Pragmatic Semiotic Information • Discussion 2

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.

Survey of Semiotic Theory Of Information • 3

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 surrounding the issue and fixed on what he called the “laws of information” as the key to answering how science works.  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.  Comparing Peirce’s theory of information, however much it remains in a rough-hewn state, with Shannon’s paradigm so pervasively informing the ongoing revolution in our understanding and use of information today, I have reason to believe Peirce’s idea is more general and has the potential, with due development, to resolve many mysteries that still bedevil our grasp of inference, information, and inquiry.

Reference

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

Sign Relations, Triadic Relations, Relations • 11

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

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 2 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 talk to that point more next time.

Pragmatic Semiotic Information • Discussion 1

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.

Pragmatic Semiotic Information (Ψ)

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, or $X \to \mathrm{Info} (X)$ as I came to notate it.  I suppose this 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.

Inquiry Driven Systems • Comment 5

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 little 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.

Sign Relations, Triadic Relations, Relations • 10

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.