Pragmatic Semiotic Information • 2

What is information that a sign may bear it?

Three more questions arise at this juncture.

  • How is a sign empowered to contain information?
  • What is the practical context of communication?
  • Why do we care about these bits of information?

A very rough answer to these questions might begin as follows.

Human beings are initially concerned solely with their own lives but then a world obtrudes on their subjective existence and so they find themselves forced to take an interest in the objective realities of its nature.

In pragmatic terms our initial aim, concern, interest, object, or pragma is expressed by the verbal infinitive to live, but the infinitive is soon reified into the derivative substantial forms of nature, reality, the world, and so on.  Against that backdrop we find ourselves cast as the protagonists on a scene of uncertainty.

The situation may be pictured as a juncture from which a manifold of options fan out before us.  It may be an issue of “truth”, “duty”, or “hope”, the last codifying a special type of uncertainty as to what regulative principle has any chance of success, but the chief uncertainty is that we are called on to make a choice and all too often we have very little clue which of the options is most fit to pick.

Just to make up a discrete example, let us suppose the cardinality of the choices before us is a finite integer n, and just to make it fully concrete let us say n = 5.  Figure 1 affords a rough picture of the situation.

Pragmatic Semiotic Information • Figure 1

This pictures a juncture, represented by a node marked ``\texttt{O}", where there are n options for the outcome of a conduct and we have no clue as to which it must be.  In a sense the degree of the node, in this case n = 5, measures the uncertainty we have at that point.

The Figure illustrates the minimal sort of setting in which a sign can make any sense at all.  A sign has significance for an agent, interpreter, or observer because its actualization, its being given or its being present, serves to reduce the uncertainty of a decision the agent has to make, whether it concerns the actions the agent ought to take in order to achieve some objective of interest, or whether it concerns the predicates the agent ought to treat as being true of some object or situation in the world.

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Pragmatic Semiotic Information • 1

Information • What’s it good for?

The good of information is its use in reducing our uncertainty about an issue which comes before us.  But uncertainty comes in many flavors and so the information which serves to reduce uncertainty can be applied in several ways.  The situations of uncertainty human agents commonly find themselves facing have been investigated under many headings, literally for ages, and the categories subtle thinkers arrived at long before the dawn of modern information theory still have their uses in setting the stage of an introduction.

Picking an example of a subtle thinker almost at random, the philosopher‑scientist Immanuel Kant surveyed the questions of human existence within the span of the following three axes.

  • What’s true?
  • What’s to do?
  • What’s to hope?

The third question is a bit too subtle for the present frame of discussion but the first and second are easily recognizable as staking out the two main axes of information theory, namely, the dual dimensions of information and control.  Roughly the same space of concerns is elsewhere spanned by the dual axes of competence and performance, specification and optimization, or just plain knowledge and skill.

A question of what’s true is a descriptive question and there exist what are called descriptive sciences devoted to answering descriptive questions about any domain of phenomena one might care to name.

A question of what’s to do, in other words, what must be done by way of achieving a given aim, is a normative question and there exist what are called normative sciences devoted to answering normative questions about any domain of problems one might care to address.

Since information plays its role on a stage set by uncertainty, a big part of saying what information is will necessarily involve saying what uncertainty is.  There is little chance the vagaries of a word like uncertainty, given the nuances of its ordinary, poetic, and technical uses, can be corralled by a single pen, but there do exist established models and formal theories which manage to address definable aspects of uncertainty and these do have enough uses to make them worth looking into.

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Survey of Pragmatic Semiotic Information • 8

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character but this line of inquiry is more open‑ended than most.  The question is —

What is information and how does it impact the spectrum of activities answering to the name of inquiry?

Setting out on what would become his lifelong quest to explore and explain the “Logic of Science”, C.S. Peirce pierced the veil of historical confusions obscuring the issue and fixed on what he called the “laws of information” as the key to solving the puzzle.

The first hints of the Information Revolution in our understanding of scientific inquiry may be traced to Peirce’s lectures of 1865–1866 at Harvard University and the Lowell Institute.  There Peirce took up “the puzzle of the validity of scientific inference” and claimed it was “entirely removed by a consideration of the laws of information”.

Fast forward to the present and I see the Big Question as follows.  Having gone through the exercise of comparing and contrasting Peirce’s theory of information, however much it yet remains in a rough‑hewn state, with Shannon’s paradigm so pervasively informing the ongoing revolution in our understanding and use of information, I have reason to believe Peirce’s idea is root and branch more general and has the potential, with due development, to resolve many mysteries still bedeviling our grasp of inference, information, and inquiry.

Inference, Information, Inquiry

Pragmatic Semiotic Information

Semiotics, Semiosis, Sign Relations

Sign Relations, Triadic Relations, Relation Theory

  • Blog Series • (1)
    • Discusssions • (1)(2)

Excursions

Blog Dialogs

References

  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”.  Online.
  • 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.  ArchiveJournal.  Online (doc) (pdf).

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Being In Time

I need to be in the state I’m in.
I need to dwell on the indwelling.
I need to unpack the original source,
Too long hidebound by habit of force.

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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 compact and 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.

Anthem

Elements

Background

Blog Series

  • Pragmatic Cosmos • (1)

Blog Dialogs

  • Architectonics of Inquiry • (1)

Developments

Applications

  • Conceptual Barriers to Creating Integrative Universities
    (Abstract) (Online)
  • Interpretation as Action • The Risk of Inquiry
    (Journal) (doc) (pdf)
  • An Architecture for Inquiry • Building Computer Platforms for Discovery
    (Online)
  • Exploring Research Data Interactively • Theme One : A Program of Inquiry
    (Online)

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Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 4

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce.  Particular attention is paid to the way the inferential rudiments combine to form the more complex patterns of analogy and inquiry.

Anthem

Blog Dialogs

Blog Series

Blog Surveys

OEIS Wiki

Ontolog Forum

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Survey of Theme One Program • 6

This is a Survey of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s.  The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning.  I had earlier developed separate programs for basic components of those tasks, namely, 2-level formal language learning and propositional constraint satisfaction, the latter using an extension of C.S. Peirce’s logical graphs as a syntax for propositional logic.  Thus arose the question of how well it might be possible to get “empiricist” and “rationalist” modes of operation to cooperate.  The long-term vision is the design and implementation of an Automated Research Tool able to double as a platform for Inquiry Driven Education.

Wiki Hub

Documentation

Blog Series

Blog Dialogs

Applications

References

  • Awbrey, S.M., and Awbrey, J.L. (May 1991), “An Architecture for Inquiry • Building Computer Platforms for Discovery”, Proceedings of the Eighth International Conference on Technology and Education, Toronto, Canada, pp. 874–875.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (January 1991), “Exploring Research Data Interactively • Developing a Computer Architecture for Inquiry”, Poster presented at the Annual Sigma Xi Research Forum, University of Texas Medical Branch, Galveston, TX.
  • 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.

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Survey of Differential Logic • 7

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.

Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models.  To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

Elements

Blog Series

Architectonics

Applications

Blog Dialogs

Explorations

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Sign Relations, Triadic Relations, Relation Theory • Discussion 12

Re: Sign Relations, Triadic Relations, Relation Theory • 1

A note from a longtime correspondent points out a search of the available texts turns up no use of the plural form “semiotics” by Peirce and just one place where he uses the plural form “Semeiotics”.  That prompts me to make the following excuse for my use or abuse of Peirce’s terms, as the case may be.

Peirce has always been one of my chief resources in the quest to understand how logic and math and science work.  There is much to be gained by getting his distinctive ideas across to active practitioners in those fields.  In doing that I find it better to tweak the words a bit, if that’s what it takes to preserve the idea, than to hallow the words at the risk of losing the idea.

As far as semiotics by any name goes, what seems to work best without too much clanging in modern ears is parsing semiotics in line with words like mathematics and cybernetics, plus we can now use the singular form as the adjective semiotic.

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Sign Relations, Triadic Relations, Relation Theory • 4

For ease of reference, here are two variants of Peirce’s 1902 definition of a sign, which he gives in the process of defining logic.

Selections from C.S. Peirce, “Carnegie Application” (1902)

No. 12.  On the Definition of Logic

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.  Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.  It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.  (NEM 4, 20–21).

No. 12.  On the Definition of Logic [Earlier Draft]

Logic is formal semiotic.  A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C.  This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time.  It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident.  The word “formal” in the definition is also defined.  (NEM 4, 54).

Reference

  • Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.

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