Providence

Posted on December 31, 2012 by Jon Awbrey

Red-breasted robins and brown-speckled starlings
Mobbing the crab-apple tree outside my window,
Stretching their necks for the frozen red berries —
The snow-sprinkled branches saved them for now.

Jon Awbrey
31 Dec 2012

Posted in Verse | Tagged | Leave a comment

Theme One • A Program Of Inquiry 3

Posted on December 31, 2012 by Jon Awbrey

Re: Peirce List • Gary Richmond

The program I wrote for my M.A. in Psych was barely a prototype, a “test of concept”, as they say, but I continued to develop and apply the underlying collection of ideas to a number of concrete problems throughout the ensuing years.

Here is a paper describing the associated program of research Susan Awbrey and I presented at a conference the following year.

  • Awbrey, J.L., and Awbrey, S.M. (August 1990), “Exploring Research Data Interactively. Theme One : A Program of Inquiry”, Proceedings of the Sixth Annual Conference on Applications of Artificial Intelligence and CD-ROM in Education and Training, Society for Applied Learning Technology, Washington, DC, pp. 9–15.  Online.
Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments

Why am I afraid of writing what I know?

Posted on December 31, 2012 by Jon Awbrey

or in a place where it might be understood?

or to a person who might understand it?

Posted in Meditation, Question, Reflection | Tagged , , | Leave a comment

Constraints and Indications • 1

Posted on December 23, 2012 by Jon Awbrey

Re: Peirce List • Christophe Menant • Jon Awbrey • Christophe Menant

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 these 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 following thoughts.

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 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 just 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.

Incidentally, Ashby’s book, in my estimation still the best introduction to classical cybernetics going, is available online in PDF form:

  • Ashby, W.R. (1956), Introduction to Cybernetics, Methuen, London, UK.  Online.
Posted in Adaptive Systems, Artificial Intelligence, Ashby, C.S. Peirce, Constraint, Control, Cybernetics, Determination, Error-Controlled Regulation, Feedback, Indication, Indicator Functions, Information, Inquiry, Inquiry Driven Systems, Intelligent Systems, Intentionality, Learning Theory, Peirce, Semiotic Information, Semiotics, Systems Theory, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Theme One • A Program Of Inquiry 2

Posted on December 21, 2012 by Jon Awbrey

Re: Peirce List • Jerry Chandler

I think I was probably the first person in that particular psychology department to submit a program as a master’s thesis, at any rate they didn’t have regular procedures set up for that kind of thing, so it fell under the cache-all of a “Plan B”.  The department accepted the program, the initial manual, and some work I did applying the program to an “Exploratory Qualitative Analysis of Sequential Observation Data” as sufficient grief for an M.A.

I’m assembling what documentation I have on the following page.

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 1

Posted on December 20, 2012 by Jon Awbrey

Re: Peirce List • Jerry Chandler • Jon Awbrey • Gary Richmond • Christophe Menant

I view psychology, throughout its many branches, as a fascinating and compelling collection of subjects, so much so I spent one of my parallel lives in the 1980s earning a Master’s degree in it, submitting a “Plan B” thesis in the form of a computer program designed to integrate a module for complex sequential learning with a module for propositional constraint satisfaction based on an extension of Peirce’s logical graphs.  I wandered through three universities during that time, taking graduate courses in math, psychology, statistics, and computer science, finally finishing in 1989.

The hot topics of Artificial Intelligence and Cognitive Science from those times have lately enjoyed a revival on the Peirce List, and though it brings me a twinge of seasonal nostalgia now and then to hear those old chestnuts being fired up again, those problems seem to me now as problems existing for and within a peculiar tradition of thought, a tradition of chasing will o’ th’ wisps Peirce side-stepped long before the chase began.

I hear in Peirce a different drummer …

I remember when others heard it, too …

cc: FB | Theme One Program • Laws of Form • Peirce List

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Semiotics, Visualization | Tagged , , , , , , , , , , , , , | 8 Comments

Constants, Inconstants, and Higher Order Propositions

Posted on December 20, 2012 by Jon Awbrey

A question arising on the Foundations Of Math List gives me an opportunity to introduce the subject of higher order propositions, which I think afford a better way to handle the situations of confusion, doubt, obscurity, uncertainty, and vagueness often approached by way of variations in the values assigned to propositions.

Re: FOM | Terminology • Irving Anellis

IA:
My own preference for t-definite, t-indefinite or f-indefinite, and f-definite, as opposed to tautology, contingent, and contradiction lies in allowing application of those terms for truth as well as for validity, for semantic and syntactic uses.

If we start with a universe of discourse X and think of propositions as being (or denoting) functions of the form f : X \to \mathbb{B}, where \mathbb{B} = \{ 0, 1 \}, then what we are charged with is choosing suitable names for higher order propositions of the form m : (X \to \mathbb{B}) \to \mathbb{B}.

The term tautology or 1-definite is true of exactly one f : X \to \mathbb{B}, namely the constant function 1 : X \to \mathbb{B}.

The term contradiction or 0-definite is true of exactly one f : X \to \mathbb{B}, namely the constant function 0 : X \to \mathbb{B}.

The term contingent or indefinite is true of all the functions f : X \to \mathbb{B} which are neither of the above.

Here is a place where I took the trouble to think up names for higher order propositions over a 1-dimensional universe.

I called the contingent propositions either informed or non-uniform.

Posted in Foundations of Mathematics, Higher Order Propositions, Irving Anellis, Logic, Mathematics | Tagged , , , , | Leave a comment

Demonstrative And Otherwise

Posted on December 17, 2012 by Jon Awbrey

I am constantly encountering what I perceive as echoes of Peircean themes in places where acquaintance with or interest in Peirce’s work is slight at best, and that leaves me with a lot of pent up thoughts that I’ve learned through trial and error can’t always be ventilated in the places that stirred them up.

The recent discussion of fuzzy set theory on the Foundations Of Math List is a prime example of that.  I see the questions arising there as falling within a larger question about the proper roles of demonstrative reasoning and non-demonstrative reasoning in the logic of inquiry.

That particular theme has recurred so frequently over the years that I’ve decided to give it a name, “Demonstrative And Otherwise” (DAO), and to start collecting the data of its cases in a more deliberate manner.

Here’s another case I view as falling under the rubric of DAO — it arose on a blog devoted to a fundamental problem in computational complexity.

And here’s a blog post where I began to gather a few reflections that bear on this computational aspect of DAO.

Posted in Abduction, Artificial Intelligence, C.S. Peirce, Computation, Computational Complexity, Cybernetics, Deduction, Induction, Inquiry, Inquiry Driven Systems, Intelligent Systems, Logic, Peirce, Programming, Semiotics | Tagged , , , , , , , , , , , , , , | 2 Comments

Paradigms, Playgrounds, Programmes, Programs

Posted on December 16, 2012 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Mounting Or Solving Open Problems

Comment 1

Sometimes the programme must simply be to keep developing our understanding of the ground on which the mountains rest.

Comment 2

It might be observed that the concept of a research programme is closely related to the concept of a research paradigm, about which much has been written.

Comment 3

As long as we’re brainstorming in a laid back sort of way …

Folks who find propositional logic — and the whole space between zeroth order logic and first order logic — more of a fascinating playground for exploration than a dog run for the questying beast might find it fun to look at the graph-theoretic calculi for propositions and boolean functions that derive from C.S. Peirce’s logical graphs.  There is an extension of Peirce’s tree-form graphs to cactus graphs that presents many interesting possibilities for efficient expression and inference.  And the resulting cactus calculus facilitates the development of differential logic, extending propositional calculus analogous to the way differential calculus extends analytic geometry.

Comment 4

The following primer on differential logic uses the cactus graph syntax to represent propositions (boolean functions $latex f : \mathbb{B}^k \to \mathbb{B}) and the operators on propositions that arise in developing the subject of differential propositional calculus.

The cactus graph syntax for propositional calculus is based on minimal negation operators.

Posted in Uncategorized | Tagged | 1 Comment

Triadic Relations, Intentions, Fuzzy Subsets • Discussion 3

Posted on December 9, 2012 by Jon Awbrey

Re: Peirce List Discussion • Gary Moore • Stefan Berwing

I intend to get back to this subject as soon as possible but the dire political situation in my home state is once again eating up a lot of my time and energy, so I’ll just post a link to what I wanted to discuss next, namely the classical sense of probability from which the modern mathematical formalization evolved, a sense expressed in words like likelihood and likely story and thus bound up with the concepts of analogues, copies, exemplars, icons, images, likenesses, metaphors, models, morphisms, paradigms, similes, simulations, and a host of similar notions.

Resources

Posted in C.S. Peirce, Fuzzy Logic, Fuzzy Sets, Intentional Contexts, Intentional Objects, Intentionality, Intentions, Logic, Logic of Relatives, Lotfi Zadeh, Mathematics, Peirce, Probability, Relation Theory, Semiotics, Triadic Relations | Tagged , , , , , , , , , , , , , , , | Leave a comment