once was thought the Mental World of Popper and Penrose).

Functions structure forms of concepts into patterns. What we normally perceive is the structure, not the pattern of objects.

Kenneth Lloyd

The pathways to physical manifestations can be seen by peripatetic travels through the arrows, which are actually forms of language (not natural language, however).

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[Gerhard Chroust]

Dear Kenneth

I would like to use your diagram in my lecture, but I would like to have a reference (from where the figure comes)

thanks in advance

gerhard

---------------------------------
Prof. Dr. Gerhard Chroust
J. Kepler University Linz
c/o Donaustr. 101/6,
A-2346 Maria Enzersdorf, Austria
+43 664 28 29 978
Gerhard...@jku.at

www.gerhard-chroust.at

>>> <kall...@gmail.com> 03.02.2023 16:50 >>>

To view this discussion on the web visit https://groups.google.com/d/msgid/syssciwg/001501d937e7%244a260900%24de721b00%24%40gmail.com.

[kall...@gmail.com]

Gerhard,

 

The figure is my own, to be found in my upcoming book under copyright, Intelligent Structures in Contexts. You may use it CC- BY,  Kenneth A. Lloyd.

 

Ken Lloyd

To view this discussion on the web visit https://groups.google.com/d/msgid/syssciwg/63DD4B940200001E0000B62C%40s05gw01.im.jku.at.

[kall...@gmail.com]

Gerhard,

 

Here is the preface to the book.

 

Ken Lloyd

 

From: syss...@googlegroups.com <syss...@googlegroups.com> On Behalf Of Gerhard Chroust

Sent: Friday, February 3, 2023 11:00 AM
To: syss...@googlegroups.com

To view this discussion on the web visit https://groups.google.com/d/msgid/syssciwg/63DD4B940200001E0000B62C%40s05gw01.im.jku.at.

[Aleksandar Malečić]

To Gerhard Chroust: It's Roger Penrose;s idea of three worlds. I agree with Ken Lloyd there are actually four worlds, I disagree with him where the fourth world is. There are four Aristotle's causes, four physical interactions... https://journals.isss.org/index.php/proceedings61st/article/view/3217

Aleksandar

To view this discussion on the web visit https://groups.google.com/d/msgid/syssciwg/006401d93818%243a1908b0%24ae4b1a10%24%40gmail.com.

[Jon Awbrey]

Cf: In the Way of Inquiry • Objections to Reflexive Inquiry
https://inquiryintoinquiry.com/2023/02/05/in-the-way-of-inquiry-objections-to-reflexive-inquiry-2/

Part 1
======

Inquiry begins when an automatic routine or normal course
of activity is interrupted and agents are thrown into doubt
concerning what is best to do next and what is really true of
their situation. If this interruptive aspect of inquiry applies
at the level of self-application then occasions for inquiry into
inquiry arise when an ongoing inquiry into any subject becomes
obstructed and agents are obliged to initiate a new order of
inquiry in order to overcome the obstacle.

At such moments agents need the ability to pause and reflect — to accept
the interruption of the inquiry in progress, to acknowledge the higher
order of uncertainty obstructing the current investigation, and finally
to examine accepted conventions and prior convictions regarding the
conduct of inquiry in general.

The next order of inquiry requires agents to articulate the assumptions
embodied in previous inquiries, to consider their practical effects in light
of their objective intents, and to reconstruct forms of conduct which formerly
proceeded through their paces untroubled by any articulate concern.

Regards,

Jon

[Jon Awbrey]

Cf: In the Way of Inquiry • Objections to Reflexive Inquiry
https://inquiryintoinquiry.com/2023/02/05/in-the-way-of-inquiry-objections-to-reflexive-inquiry-2/

Part 2
======

Our agent of inquiry is brought to the threshold of two questions:

• What actions are available to achieve the aims of the present activity?
• What assumptions already accepted are advisable to amend or abandon?

The inquirer is faced in the object of inquiry with an obstinately oppositional
state of affairs, a character marked by the Greek word “pragma” for “object”,
whose manifold of senses and derivatives includes among its connotations the
ideas of purposeful objectives and problematic objections, and not too
incidentally both inquiries and expositions.

Regards,

Jon
https://mathstodon.xyz/@Inquiry

[Jon Awbrey]

Cf: In the Way of Inquiry • Objections to Reflexive Inquiry
https://inquiryintoinquiry.com/2023/02/05/in-the-way-of-inquiry-objections-to-reflexive-inquiry-2/

Part 3
======

An episode of inquiry bears the stamp of an interlude — it begins and ends in medias res with respect to actions and
circumstances neither fixed nor fully known. As easy as it may be to overlook the contingent character of the inquiry
process it’s just as essential to observe a couple of its consequences:

First, it means genuine inquiry does not touch on the inciting action at points of total doubt or absolute certainty.
An incident of inquiry does not begin or end in absolute totalities but only in the differential and relative measures
which actually occasion its departures and resolutions.

Inquiry as a process does not demand absolutely secure foundations from which to set out or any “place to stand” from
which to examine the balance of onrushing events. It needs no more than it does in fact have at the outset —
assumptions not in practice doubted just a moment before and a circumstance of conflict that will force the whole
situation to be reviewed before returning to the normal course of affairs.

Second, the interruptive character or escapist interpretation of inquiry is especially significant when contemplating
programs of inquiry with recursive definitions, as the motivating case of inquiry into inquiry. It means the
termination criterion for an inquiry subprocess is whatever allows continuation of the calling process.

Regards,

Jon
https://mathstodon.xyz/@Inquiry