#inquiry-driven-systems — Public Fediverse posts

Reflection On Recursion • Discussion 1

Re: Reflection On Recursion • 1
Re: Laws of Form • John Mingers

Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.

Thanks, John.  Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few.  But one thing I need to emphasize from the start is how radically different such concepts appear when viewed under x‑rays of Peirce’s pragmatic semiotics.

I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

After a while, it simply becomes time to change the paradigm …

Just by way of a first example, take the very idea of “self‑reference”.  The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.  And when we think to ask, “What is this that we call an interpreter?”, the pragmatic theory of signs tells us we do not know when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

Everything I’ll be working at here will be done within a framework like that.

Regards,
Jon

Resources

• Inquiry Driven Systems • Inquiry Into Inquiry
• Reflective Interpretive Frameworks
• The Phenomenology of Reflection
• Higher Order Sign Relations

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Reflection On Recursion • 4

A feature of special note in the recursion diagram is the function traversing the square from one triadic node to the other.  It preserves an image of the object all the while its precedent is being retrieved and processed — thus it injects a measure of parallel process and a modicum of extra memory over and above that afforded by the serial composition of functions.

Resources

• Inquiry Driven Systems • Inquiry Into Inquiry
• Reflective Interpretive Frameworks
• The Phenomenology of Reflection
• Higher Order Sign Relations

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Reflection On Recursion • 3

One other feature of syntactic recursion deserves to be brought into higher relief.  Evidence of it can be found in the recursion diagram by examining the places where three paths meet.  On the descending side there is the point where three paths diverge.  On the ascending side there is the point where the middlemost of the three divergent paths joins the upshot arrow in medias res.

The arrows of the diagram represent functions, a species of dyadic relations, but nodes of degree three signify aspects of triadic relations somewhere in the mix.

• The three arrows from the initial node represent a function such that
• The three arrows at the penultimate node represent a function such that

For the sake of a first approach, many questions about triadic relations which might arise at this point can be safely left to later discussions, since the current level of generality is comprehensible enough in functional terms.

Resources

• Inquiry Driven Systems • Inquiry Into Inquiry
• Reflective Interpretive Frameworks
• The Phenomenology of Reflection
• Higher Order Sign Relations

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Reflection On Recursion • 2

Turning to the form of a simple recursive function the clause we used to define it earns the title of “syntactic recursion” due to the way the function name occurring in the defined phrase re‑occurs in the defining phrase

It needs to be clear there is no circle in the definition — each instance of the type is defined in terms of an instance one step simpler until the base case is reached and fixed by fiat.  Instead of a circle then we have two gyres, the gyre down via the predecessor function and the gyre up via the modifier function

Resources

• Inquiry Driven Systems • Inquiry Into Inquiry
• Reflective Interpretive Frameworks
• The Phenomenology of Reflection
• Higher Order Sign Relations

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2) (3)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 18

Tangent and Remainder Maps

If we follow the classical line which singles out linear functions as ideals of simplicity then we may complete the analytic series of the proposition in the following way.

The next venn diagram shows the differential proposition we get by extracting the linear approximation to the difference map at each cell or point of the universe   What results is the logical analogue of what would ordinarily be called the differential of but since the adjective differential is being attached to just about everything in sight the alternative name tangent map is commonly used for whenever it’s necessary to single it out.

To be clear about what’s being indicated here, it’s a visual way of summarizing the following data.

To understand the extended interpretations, that is, the conjunctions of basic and differential features which are being indicated here, it may help to note the following equivalences.

Capping the analysis of the proposition in terms of succeeding orders of linear propositions, the final venn diagram of the series shows the remainder map which happens to be linear in pairs of variables.

Reading the arrows off the map produces the following data.

In short, is a constant field, having the value at each cell.

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 17

Enlargement and Difference Maps

Continuing with the example the following venn diagram shows the enlargement or shift map in the same style of field picture we drew for the tacit extension

A very important conceptual transition has just occurred here, almost tacitly, as it were.  Generally speaking, having a set of mathematical objects of compatible types, in this case the two differential fields and both of the type is very useful, because it allows us to consider those fields as integral mathematical objects which can be operated on and combined in the ways we usually associate with algebras.

In the present case one notices the tacit extension and the enlargement are in a sense dual to each other.  The tacit extension indicates all the arrows out of the region where is true and the enlargement indicates all the arrows into the region where is true.  The only arc they have in common is the no‑change loop at   If we add the two sets of arcs in mod 2 fashion then the loop of multiplicity 2 zeroes out, leaving the 6 arrows of shown in the following venn diagram.

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 15

Differential Fields

The structure of a differential field may be described as follows.  With each point of there is associated an object of the following type:  a proposition about changes in that is, a proposition   In that frame of reference, if is the universe generated by the set of coordinate propositions then is the differential universe generated by the set of differential propositions   The differential propositions and may thus be interpreted as indicating and respectively.

A differential operator of the first order type we are currently considering, takes a proposition and gives back a differential proposition   In the field view of the scene, we see the proposition as a scalar field and we see the differential proposition as a vector field, specifically, a field of propositions about contemplated changes in

The field of changes produced by on is shown in the following venn diagram.

The differential field specifies the changes which need to be made from each point of in order to reach one of the models of the proposition that is, in order to satisfy the proposition

The field of changes produced by on is shown in the following venn diagram.

The differential field specifies the changes which need to be made from each point of in order to feel a change in the felt value of the field

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 14

Field Picture

Let us summarize the outlook on differential logic we’ve reached so far.  We’ve been considering a class of operators on universes of discourse, each of which takes us from considering one universe of discourse to considering a larger universe of discourse   An operator of that general type, namely, acts on each proposition of the source universe to produce a proposition of the target universe

The operators we’ve examined so far are the enlargement or shift operator and the difference operator   The operators and act on propositions in that is, propositions of the form which amount to propositions about the subject matter of and they produce propositions of the form which amount to propositions about specified collections of changes conceivably occurring in

At this point we find ourselves in need of visual representations, suitable arrays of concrete pictures to anchor our more earthy intuitions and help us keep our wits about us as we venture into ever more rarefied airs of abstraction.

One good picture comes to us by way of the field concept.  Given a space a field of a specified type over is formed by associating with each point of an object of type   If that sounds like the same thing as a function from to the space of things of type — it is nothing but — and yet it does seem helpful to vary the mental images and take advantage of the figures of speech most naturally springing to mind under the emblem of the field idea.

In the field picture a proposition becomes a scalar field, that is, a field of values in

For example, consider the logical conjunction shown in the following venn diagram.

Each of the operators takes us from considering propositions here viewed as scalar fields over to considering the corresponding differential fields over analogous to what in real analysis are usually called vector fields over

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Differential Logic • 13

Transforms Expanded over Ordinary and Differential Variables

Two views of how the difference operator acts on the set of sixteen functions are shown below.  Table A5 shows the expansion of over the set of ordinary variables and Table A6 shows the expansion of over the set of differential variables.

Difference Map Expanded over Ordinary Variables

Difference Map Expanded over Differential Variables

Resources

• Logic Syllabus
• Minimal Negation Operator
• Survey of Differential Logic
• Survey of Animated Logical Graphs

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon (1) (2)
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

Higher Order Sign Relations • Discussion 1
• https://inquiryintoinquiry.com/2025/03/27/higher-order-sign-relations-discussion-1-a/

Re: FB | Charles S. Peirce Society • John Corcoran
• https://www.facebook.com/groups/peircesociety/posts/1768975423238442/

Questions about the proper treatment of use and mention from the standpoint of Peirce’s theory of signs came up recently in discussions on Facebook. In pragmatic semiotics the trade‑off between “signs-of-objects” and “signs-as-objects” opens up the wider space of Higher Order Sign Relations. In previous work on Inquiry Driven Systems I introduced the subject in the following way.

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections. They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations. The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.

References —

John Corcoran
• https://johncorcoran.academia.edu/

Schemata : The Concept of Schema in the History of Logic
• https://www.academia.edu/12691868/SCHEMATA_THE_CONCEPT_OF_SCHEMA_IN_THE_HISTORY_OF_LOGIC

Use And Mention, Use Without Mention, Mention Without Use
• https://www.academia.edu/s/ea64a3484e/schemata#comment_525151

Resources —

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Inquiry #Logic #Mathematics #Reflection
#Semiotics #SignRelations #HigherOrderSignRelations
#InquiryDrivenSystems #ReflectiveInterpretiveFrameworks
#Arithmetization #GödelNumbers #Quotation #UseAndMention

Higher Order Sign Relations • 1
• https://inquiryintoinquiry.com/2025/03/22/higher-order-sign-relations-1-a/

Higher Order Sign Relations • Introduction —

When interpreters reflect on their use of signs they require an appropriate technical language in which to pursue their reflections. They need signs referring to sign relations, signs referring to elements and components of sign relations, and signs referring to properties and classes of sign relations. The orders of signs developing as reflection evolves can be organized under the heading of “higher order signs” and the reflective sign relations involving them can be referred to as “higher order sign relations”.

Some years ago I was formatting my old dissertation proposal on Inquiry Driven Systems for the web when the subject of “signs about signs” arose on the Peirce List. It called to mind the part of my document on Higher Order Sign Relations, on which basis Reflective Interpretive Frameworks are constructed, and the introduction to which begins as above.

Resources —

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

Reflective Interpretive Frameworks
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_10#Reflective_Interpretive_Frameworks

Higher Order Sign Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_12#Higher_Order_Sign_Relations

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Inquiry #Logic #Mathematics #Reflection
#Semiotics #SignRelations #HigherOrderSignRelations
#InquiryDrivenSystems #ReflectiveInterpretiveFrameworks

Theory and Therapy of Representations • 5
• https://inquiryintoinquiry.com/2025/02/25/theory-and-therapy-of-representations-5-b/

Re: R.J. Lipton and K.W. Regan • Legal Complexity
• https://rjlipton.com/2022/09/04/legal-complexity/

❝I do not pretend to understand the moral universe;
the arc is a long one, my eye reaches but little ways;
I cannot calculate the curve and complete the figure by
the experience of sight; I can divine it by conscience.
And from what I see I am sure it bends towards justice.❞

🙞 Theodore Parker
• https://web.archive.org/web/20200302045624/https://books.google.com/books?id=eHgYAAAAYAAJ&pg=PA48#v=onepage&q&f=false

The arc of the moral universe may bend toward justice — there's hope it will.
For the logic of laws to converge on justice may take some doing on our part.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Theory and Therapy of Representations • 4
• https://inquiryintoinquiry.com/2025/02/24/theory-and-therapy-of-representations-4-b/

Re: Ontolog Forum • Paola Di Maio
• https://groups.google.com/g/ontolog-forum/c/Ek_7cCCyFkQ/m/qI0kQv4UAgAJ

JA: What are the forces distorting our representations of what's observed, what's expected, and what's intended?

PDM: The short answer is — the force behind all distortions is our own unenlightened mind, and all the shortfalls this comes with.

I think that's true, we have to keep reflecting on the state of our personal enlightenments. If we can do that without losing our heads and our systems thinking caps, there will be much we can do to promote the general Enlightenment of the State.

On both personal and general grounds we have a stake in the projects of self‑governing systems — whether it is possible for them to exist and what it takes for them to thrive in given environments. Systems on that order have of course been studied from many points of view and at many levels of organization. Whether we address them under the names of adaptive, cybernetic, error-correcting, intelligent, or optimal control systems they all must be capable to some degree of learning, reasoning, and self‑guidance.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Differential Logic
• https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Theory and Therapy of Representations • 3.2
• https://inquiryintoinquiry.com/2025/02/23/theory-and-therapy-of-representations-3-b/

Scene 2. Theory and Therapy of Representations • 1
• https://inquiryintoinquiry.com/2025/02/21/theory-and-therapy-of-representations-1-b/

Statistics were originally the data a ship of state needed for stationkeeping and staying on course. The Founders of the United States, like the Cybernauts of the Enlightenment they were, engineered a ship of state with checks and balances and error-controlled feedbacks for the sake of representing both reality and the will of the people. In that connection Max Weber saw how a state's accounting systems are intended as representations of realities its crew and passengers must observe or perish.

That brings us to Question 2 —

• What are the forces distorting our representations of what's observed, what's expected, and what's intended?

Resources ─

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Pragmatic Theory Of Truth
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Theory and Therapy of Representations • 3.1
• https://inquiryintoinquiry.com/2025/02/23/theory-and-therapy-of-representations-3-b/

Representation is a concept we find at the intersection of cybernetics, epistemology, logic, mathematics, psychology, and sociology. In my studies it led me from math to psych and back again, with sidelong glances at the history of democratic governance. Its time come round again, I find myself returning to the scenes of two recurring questions.

Scene 1. Pragmatic Truth • Discussion 18
• https://inquiryintoinquiry.com/2019/11/14/pragmatic-truth-discussion-18/

We do not live in axiom systems. We do not live encased in languages, formal or natural. There is no reason to think we will ever have exact and exhaustive theories of what's out there, and the truth, as we know, is “out there”. Peirce understood there are more truths in mathematics than are dreamt of in logic — and Gödel’s realism should have put the last nail in the coffin of logicism — but some ways of thinking just never get a clue.

That brings us to Question 1 —

• What are formalisms and all their embodiments in brains and computers good for?

Resources ─

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Pragmatic Theory Of Truth
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Theory and Therapy of Representations • 2
• https://inquiryintoinquiry.com/2025/02/22/theory-and-therapy-of-representations-2-b/

In a complex society, people making decisions and taking actions at places remote from you have the power to affect your life in significant ways. Those people govern your life, they are your government, no matter what spheres of influence they inhabit, private or public. The only way you get a choice in that governance is if there are paths of feedback permitting you to affect the life of those decision makers and action takers in significant ways. That is what accountability, response-ability, and representative government are all about.

Naturally, some people are against that.

In the United States there has been a concerted campaign for as long as I can remember — but even more concerted since the Reagan Regime — to get the People to abdicate their hold on The Powers That Be and just let some anonymous corporate entity send us the bill after the fact. They keep trying to con the People into thinking they can starve the beast, to limit government, when what they are really doing is feeding the beast of corporate control, weakening their own power over the forces that govern their lives.

That is the road to perdition as far as responsible government goes. There is not much of anything one leader or one administration can do unsupported if the People do not constantly demand a government of, by, and for the People.

Resource ─

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Theory and Therapy of Representations • 1
• https://inquiryintoinquiry.com/2025/02/21/theory-and-therapy-of-representations-1-b/

❝Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors?❞

─ Plato • Alcibiades 135 A

Statistics were originally the data a ship of state needed for stationkeeping and staying on course. The Founders of the United States, like the Cybernauts of the Enlightenment they were, engineered a ship of state with checks and balances and error‑controlled feedbacks for the sake of representing both reality and the will of the people. In that connection Max Weber saw how a state's accounting systems are intended as representations of realities its crew and passengers must observe or perish.

The question for our time is —

• What are the forces distorting our representations of what's observed, what's expected, and what's intended?

Repercussions ─

The Place Where Three Wars Meet
• https://inquiryintoinquiry.com/2012/06/21/the-place-where-three-wars-meet/

Resource ─

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

#AdaptiveSystems #Cybernetics #SystemsTheory #Governance #Democracy
#Plato #Peirce #MaxWeber #Accountability #Representation #Statistics
#Inquiry #InquiryDrivenSystems #Observation #Expectation #Intention

Basal Ingredients Of Society • ℞
• https://inquiryintoinquiry.com/2025/02/20/basal-ingredients-of-society-%e2%84%9e-a/

❝THE SOCIAL COMPACT❞

❝If then we discard from the social compact what is not of its essence, we shall find that it reduces itself to the following terms:

❝“Each of us puts his person and all his power in common under the supreme direction of the general will, and, in our corporate capacity, we receive each member as an indivisible part of the whole.”❞

Reference —

Jean Jacques Rousseau, “The Social Contract”, G.D.H. Cole (trans.), Great Books of The Western World, Volume 38.

#AdaptiveSystems #Cybernetics #Democracy #Governance
#Inquiry #InquiryDrivenSystems #LearningOrganizations
#Reciprocity #Rousseau #SocialCompact #Sustainability

Basal Ingredients Of Society • Prologue
• https://inquiryintoinquiry.com/2025/02/18/basal-ingredients-of-society-prologue-a/

I settled on the acronym BIOS to suggest the vital elements of life in society, a life in association with others, and not just any association but one whose flickers of life are sustained for more than a few vicissitudes of history. Sustainability in that life requires democracy, a society based on a distinctive form of social compact.

• https://www.academia.edu/community/54MZbO
• https://bsky.app/profile/inquiryintoinquiry.bsky.social/post/3lihriaerw224
• https://www.researchgate.net/post/Basal_Ingredients_Of_Society

#AdaptiveSystems #Cybernetics #Democracy #Governance
#Inquiry #InquiryDrivenSystems #LearningOrganizations
#Reciprocity #Rousseau #SocialCompact #Sustainability

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

• Logic Syllabus
• Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

Pragmatic Truth • 3.2
• https://inquiryintoinquiry.com/2024/07/12/pragmatic-truth-3/

Truth Predicates —

One of the first questions to be asked in this setting concerns the relationship between the significant performance and its reflective critique. If one expresses oneself in a particular fashion, and someone says “that’s true”, is there anything useful at all to be said in general terms about the relationship between those two acts? For instance, does the critique add value to the expression criticized, does it say something significant in its own right, or is it but an insubstantial echo of the original sign?

Resources —

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Pragmatic Maxim
• https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-a/

Truth Theory
• https://oeis.org/wiki/Truth_theory

Pragmatic Theory Of Truth • Document History
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth#Document_history

Correspondence Theory Of Truth
• https://oeis.org/wiki/Correspondence_Theory_Of_Truth

#Peirce #Logic #Inquiry #Truth #PragmaticTruth #TruthTheory #Semiotics #Meaning
#JohnDewey #WilliamJames #PragmaticMaxim #Pragmatism #InquiryDrivenSystems

Pragmatic Truth • 3.1
• https://inquiryintoinquiry.com/2024/07/12/pragmatic-truth-3/

Truth Predicates —

An inquiry into the character of truth generally begins with the idea of an informative, meaningful, or significant element, the goodness of whose information, meaning, or significance may be put in question and needs to be evaluated. Depending on context, the element may be called an artefact, expression, image, impression, lyric, mark, performance, picture, sentence, sign, string, symbol, text, thought, token, utterance, word, work, and so on. However that may be, one has the task of judging whether the bearers of information, meaning, or significance are indeed truth‑bearers or not. That judgment is typically expressed in the form of a specific “truth predicate”, whose positive application to a sign, or so on, asserts the truth of the sign.

Considered within the broadest horizon, there is little reason to imagine the process of judging a work, which leads to a predication of false or true, is necessarily amenable to formalization, and that task may always remain what is commonly called a judgment call. But there are many well-circumscribed domains where it is useful to consider disciplined forms of evaluation and the observation of those limits allows for the institution of what is called a “method” of judging truth and falsity.

Resources —

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Pragmatic Maxim
• https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-a/

Truth Theory
• https://oeis.org/wiki/Truth_theory

Pragmatic Theory Of Truth
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth

Correspondence Theory Of Truth
• https://oeis.org/wiki/Correspondence_Theory_Of_Truth

#Peirce #Logic #Inquiry #Truth #PragmaticTruth #TruthTheory
#InquiryDrivenSystems #PragmaticMaxim #Pragmatism #Semiotics

Pragmatic Truth • 2
• https://inquiryintoinquiry.com/2024/07/10/pragmatic-truth-2/

Truth as the Good of Logic —

Pragmatic theories of truth enter on a stage set by the philosophies of former ages, with special reference to the Ancient Greeks, the Scholastics, and Immanuel Kant. Recalling a few elements of that background can provide valuable insight into the play of ideas as they have developed up through our time. Because pragmatic ideas about truth are often confused with a number of quite distinct notions it is useful say a few words about those other theories and to highlight the points of significant contrast.

In one classical formulation, truth is defined as the good of logic, where logic is classed as a normative science, in other words, an inquiry into a good or value which seeks to arrive at knowledge of it and the means to achieve it. In that view, truth cannot be discussed to much effect outside the context of inquiry, knowledge, and logic, all very broadly conceived.

Resources —

Logic Syllabus
• https://inquiryintoinquiry.com/logic-syllabus/

Pragmatic Maxim
• https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-a/

Truth Theory
• https://oeis.org/wiki/Truth_theory

Pragmatic Theory Of Truth • Document History
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth
• https://oeis.org/wiki/Pragmatic_Theory_Of_Truth#Document_history

Correspondence Theory Of Truth
• https://oeis.org/wiki/Correspondence_Theory_Of_Truth

#Peirce #Logic #Inquiry #Truth #PragmaticTruth #TruthTheory #Semiotics #Meaning
#JohnDewey #WilliamJames #PragmaticMaxim #Pragmatism #InquiryDrivenSystems

Constraints and Indications • 2
• https://inquiryintoinquiry.com/2024/07/04/constraints-and-indications-2-a/

Coping with collaboration, communication, context, integration, interoperability, perspective, purpose, and the reality of the information dimension demands a transition from conceptual environments bounded by dyadic relations to those informed by triadic relations, especially the variety of triadic sign relations employed by pragmatic semiotics.

Along the lines of my first post on this topic I am presently concerned with the logical and mathematical requirements of dealing with constraints but when it comes to the constraints involved in communicating across cultural and disciplinary barriers I could recommend a paper Susan Awbrey and I wrote for a conference devoted to those very issues.

Conference Presentation —

Awbrey, S.M., and Awbrey, J.L. (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.
• https://cspeirce.com/menu/library/aboutcsp/awbrey/integrat.htm

Published Paper —

Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.
• https://journals.sagepub.com/doi/abs/10.1177/1350508401082013
• https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

#Peirce #Logic #Semiotics #Indication #Inference #Information #Inquiry
#Ashby #Cybernetics #Constraint #Control #Regulation #RequisiteVariety
#AdaptiveSystems #IntelligentSystems #InquiryDrivenSystems #Pragmatics

Constraints and Indications • 1.2
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

Re: Peirce List • Kaina Stoicheia and the Symbol Grounding Problem
• https://web.archive.org/web/20121231182129/http://comments.gmane.org/gmane.science.philosophy.peirce/9165

Reference —

• Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.

Resources —

Survey of Cybernetics
• https://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Pragmatic Semiotic Information
• https://inquiryintoinquiry.com/2024/03/01/survey-of-pragmatic-semiotic-information-8/

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems #PragmaticSemioticInformation
#Constraint #ControlSystems #Indication #Information #Inquiry #IntelligentSystems
#AdaptiveSystems #ErrorControlledRegulation #Feedback #SystemsTheory #Uncertainty
#Determination #Intentionality #Learning #Reasoning #SemioticInformation #Semiotics

Constraints and Indications • 1.1
• https://inquiryintoinquiry.com/2024/07/02/constraints-and-indications-1-a/

The system‑theoretic concept of “constraint” is one that unifies a manifold of other notions — definition, determination, habit, information, law, predicate, regularity, and so on. Indeed, it is often the best way to understand the entire complex of concepts.

Entwined with the concept of “constraint” is the concept of “information”, the power signs bear to reduce uncertainty and advance inquiry. Asking what consequences those ideas have for Peirce’s theory of triadic sign relations led me some years ago to the thoughts recorded on the following page.

Pragmatic Semiotic Information
• https://oeis.org/wiki/Pragmatic_Semiotic_Information

Here I am thinking of the concept of constraint that constitutes one of the fundamental ideas of classical cybernetics and mathematical systems theory.

For example, here is how W. Ross Ashby introduces the concept of constraint in his Introduction to Cybernetics (1956).

❝A most important concept, with which we shall be much concerned later, is that of “constraint”. It is a relation between two sets, and occurs when the variety that exists under one condition is less than the variety that exists under another. Thus, the variety of the human sexes is 1 bit; if a certain school takes only boys, the variety in the sexes within the school is zero; so as 0 is less than 1, constraint exists.❞ (1964 ed., p. 127).

At its simplest, then, constraint is an aspect of the subset relation.

The objective of an agent, organism, or similar regulator is to keep within its viable region, a particular subset of its possible state space. That is the constraint of primary interest to the agent.

#Peirce #Ashby #Cybernetics #InquiryDrivenSystems

Survey of Inquiry Driven Systems • 6
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

This is a Survey of work in progress on Inquiry Driven Systems, material I plan to refine toward a more systematic treatment of the subject.

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

Please follow the above link for the full set of resources.
Articles treating the more central ideas are linked below.

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

Background —

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

Functional Logic • Quantification Theory
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Quantification_Theory

Functional Logic • Higher Order Propositions
• https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Higher_Order_Propositions

Developments —

Inquiry Driven Systems • Inquiry Fields
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Inquiry_Fields

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

Applications —

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

Interpretation as Action • The Risk of Inquiry
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_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

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

#Peirce #Inquiry #InquiryDrivenSystems #InformationStateSpace
#Semiotics #SignRelations #Interpretation #SystemsEngineering
#Abduction #Deduction #Induction #Analogy #DynamicsOfInquiry

Survey of Cybernetics • 4
• http://inquiryintoinquiry.com/2024/01/25/survey-of-cybernetics-4/

❝Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors?❞

— Plato • Alcibiades • 135 A

This is a Survey of blog posts relating to Cybernetics. It includes the selections from Ashby's “Introduction to Cybernetics” and the comments on them I've posted so far, plus two series of reflections on the governance of social systems in light of cybernetic and semiotic principles.

Please follow the above link for the full set of resources. By way of a selection, links for the series on “Basal Ingredients Of Society” are given below.

Basal Ingredients Of Society (BIOS) —

Prologue
• https://inquiryintoinquiry.com/2015/09/01/basal-ingredients-of-society-prologue/

Comments
1 https://inquiryintoinquiry.com/2015/09/02/basal-ingredients-of-society-comment-1/
2 https://inquiryintoinquiry.com/2015/09/03/basal-ingredients-of-society-comment-2/
3 https://inquiryintoinquiry.com/2015/09/04/basal-ingredients-of-society-comment-3/
4 https://inquiryintoinquiry.com/2015/09/06/basal-ingredients-of-society-comment-4/
5 https://inquiryintoinquiry.com/2015/09/06/basal-ingredients-of-society-comment-5/
6 https://inquiryintoinquiry.com/2015/09/07/basal-ingredients-of-society-comment-6/
7 https://inquiryintoinquiry.com/2015/09/07/basal-ingredients-of-society-comment-7/

Prescription
• https://inquiryintoinquiry.com/2015/09/10/basal-ingredients-of-society-%e2%84%9e/

#Cybernetics #Information #Control #Governance #Plato #Ashby
#Peirce #Semiotics #Semiosis #Inquiry #InquiryDrivenSystems

Survey of Definition and Determination • 3
• https://inquiryintoinquiry.com/2024/01/24/survey-of-definition-and-determination-3/

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from signs and scientific inquiry to logic and information theory.

Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as Peirce used them in his logic and semiotics but as researchers in areas as diverse as computer science, cybernetics, physics, and systems science would find themselves forced to reconsider the concepts in later years. That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination. There are copies of those selections at the following sites.

Collection Of Source Materials
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS

Excerpts on Definition
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Definition

Excerpts on Determination
• https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Determination

What follows is a Survey of blog and wiki posts on Definition and Determination, with a focus on the part they play in Peirce’s interlinked theories of signs, information, and inquiry. In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force when we view the overarching concept of constraint from an information-theoretic point of view, as Peirce did beginning in the 1860s.

#Peirce #Logic #Definition #Determination #DifferentialLogic
#Inference #Information #Inquiry #Semiotics #SignRelations
#AI #Cybernetics #IntelligentSystems #InquiryDrivenSystems

In the Way of Inquiry • Objections to Reflexive Inquiry 3
• https://inquiryintoinquiry.com/2023/02/05/in-the-way-of-inquiry-objections-to-reflexive-inquiry-a/

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.

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

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

#Peirce #Inquiry #InquiryIntoInquiry #InquiryDrivenSystems
#Recursion #Reflection #Refraction #InformationResistance
#Interruption #Obstruction #Reconstruction #Reconstitution