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 , , , , , , , , , , , , | 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.

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 , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Pragmatic Semiotic Information • Ψ

Posted on August 21, 2018 by Jon Awbrey

I remember it was back in ’76 when I began to notice a subtle shift of focus in the computer science journals I was reading, from discussing X to discussing Information About X, a transformation I noted mentally as X \to \mathrm{Info}(X) whenever I ran across it.  I suppose that small arc of revolution had been building for years but it struck me as crossing a threshold to a more explicit, self‑conscious stage about that time.

cc: FB | Semeiotics • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Inquiry Driven Systems • Comment 5

Posted on August 19, 2018 by Jon Awbrey

Re: Ontolog Forum • Bruce Schuman

I would call that the pragmatic semiotic point of view and not find anything shocking in it.

One can find earlier foreshadowings — Plato’s Cratylus and the Stoic lekton are often mentioned in this connection — but the clearest precursor of the pragmatic semiotic perspective occurs in Aristotle’s recognition of the triadic sign relation, most succinctly in his treatise On Interpretation.

Here’s the essay Susan Awbrey and I wrote on that, tracing the continuities of pragmatic semiotics from Aristotle up through Peirce and Dewey and teasing out the intimate relationship between the theory of signs and the theory of inquiry.

cc: Ontolog Forum

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 9 Comments

Sign Relations, Triadic Relations, Relations • 10

Posted on August 15, 2018 by Jon Awbrey

Re: Ontolog Forum • Ravi Sharma

The words predicate, proposition, relation, and so on are affected by many variations in usage.  Some of their uses are associated with philosophical habits unlikely to change any time soon.  But there are a number of compromise positions and technical strategies that allow us to negotiate between the variant practices and render them understandable in terms of each other.

⁂

I found that start of a reply in my phone’s draft folder.  It’s been a month’s hard labor putting our house on the market and it looks like the busy-ness is just getting under way — so I’ll post that much to remind me what I need to do when I get my concentration and computer back on line.

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, Icon Index Symbol, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 14 Comments

Sign Relations, Triadic Relations, Relations • 9

Posted on August 14, 2018 by Jon Awbrey

Re: Ontolog Forum • Ronald Stamper

Concrete examples are very instructive in this arena, and when it comes to refutations a single counter-example serves to puncture many a fallacious general proposition.

Here’s a couple of articles, illustrated with concrete examples of a fundamental character, affording a bare minimum introduction to triadic relations along with their reducibility and irreducibility properties.

cc: Ontolog Forum • Structural Modeling • Systems Science

Posted in C.S. Peirce, Icon Index Symbol, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 14 Comments

Inquiry Driven Systems • Comment 4

Posted on August 12, 2018 by Jon Awbrey

Re: Ontolog Forum • Matthew West

In the systems approach to inquiry I’ve been pursuing, all specifications, state descriptions, or values of variables come in three modalities:  expected, intended, and actually observed.

  • A difference between expectation and observation is accounted as a “surprise” and calls for an explanation.
  • A difference between intention and observation is accounted as a “problem” and calls for a plan of action.

There’s more discussion in the following article and section.

cc: Ontolog Forum

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 8 Comments

Sign Relations, Triadic Relations, Relations • 8

Posted on July 6, 2018 by Jon Awbrey

Re: Ontolog Forum • Ferenc Kovacs

Our thoughts live in natural and artificial languages the
way fish swim in natural and artificial bodies of water.

One of the lessons most strikingly impressed on me by my first‑year physics course and the mass of collateral reading I did at the time was to guard against the errors that arise from “projecting the properties and structures of any language or symbol system on the external world”.  This was mentioned especially often in discussions of quantum mechanics — it was a common observation that our difficulties grasping wave‑particle duality might be due to our prior conditioning to see the world through the lenses of our subject‑predicate languages and logics.  Soon after, I learned about the Sapir–Whorf hypothesis, and today I lump all these cautionary tales under the heading of GRAM (“Grammar Recycled As Metaphysics”).

Resources

cc: Ontolog Forum • Structural Modeling • Systems Science

Posted in C.S. Peirce, Icon Index Symbol, Knowledge Representation, Logic, Logic of Relatives, Mathematics, Ontology, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , | 16 Comments

Constraints and Indications • 2

Posted on July 4, 2018 by Jon Awbrey

Re: Ontolog Forum • Joseph Simpson

Coping with collaboration, communication, context, integration, interoperability, perspective, purpose, and the reality of the information dimension demands a transition from conceptual environments bounded by dyadic relations to those informed by triadic relations, especially the variety of triadic sign relations employed by pragmatic semiotics.

Along the lines of my first post on this topic I am presently concerned with the logical and mathematical requirements of dealing with constraints but when it comes to the constraints involved in communicating across cultural and disciplinary barriers I could recommend a paper Susan Awbrey and I wrote for a conference devoted to those very issues.

Conference Presentation

  • Awbrey, S.M., and Awbrey, J.L. (1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.

Published Paper

  • Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  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 , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Inquiry Driven Systems • Comment 3

Posted on July 2, 2018 by Jon Awbrey

Re: Ontolog Forum • Michael DeBellis

I remember Doug Medin from the year I was at Illinois and I recall a colloquium talk Frank Keil gave at Michigan State which intrigued me because he echoed ideas from Kant about the synthetic à priori, but I didn’t get a chance to ask him more about it.

As far as Fodor’s line goes, I’m generally sympathetic to faculty psychology, if only because it suits the ways mathematicians and programmers analyze and synthesize both functions and structures, but the faculties required for intelligence and inquiry interact with each other and have mutual recourse to each other far too intricately to deserve the name modules in the strictest technical sense.

Still, if all we’re talking about is a native knack or a natural instinct for latching onto subsumptions wherever they may occur then I could go along with that for the sake of further argument.

I agree with previous comments that “subsumption” suffers from a surfeit of senses but here’s two places where I found it natural to use “subsumes” or one of its synonyms, once in a logical sense and once in a grammatical sense.

There are reasons arising from Peirce’s logic and mathematical category theory for this usage but I’ll have to save that for another time.

cc: Ontolog Forum

Posted in Animata, Artificial Intelligence, C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Learning Systems, Logic, Logical Graphs, Peirce, Semiotics, Sign Relations, Visualization | Tagged , , , , , , , , , , , , , , | 8 Comments