## Pragmatic Semiotic Information • Discussion 8

Re: Ontolog ForumJS

The concept of a triadic sign relation, in typical form $L \subseteq O \times S \times I,$ where $O$ is the object domain (think universe of discourse) and $S$ and $I$ are domains of signs (think channels or languages) being used to talk and think about $O,$ is most often applied in one of two ways.

1. $S$ and $I$ are really the same channel, language, medium, set of signs, or state space of a system we are using to convey information about $O.$  In cases where $S = I$ we are often concerned with transformations taking place within a single set of signals and we may write $I = S^\prime$ to signify our focus on sign relational triples of the form $(o, s, s^\prime)$ where $s^\prime$ is a sign that follows $s$ in a logical or temporal sequence, in short, where $s^\prime$ is contemplated as a next state of $s.$
2. $S$ and $I$ are two different channels, languages, media, sets of signs, or state spaces of systems being used to convey information about $O.$  In this case the issue is one of translation or interoperability.

### Reference

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

## Pragmatic Semiotic Information • Discussion 7

Re: Ontolog ForumJS

JS:
It appears to me that it is very difficult to fully grasp the fundamental issues associated with pragmatic semiotic information when the natural language of the individual conducting the inquiry is the main object of study.

That one took me a double take but if I take the when clause as a hypothetical condition and not the assertion of a fixed intention then I’d naturally agree:

IF
The natural language of the individual conducting the inquiry is the main object of study
THEN
It is very difficult to fully grasp the fundamental issues associated with pragmatic semiotic information.

It is well worth the candle to reflect on the properties of our embedding languages but we normally meet with limited, partial, and well-circumscribed success on any given trial.  That is why we study formalized object languages as microcosms of our yet unformalized semiotic contexts.

### Reference

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

## Where Is Fancy Bred? • Comment 1

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.

## Pragmatic Semiotic Information • Discussion 6

Re: Ontolog ForumJS

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:

To be continued …

### Reference

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

## Pragmatic Semiotic Information • Discussion 5

Re: Ontolog ForumAA

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. 16a4).

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.

## Pragmatic Semiotic Information • Discussion 4

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.

## Differential Logic, Dynamic Systems, Tangent Functors • 1

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 pre-ramble …

• 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.