Forgetfulness Of Purpose • 5

Recall the game between R and D determined by the following data.

\begin{array}{cc|ccc}  \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt]  & & & R & \\  & & \alpha & \beta & \gamma \\  \hline    & 1 & b & a & c \\  D & 2 & a & c & b \\    & 3 & c & b & a  \end{array}

Here is Ashby’s analysis of how it plays out.

Examination of the table soon shows that with this particular table R can win always.  Whatever value D selects first, R can always select a Greek letter that will give the desired outcome.  Thus if D selects 1, R selects β;  if D selects 2, R selects α;  and so on.  In fact, if R acts according to the transformation

\begin{array}{cccc}  & 1 & 2 & 3 \\  \downarrow & & & \\  & \beta & \alpha & \gamma  \end{array}

then he can always force the outcome to be a.

R‘s position, with this particular table, is peculiarly favourable, for not only can R always force a as the outcome, but he can as readily force, if desired, b or c as the outcome.  R has, in fact, complete control of the outcome.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory | Tagged , , , , , , , , | 2 Comments

Forgetfulness Of Purpose • 4

Ashby now invites us to consider a series of games, beginning as follows.

11/3.   Play and outcome.  Let us therefore forget all about regulation and simply suppose that we are watching two players, R and D, who are engaged in a game.  We shall follow the fortunes of R, who is attempting to score an a.  The rules are as follows.  They have before them Table 11/3/1, which can be seen by both:

\begin{array}{cc|ccc}  \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt]  & & & R & \\  & & \alpha & \beta & \gamma \\  \hline    & 1 & b & a & c \\  D & 2 & a & c & b \\    & 3 & c & b & a  \end{array}

D must play first, by selecting a number, and thus a particular row.  R, knowing this number, then selects a Greek letter, and thus a particular column.  The italic letter specified by the intersection of the row and column is the outcome.  If it is an a, R wins;  if not, R loses.

I’ll pause the play here and give readers a chance to contemplate strategies.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory | Tagged , , , , , , , , | 2 Comments

Forgetfulness Of Purpose • 3

Here is the first part of Ashby’s setup for the schematic example I had in mind.

Requisite Variety

11/1.   In the previous chapter we considered regulation from the biological point of view, taking it as something sufficiently well understood.  In this chapter we shall examine the process of regulation itself, with the aim of finding out exactly what is involved and implied.  In particular we shall develop ways of measuring the amount or degree of regulation achieved, and we shall show that this amount has an upper limit.

11/2.   The subject of regulation is very wide in its applications, covering as it does most of the activities in physiology, sociology, ecology, economics, and much of the activities in almost every branch of science and life.  Further, the types of regulator that exist are almost bewildering in their variety.  One way of treating the subject would be to deal seriatim with the various types;  and chapter 12 will, in fact, indicate them.  In this chapter, however, we shall be attempting to get at the core of the subject — to find what is common to all.

What is common to all regulators, however, is not, at first sight, much like any particular form.  We will therefore start anew in the next section, making no explicit reference to what has gone before.  Only after the new subject has been sufficiently developed will we begin to consider any relation it may have to regulation.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory | Tagged , , , , , , , , | 1 Comment

Forgetfulness Of Purpose • 2

I had planned to get down to brass tacks as quickly as possible, with an object example from Ashby’s Cybernetics that made an impression on me at an early stage in my thinking about intelligent systems.  But while I was looking for that my eye fell on on another passage that so well articulates one of the deepest roots of scientific reasoning that I could not resist reciting it here.

Quantity of Variety

7/1.   In Part I we considered the main properties of the machine, usually with the assumption that we had before us the actual thing, about which we would make some definite statement, with reference to what it is doing here and now.  To progress in cybernetics, however, we shall have to extend our range of consideration.  The fundamental questions in regulation and control can be answered only when we are able to consider the broader set of what it might do, when “might” is given some exact specification.

Throughout Part II, therefore, we shall be considering always a set of possibilities.  The study will lead us into the subjects of information and communication, and how they are coded in their passages through mechanism.  This study is essential for the thorough understanding of regulation and control.  We shall start from the most elementary or basic considerations possible.

7/2.   A second reason for considering a set of possibilities is that science is little interested in some fact that is valid only for a single experiment, conducted on a single day;  it seeks always for generalisations, statements that shall be true for all of a set of experiments, conducted in a variety of laboratories and on a variety of occasions.  Galileo’s discovery of the law of the pendulum would have been of little interest had it been valid only for that pendulum on that afternoon.  Its great importance is due precisely to the fact that it is true over a great range of space and time and materials.  Science looks for the repetitive.

7/3.   This fact, that it is the set that science refers to, is often obscured by a manner of speech.  “The chloride ion …”, says the lecturer, when clearly he means his statement to apply to all chloride ions.  So we get references to the petrol engine, the growing child, the chronic drunkard, and to other objects in the singular, when the reference is in fact to the set of all such objects.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
Posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory | Tagged , , , , , , , , | 1 Comment

Forgetfulness Of Purpose • 1

Naturally I had purposes and reflected on my purposes for as long as I can remember but I don’t think I thought about the concept of purpose in a systematic way until I began taking courses on cybernetics and systems theory in college.  So I’ll try beginning this anamnesis with the readings that stick in my memory from those times.

Posted in Anamnesis, Ashby, C.S. Peirce, Cybernetics, Memory, Peirce, Pragmata, Purpose, Systems Theory | Tagged , , , , , , , , | 3 Comments

Forgetfulness Of Purpose

Posted in Uncategorized | Tagged | 1 Comment

You Say “Réseau” • I Say “Rousseau” • 3

Re: Michael HarrisMy RéseauNetworks in Action in French Economics

Readers of Peirce know the concept of community is integral to his treatment of inquiry, interpretation, knowledge, reality, and truth.  The following statement is a nice résumé of all the main points.

The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you.  Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a community, without definite limits, and capable of an indefinite increase of knowledge.  (CP 5.311).

Peirce, C.S. (1868), “Some Consequences of Four Incapacities”, Journal of Speculative Philosophy 2 (1868), 140–157. Reprinted (Collected Papers 5.264–317), (Writings 2, 211–242), (Essential Peirce 1, 28–55).  Online.

More casual or selective readers may take Peirce for a pioneer in the sociology of knowledge and jump to the conclusion his social theory is tantamount to a “coherence theory” or a “consensus theory” of truth.  But a leap like that underestimates the gulf between actual finite communities and what is actually a regulative ideal, a community without definite limits capable of an indefinite increase of knowledge.  The relation between the two is like that between an empirical sample and a theoretical population of unknown extent.

Posted in C.S. Peirce, Community, Community of Inquiry, Community of Interpretation, Inquiry, Manifolds, Mathematics, Michael Harris, Networks, Réseau, Reality, Rousseau, Semiotics, Social Compact, Social Networks, Sociology | Tagged , , , , , , , , , , , , , , , | Leave a comment

You Say “Réseau” • I Say “Rousseau” • 2

Re: Michael HarrisMy RéseauNetworks in Action in French Economics

No true Peircean could fail to be reminded of the following statement whenever the subjects of community or reality come up.

The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you.  Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of an indefinite increase of knowledge.  (Peirce 1868, CP 5.311).

Reference

Peirce, C.S. (1868), “Some Consequences of Four Incapacities”, Journal of Speculative Philosophy 2 (1868), 140–157. Reprinted (Collected Papers 5.264–317), (Writings 2, 211–242), (Essential Peirce 1, 28–55).  Online.

Posted in Community, Community of Inquiry, Community of Interpretation, Inquiry, Manifolds, Mathematics, Michael Harris, Networks, Peirce, Reality, Rousseau, Semiotics, Social Compact, Social Networks, Society | Tagged , , , , , , , , , , , , , , | 2 Comments

You Say “Réseau” • I Say “Rousseau” • 1

Re: Michael HarrisMy RéseauNetworks in Action in French Economics

The above two posts by Michael Harris sparked a series of reflections that I have yet to reign in fully but I thought I might pause a moment to record a scintilla or two …

But first a bit of verse, if you’re not averse —

U Say Réseau, I Say Rousseau,
Let’s Call The Whole Thing 1.

Social compacts come and go,
And may converge to 1 1 day,
1 that comes and never goes.
So reap again what u réseau,
Until u reap what regrows u.

Posted in Community, Community of Inquiry, Community of Interpretation, Inquiry, Manifolds, Mathematics, Michael Harris, Networks, Peirce, Reality, Rousseau, Semiotics, Social Compact, Social Networks, Society | Tagged , , , , , , , , , , , , , , | Leave a comment

In the Way of Inquiry • Objections to Reflexive Inquiry

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.

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.

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.

cc: Conceptual GraphsCyberneticsLaws of FormMathstodonOntolog
cc: FB | Inquiry Driven SystemsStructural ModelingSystems Science

Posted in Animata, C.S. Peirce, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Semiotics | Tagged , , , , , , | 5 Comments