Peircean Semiotics and Triadic Sign Relations • 3

Posted on November 1, 2013 by Jon Awbrey

Having labored mightily to bring out a new edition of my article on sign relations, including material on the pivotal concept of semiotic equivalence relations which had fallen into obscurity elsewhere, I thought it worth the candle to post a notice of the new version here.

☞ Sign Relations • Semiotic Equivalence Relations

Posted in C.S. Peirce, Inquiry, Logic, Logic of Relatives, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | 2 Comments

Every Day Is All Hallows Night

Posted on October 31, 2013 by Jon Awbrey

The film of nightmare that covers the world.
The work it takes to make it mean something.

Posted in Anthem | Tagged | 4 Comments

Architectonics of Inquiry • 1

Posted on October 23, 2013 by Jon Awbrey

Re: R.J. Lipton • Teaching Helps Research

Along these lines, if somewhat tangentially, are some questions that I’ve wondered about for many years.

  • How do research and teaching interact, and how might they act to catalyze one another in the best of possible practices?
  • What sort of role could information technology play in integrating the two missions of inquiry and instruction?
  • What are the obstacles that inhibit the process of integration?

Readings

Abstract

More and more we hear the complaint that the gap between research and instruction is widening and a vital sense of motivation is falling between the cracks.  It is our vision that intelligent computing systems will become a partner in the reintegration of discovery and learning within the inquiry process.  We will address certain issues that must be faced if computer media are to have the characteristics necessary to support this integration.  The development of the computer to date has required a careful attention to the syntax and semantics of the rather limited symbol systems we have induced them to use.  A capacity for communicating in multiple modalities with non-uniform communities of symbol users — for sharing in the discovery of a pluralistic universe — will demand a quantum leap in our understanding of the pragmatic dimensions of symbol use.  In the future the capacity for inquiry must permeate the living architecture of the computer system.  A computer program that begins to embody these ideas will be discussed.

Posted in Artificial Intelligence, Automated Research Tools, C.S. Peirce, Discovery, Educational Systems Design, Educational Technology, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Instruction, Peirce, Research Technology | Tagged , , , , , , , , , , , | 3 Comments

Differential Analytic Turing Automata • Discussion 1

Posted on October 14, 2013 by Jon Awbrey

Re: R.J. Lipton and K.W. Regan • Proving Cook’s Theorem

Synchronicity Rules❢

I just started reworking an old exposition of mine on Cook’s Theorem, where I borrowed the Parity Function example from Wilf (1986), Algorithms and Complexity, and translated it into the cactus graph syntax for propositional calculus I developed as an extension of Peirce’s logical graphs.

By way of providing a simple illustration of Cook’s Theorem, namely, that “Propositional Satisfiability is NP-Complete”, I will describe one way to translate finite approximations of turing machines into propositional expressions, using the cactus language syntax for propositional calculus to be described in more detail as we proceed.

Posted in Algorithms, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Logic, Logical Graphs, Peirce, Propositional Calculus, Turing Machines | Tagged , , , , , , , , , , , | 2 Comments

Definition and Determination • 10

Posted on October 7, 2013 by Jon Awbrey
The moment, then, that we pass from nothing and the vacuity of being to any content or sphere, we come at once to a composite content and sphere.  In fact, extension and comprehension — like space and time — are quantities which are not composed of ultimate elements;  but every part however small is divisible.

The consequence of this fact is that when we wish to enumerate the sphere of a term — a process termed division — or when we wish to run over the content of a term — a process called definition — since we cannot take the elements of our enumeration singly but must take them in groups, there is danger that we shall take some element twice over, or that we shall omit some.  Hence the extension and comprehension which we know will be somewhat indeterminate.  But we must distinguish two kinds of these quantities.  If we were to subtilize we might make other distinctions but I shall be content with two.  They are the extension and comprehension relatively to our actual knowledge, and what these would be were our knowledge perfect.

Peirce, CE 1, 462

Peirce, C.S., “The Logic of Science;  or, Induction and Hypothesis”, [Lowell Lectures of 1866], pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Additional References

Incidental References

cc: Inquiry List • Peirce List (1) (2) (3)

Posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Indication, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Semiotics, Sources | Tagged , , , , , , , , , , , , , , , , | 11 Comments

And Now A Word From Our Sponsor …

Posted on October 1, 2013 by Jon Awbrey

Does your dualism lose its flavor on the bedpost overnight?
Unblock your inquiry with a dose of Peirce’s Elixir Triadic❢

☞ Inquiry Driven Systems • Are There Apps For That?

Frequently encountered complementarities, dualities, or design trade-offs

  • Integrating data-driven (empiricist) and concept-driven (rationalist) modes of inquiry.
  • Integrating model-theoretic and proof-theoretic methods for evaluating theories.
  • Bridging the gap between qualitative and quantitative research methodologies.
  • Relationship between emergent-evolved systems and engineered systems.
  • Relationship between descriptive sciences and normative sciences.

Relationship between emergent-evolved systems and engineered systems

I am taking a systems-theoretic view of the inquiry process, but I am focused on the kinds of systems we engineer to a specific purpose, for example, computational support for scientific inference. With that aim in mind the kinds of understanding we gain from connectionist, emergent property, genetic algorithm, or self-organizing systems research typically falls short of telling us how scientific inquiry can manage to work in the frame of time that human beings have at their command.

When we set about engineering artificial systems to augment our natural capacities — the way we build microscopes and telescopes to extend the reach of our eyes — our success in doing that naturally depends on how well we understand the natural system we are trying to extend.

One form of understanding is achieved when we draw on principles embodied in a natural system that are general enough to be embodied in very different artificial systems. That is the method of analogical extension, and it turns on the recognition of an abstract principle that can be shared by otherwise diverse systems.

Posted in Analogy, C.S. Peirce, Dualism, Dyadicism, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Inquiry Support Technology, Intelliscope, Pragmatism, Reductionism, Tertium Quid, Thirdness, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 8 Comments

Definition and Determination • 9

Posted on September 12, 2013 by Jon Awbrey

Re: Cathy O’Neil • The Art of Definition

In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force if you view the overarching concept of constraint from an information-theoretic point of view, as C.S. Peirce did beginning in the 1860s.  That makes an understanding of these intertwined concepts critical to the application of Peirce’s theories of information and inquiry.

Here’s a running thread with links to a collection of notes I’ve been gathering.

cc: Inquiry List • Peirce List (1) (2) (3)

Posted in C.S. Peirce, Definition, Determination, Inquiry, Logic, Mathematics, Peirce, Phenomenology, Semiotics | Tagged , , , , , , , , | 7 Comments

Objects, Models, Theories • 1

Posted on September 10, 2013 by Jon Awbrey

Happy Birthday, Charles Sanders Peirce❢ — September 10, 1839

Re: Artem Kaznatcheev • Three Types of Mathematical Models

Comment 1

In speaking of models one tends to find denizens of different disciplines talking at cross purposes to one another.  Logicians use the word to describe what may be distinguished as logical models, saying a model is whatever satisfies a theory, anything a theory holds true of, and this is the sense used in the logical subject of model theory.  Almost everyone else uses the word to describe what may be called analogical models, analogues being things holding enough properties in common with other things that learning about Thing 2 (the analogue system) can teach us about Thing 1 (the object system).  It is actually quite easy to integrate these senses of the word model into a coherent picture of the whole situation, namely, the triadic relationship among objects, analogues, and theories.

Comment 2

I’m presently in the middle of some very tedious work and will have to keep my nose to the grindstone for fear of never working up the fortitude to face it again, so for now I’ll just link to some very rough notes and hope for a chance to give them a proper set-up later.  (Full disclosure — I view almost everything from a Peircean perspective.)

Posted in Adaptive Systems, Analogy, Biological Systems, C.S. Peirce, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mathematics, Mental Models, Model Theory, Pragmata, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , | 8 Comments

What To Do?

Posted on August 28, 2013 by Jon Awbrey

Re: What To Do?

You are headed toward a grabitational singularity, and someone offers you a ton of gold.  What good is that?  Feathers and cannonballs all fall the same, I’m told.  If you have a way to convert the mass to energy and fire it in the right direction — Does feeding the beast make it worse for you?  Then maybe a bit tangentially, I dunno — you might have a ghost of a chance of saving your ectoplasm for another day.  Meanwhile aliens — they might as well be aliens for all they understand of humanity — are terraforming your planet into something only an alien could love.  What to do?  What to do?  Indeed …

Posted in Grabitational Singularity, Singularity | Tagged , | Leave a comment

Where Is Fancy Bred?

Posted on August 24, 2013 by Jon Awbrey

Re: Artem Kaznatcheev • Fitness Landscapes as Mental & Mathematical Models of Evolution

The question of “mental models” has occupied my thoughts for quite a while.

As intelligent agents with a capacity for inquiry, we have ways of forming and transforming independent representations of reality — “reality” being one of many names we give the imagined source of impressions that persist in impressing themselves on us and that we sort on a trial basis to the bins of our external and internal worlds.

As social agents with a capacity for communication, we have ways of impressing our personal representations on external media and sharing them with other sign-using agents, with all the contingencies and difficulties that bedevil our partly phylogenetic and partly ontogenetic capacity for sharing signs.

I tend to come at these questions from a system-theoretic direction, asking “Where is the threshold of system-theoretic complexity that must be crossed in order to achieve the first signs of these capacities?”

Posted in Adaptive Systems, Analogy, Artem Kaznatcheev, Artificial Intelligence, Biological Systems, Communication, Computational Complexity, Control, Evolution, Fitness Landscapes, Imagination, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Mathematical Models, Mental Models, Natural Intelligence, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , | 1 Comment