Theory and Therapy of Representations • 5

Posted on February 25, 2025 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • 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

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

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Theory and Therapy of Representations • 4

Posted on February 24, 2025 by Jon Awbrey

Re: Theory and Therapy of Representations • 3
Re: Ontolog Forum • Paola Di Maio

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

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Theory and Therapy of Representations • 3

Posted on February 23, 2025 by Jon Awbrey

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

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?

Scene 2.  Theory and Therapy of Representations • 1

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

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Theory and Therapy of Representations • 2

Posted on February 22, 2025 by Jon Awbrey

December 19, 2011

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

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Theory and Therapy of Representations • 1

Posted on February 21, 2025 by Jon Awbrey
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

Resource

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Basal Ingredients Of Society • ℞

Posted on February 20, 2025 by Jon Awbrey

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.

Resource

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Basal Ingredients Of Society • Prologue

Posted on February 18, 2025 by Jon Awbrey

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.

Resource

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Tenacity, Authority, Plausibility, Inquiry

Posted on February 14, 2025 by Jon Awbrey

Re: Peter Cameron • Mathematics and Logic

My favorite polymathematician, Charles Sanders Peirce, gave a fourfold classification of what he called “methods of fixing belief”, or “settling opinion”, most notably and seminally in his paper, “The Fixation of Belief” (1877).  Adjusting his nomenclature very slightly, if only for the sake of preserving a mnemonic rhyme scheme, we may refer to his four types as Tenacity, Authority, Plausibility (à priori pleasing praiseworthiness), and full-fledged Scientific Inquiry.

Reference

  • Peirce, C.S. (1877), “The Fixation of Belief”, Popular Science Monthly 12, 1–15.  Online.

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Interpreter and Interpretant • Selection 10

Posted on February 11, 2025 by Jon Awbrey

Transfer

Returning to the scene of Dewey’s “Sign of Rain” example, let’s continue examining how the transfer of knowledge through the analogy of experience works in that case.

By way of a recap, we began by considering a fragment K_\mathrm{pres} of the reasoner’s knowledge base which is logically equivalent to a conjunction of two rules.

K_\mathrm{pres} \Leftrightarrow (B \Rightarrow A) \land (B \Rightarrow D).

K_\mathrm{pres} may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.

Next we found it convenient to express all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.

  • Let E_\mathrm{past} be the chosen set of experiences, or the circumstances in mind under “past experience”.
  • Let E_\mathrm{poss} be the collective set of experiences, or the prospective total of possible circumstances.
  • Let E_\mathrm{pres} be the current experience, or the circumstances immediately present to the reasoner.

If we think of the knowledge base K_\mathrm{pres} as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.

Figure 4 shows the subsumption relations involved in the analogy of experience.

Analogy of Experience
\text{Figure 4. Analogy of Experience}

In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.

  • Step 1 is Inductive, abstracting a Rule from a Case and a Fact.

\begin{array}{lll} E_\mathrm{past} \Rightarrow E_\mathrm{poss}, & \text{Chosen events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{past} \Rightarrow K_\mathrm{pres}, & \text{Chosen events support the Knowledge regime.} & \text{Fact} \\ \hline E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \end{array}

  • Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.

\begin{array}{lll} E_\mathrm{pres} \Rightarrow E_\mathrm{poss}, & \text{Current events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \\ \hline E_\mathrm{pres} \Rightarrow K_\mathrm{pres}, & \text{Current events support the Knowledge regime.} & \text{Fact} \end{array}

References

  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).
  • Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA.  Reprinted (1991), Prometheus Books, Buffalo, NY.  Online.

Resources

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Interpreter and Interpretant • Selection 9

Posted on January 27, 2025 by Jon Awbrey

Transfer

Let’s examine how the transfer of knowledge through the analogy of experience works in the case of Dewey’s “Sign of Rain” example.

For concreteness, consider a fragment K_\mathrm{pres} of the reasoner’s knowledge base which is logically equivalent to a conjunction of two rules.

K_\mathrm{pres} \Leftrightarrow (B \Rightarrow A) \land (B \Rightarrow D).

K_\mathrm{pres} may be thought of as a piece of knowledge or item of information allowing for the possibility of certain conditions, expressed in the form of a logical constraint on the present universe of discourse.

It is convenient to have the option of expressing all logical statements in terms of their models, that is, in terms of the primitive circumstances or elements of experience over which they hold true.

  • Let E_\mathrm{past} be the chosen set of experiences, or the circumstances in mind under “past experience”.
  • Let E_\mathrm{poss} be the collective set of experiences, or the prospective total of possible circumstances.
  • Let E_\mathrm{pres} be the current experience, or the circumstances immediately present to the reasoner.

If we think of the knowledge base K_\mathrm{pres} as referring to the “regime of experience” over which it is valid, then the sets of models involved in the analogy may be ordered according to the relationships of set inclusion or logical implication existing among them.

In logical terms, the analogy of experience proceeds by inducing a Rule about the validity of a current knowledge base and then by deducing a Fact, the applicability of that knowledge base to a current experience.

  • Step 1 is Inductive, abstracting a Rule from a Case and a Fact.

\begin{array}{lll} E_\mathrm{past} \Rightarrow E_\mathrm{poss}, & \text{Chosen events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{past} \Rightarrow K_\mathrm{pres}, & \text{Chosen events support the Knowledge regime.} & \text{Fact} \\ \hline E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \end{array}

  • Step 2 is Deductive, admitting a Case to a Rule and arriving at a Fact.

\begin{array}{lll} E_\mathrm{pres} \Rightarrow E_\mathrm{poss}, & \text{Current events fairly sample Collective events.} & \text{Case} \\ E_\mathrm{poss} \Rightarrow K_\mathrm{pres}, & \text{Collective events support the Knowledge regime.} & \text{Rule} \\ \hline E_\mathrm{pres} \Rightarrow K_\mathrm{pres}, & \text{Current events support the Knowledge regime.} & \text{Fact} \end{array}

References

  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).
  • Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA.  Reprinted (1991), Prometheus Books, Buffalo, NY.  Online.

Resources

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cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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