Inquiry Into Inquiry

Where Is Fancy Bred? • Comment 1

Posted on September 14, 2018 by Jon Awbrey

Re: Artem Kaznatcheev • Labyrinth : Fitness Landscapes As Mazes, Not Mountains

A species in progress, with its naturally evolved organs of sensitivity, effectivity, and discernment, in its trials to learn the properties of its environment, cannot be expected to know in advance the full dimensionality of the space it inhabits on a mundane basis and through which it charts its eventual evolution.

An adaptive mutation in one of those capacities will expand its grasp of its environment into a larger space of states.

Related Ruminations

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 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 | Leave a comment

Pragmatic Semiotic Information • Discussion 6

Posted on September 12, 2018 by Jon Awbrey

Re: Ontolog Forum • JS

The subject of natural languages and their relation to formal languages, for example, logical calculi, logical graphs, mathematical formalisms, and programming languages, has come up periodically in our discussions and I’ve been struggling to arrive at something both cogent and coherent to say about it. But what the heck, here’s a few thoughts off the cuff.

We naturally use our mother tongues as metalanguages to talk among ourselves in fora like these, not only about well-formalized object languages but also about the object domains that supply them with semantic substance, in a word, “meaning”. Nothing about that makes “the natural language of the individual conducting the inquiry … the main object of study”. At least, that is not how I’d personally understand the task at hand.

I began using the run-on formula “pragmatic-semiotic point of view” during a few exchanges with Bruce Schuman and John Sowa as a way of alluding to the line of thinking about signs stretching from Aristotle to Peirce, Dewey, and pragmatists of that stripe. Here’s a link to my blog rehash of that episode:

Inquiry Driven Systems • Comment 5

To be continued …

Reference

Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

cc: Systems Science • Structural Modeling

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | 8 Comments

Pragmatic Semiotic Information • Discussion 5

Posted on September 10, 2018 by Jon Awbrey

Re: Ontolog Forum • AA

Of course it’s not that simple. I called it a cornerstone not a whole building but it gives us a starting point and a first approach to a pragmatic semiotic architecture still being built as we speak.

There is more detail and a trace of semiotic’s later development in this paper:

Awbrey and Awbrey (1995), “Interpretation as Action : The Risk of Inquiry” (1) (2)

We began by quoting the founding paragraph from Aristotle:

Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (semeia), are the same for the whole of mankind, as are also the objects (pragmata) of which those affections are representations or likenesses, images, copies (homoiomata). (Aristotle, De Interp. i. 16^a4).

We used the following Figure to highlight the structure of the triadic relation among objects (pragmata), affections or impressions (pathemata), and symbols or signs (symbola, semeia) as given in Aristotle’s account:

Figure 1. The Sign Relation in Aristotle

The triadic nexus marked “R” in the Figure is what graph theorists call a node or point of degree 3 and it provides a graphical picture of a relational triple that may be taken in any convenient order so long as we keep it constant throughout a given discussion. For example, we could take Aristotle’s object, sign or symbol, and impression in the order $(o, s, i),$ mostly just because I find that convenient in later developments.

Diagrams of that sort, whether triangular or tri-radial in form, have long been in common use for conveying the properties of triadic sign relations. But I have discovered to my dismay over the intervening years that people tend to be led astray by pictures like that, often getting stuck on square one, or rather triangle one. That is, they get stuck on single triples of sign relations rather than grasping them as they should, as prototypical examples of a whole class of ordered triples.

cc: Systems Science • Structural Modeling

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Peter Woit, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Peter Woit, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | 8 Comments

Pragmatic Semiotic Information • Discussion 4

Posted on September 8, 2018 by Jon Awbrey

Re: Is Quantum Mechanics A Probabilistic Theory? • What Is Measurement?

Measurement is an extension of perception. Measurement gives us data about an object system the way perception gives us percepts, which we may consider just a species of data.

If we ask when we first became self-conscious about this whole process of perception and measurement, I don’t know, but Aristotle broke ground in a very articulate way with his treatise On Interpretation. Sense data are impressions on the mind and they have their consensual, communicable derivatives in spoken and written signs. This triple interaction among objects, ideas, and signs is the cornerstone of our contemporary theories of signs, collectively known as semiotics.

cc: Ontolog Forum • Systems Science • Structural Modeling

Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Peter Woit, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Peter Woit, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | 8 Comments

Differential Logic, Dynamic Systems, Tangent Functors • 1

Posted on September 5, 2018 by Jon Awbrey

People interested in category theory as applied to systems may wish to check out the following article, reporting work I carried out while engaged in a systems engineering program at Oakland University.

The problem addressed is a longstanding one, that of building bridges to negotiate the gap between qualitative and quantitative descriptions of complex phenomena, like those we meet in analyzing and engineering systems, especially intelligent systems endowed with a capacity for processing information and acquiring knowledge of objective reality.

One of the ways this problem arises has to do with describing change in logical, qualitative, or symbolic terms, long before we grasp the reality beneath the appearances firmly enough to cast it in measured, quantitative, real number form.

Development on the quantitative shore got no further than a Sisyphean beachhead until the discovery/invention of differential calculus by Leibniz and Newton, after which things advanced by leaps and bounds.

And there’s our clue what we need to do on the qualitative shore, namely, to discover/invent the missing logical analogue of differential calculus.

With that preamble …

Differential Logic and Dynamic Systems

This article develops a differential extension of propositional calculus and applies it to a context of problems arising in dynamic systems. The work pursued here is coordinated with a parallel application that focuses on neural network systems, but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.

Resources

Differential Propositional Calculus • Part 1 • Part 2
Differential Logic • Part 1 • Part 2 • Part 3
Differential Logic and Dynamic Systems
• Part 1 • Part 2 • Part 3 • Part 4 • Part 5

cc: Cybernetics (1) (2) • Ontolog • Peirce List • Structural Modeling • Systems Science

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | Tagged Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Information Theory, Inquiry Driven Systems, Intelligent Systems, Knowledge Representation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Systems, Visualization | 14 Comments

Pragmatic Semiotic Information • Discussion 3

Posted on September 4, 2018 by Jon Awbrey

Re: Ontolog Forum • JFS

What I find lacking in these static ontological hierarchies is the dynamic, functional, transformational side of scientific inquiry, the process that produces the product known as knowledge. If sciences are bodies of organized knowledge, what is the physiology of those bodies? That is the variety of systems theory I learned in my schools, focusing on the states of systems and how they change over time.

When we apply that systems perspective to information systems, knowledge systems, systems of belief, received opinion, whatever, the state under investigation is a state of information, knowledge, and so on, and the question becomes, “What influences and operations actually do and optimally ought to update that state of information over time?”

cc: Systems Science • Structural Modeling

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Peirce, Pragmatism, Scientific Method, Semiotic Information, Semiotics, Sign Relations | Tagged Abduction, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Logic, Logic of Science, Peirce, Pragmatism, Scientific Method, Semiotic Information, Semiotics, Sign Relations | 8 Comments

Pragmatic Semiotic Information • Discussion 2

Posted on September 2, 2018 by Jon Awbrey

I’ve been following the discussion on the Sys Sci list that asks the question, “What Is Systems Science?”. I haven’t found the time to join in yet but it is very interesting to me on account of the fact my work on Inquiry Driven Systems for the last 30 years or so can be seen to ask the converse question, “How Is Science a (Cybernetic or Dynamic) System?”.

The idea that sciences operate as (some order of) cybernetic systems is nothing new but there remains a lot of work to do detailing that insight and especially building intelligent software systems that assist scientific research by availing themselves of that task and user model.

cc: Ontolog Forum • Systems Science • Structural Modeling

Survey of Semiotic Theory Of Information • 3

Posted on August 30, 2018 by Jon Awbrey

This is a Survey of previous blog and wiki posts on the Semiotic Theory Of Information. All my projects are exploratory in essence 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 that answer 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. This was in 1865 and 1866, detailed in his lectures at Harvard University and the Lowell Institute.

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

OEIS Wiki • Information = Comprehension × Extension

Blog Series • { Information = Comprehension × Extension }

Selections • (1) • (2) • (3) • (4) • (5) • (6)

Comments • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8)

Discussions • (1) • (2) • (3) • (4) • (5) • (6) • (7)

Excursions

Blog Dialogs

Semiotic Theory Of Information • (1) • (2) • (3) • (4) • (5) • (6)

Reference

C.S. Peirce • Upon Logical Comprehension and Extension

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | 1 Comment

Sign Relations, Triadic Relations, Relations • 11

Posted on August 24, 2018 by Jon Awbrey

Re: Ontolog Forum • Ravi Sharma

In pursuing applications of pragmatic semiotics to scientific research the following distinctions are crucial.

We have the relational roles known as Object, Sign, and Interpretant Sign. These are places or roles a thing may occupy in a given moment in a given context. They are not absolute essences or fixed ontological characters.

We can formalize the “moment” mentioned above as an ordered triple $(o, s, i),$ where $o$ is the object, $s$ is the sign, and $i$ is the interpretant sign in view.

We can formalize the “context” mentioned above as a set of ordered triples, each one having the form $(o, s, i).$ This set is called a sign relation.

We can formalize a given sign relation $L$ as a subset of a cartesian product, $L \subseteq O \times S \times I,$ where $O$ is the set of objects under consideration in a given context, $S$ is the set of signs, and $I$ is the set of interpretant signs being considered in the same context.

It is critically important to distinguish the triples $(o, s, i),$ which may be called elementary sign relations, from the sign relation proper, $L \subseteq O \times S \times I.$ Among other things, this is important because sets have properties their elements do not and it amounts to a category mistake to confuse the two levels. In particular, the properties of reducibility and irreducibility are defined at the level of whole sign relations, not their individual elements.

Another very important distinction we have to keep in mind is the difference between the formal objects we are discussing and the formal signs and syntax we use to discuss them. I’ll speak to that point next time.

Resources

Logic Syllabus	Sign Relations
Relational Concepts	Triadic Relations
Relation Reduction	Relation Theory

cc: Ontolog Forum • Structural Modeling • Systems Science

Posted in C.S. Peirce, Inquiry, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged C.S. Peirce, Inquiry, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Visualization | 16 Comments

Pragmatic Semiotic Information • Discussion 1

Posted on August 22, 2018 by Jon Awbrey

Re: Systems Science • Kenneth Lloyd

Ken’s comment made me realize that the notation $\mathrm{Info}(X)$ is probably not the best. It tends to mislead us into thinking we already have $X$ in hand, in other words, that we already have perfect information about $X$ and are merely abstracting $\mathrm{Info}(X)$ as some derivative of it. But that is not the sort of situation we are concerned with here.

It might be better to say that $\mathrm{Info}$ is all the information we have at a given moment of investigation and $X$ abstracts the portion of $\mathrm{Info}$ that has to do with $X.$ That might lead us to notate it as $X(\mathrm{Info}).$ This brings to mind the way we speak of observables in physics, as operators on the wave function that represents the total state of the system observed.

If I had to concoct an informal linguistic example — which I’d do solely by way of rough analogy to the formal mathematical cases we’d have much hope of resolving in our lifetimes — I’d say the sorts of $X$ we’re facing are what used to be called definite descriptions like “Desdemona’s infidelity” or “Manafort’s guilt on the 10 mistried counts”.

In those sorts of situations, discussed to death in years gone by, what a modicum of pragmatic-semiotic insight adds to the mix is that all descriptions are indefinite to some degree, all syntax lax to some extent.

Not too surprisingly, we find foresights of that insight throughout Peirce’s work. And that is what I’ll be getting around to presently.

	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Icon, Likeness, Like… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Survey of Semiotics,… on Icon, Likeness, Likely Story,…
	Backpack Ben on Abduction, Deduction, Inductio…
	Peirce’s Categ… on Survey of Precursors Of Catego…

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