Semiotic Theory Of Information : 6

2014 Oct 14

Through the 1970s I gradually recovered from my early traumas with Fortran, and with the aid of more symbol-friendly programming languages like Lisp and Pascal began to play around again with implementing simple forms of graphical calculi inspired by Peirce and Spencer-Brown in the form of programs that carried out the requisite transformations in automatic or semi-automatic guided fashions.

Experiments like these, moving from scribblings on paper to algorithms and data structures in electronic media, brought about a transformation in my perspective on symbolic logic and other semiotic processes. The shift was very gradual over the decade that followed, but I think it began with thinking of computer memory as very like a sheet of paper, a tabula rasa, or a Sheet of Assertion as Peirce dubbed the unmarked state in his systems of logical graphs.

Thinking this way naturally brings out the system-theoretic aspects of semiosis in general and logic in particular. One begins with sign relations as subsets of cartesian products ${O \times S \times I},$ where ${O, S, I}$ are sets of objects, signs, and interpretant signs, respectively, and over time one begins to see dynamic systems in place of those sets. Then one day in the mid 1980s I distinctly remember flashing on the fact that the graph-theoretic data structures I and my programs were manipulating in memory were actually diagrams in Peirce’s sense.

With that pre-ramble, here is a bit of background from (Awbrey & Awbrey, 1990) that describes our system-theoretic approach to agents with a capacity for learning and reasoning.

The State Space Approach to Intelligent Systems

The common definition of a system as a list of variables is useful but not absolute. It characterizes the system only as measured from a particular frame of observation. The property of a system that we really care about is its state space, or a representation showing the possible states of a system. When considering systems that exhibit complex sets of properties, such as being able to transform information and to act with intelligent purpose, it becomes more difficult to specify in advance the exact nature of the state space, or even whether a space exists that satisfies a given set of specifications. Therefore we do not consider the state space of intelligent systems to be given absolutely, as the subset of some predefined space (like ${\mathbb{R}^{n}}$), but defined provisionally, subject to a list of constraints and subject to revision.

When considering intelligent behavior, we are most interested in the state of information that an interpreter system has about an object system, and this information has its expression in a system of signs. The characterizations sign, object, interpreter are not so much exclusive categories of entities as roles that systems may play within the so-called sign relation. Although interested in the nature and relations of these systems in themselves, whatever we can say about them takes place within the domain of signs. As we use the words, sign is the general category, while symbol is a particular type of sign. From the pragmatic point of view, almost all the actual work of computation is involved with transformations between expressions in the symbolic domain.

To be continued …

Semiotic Theory Of Information : 5

2014 Oct 09

I will continue assembling an assortment of background materials and links to other resources that I think are useful in understanding Peirce’s notion of information and how it has the potential to extend and generalize both our intuitive notions of information and the more or less formalized theories of information that have become standard in contemporary scientific practice.

The next bit of background material I wanted to add to the account is the perspective on signs and information that Susan Awbrey and I outlined in the paper we gave at a Society for Applied Learning Technology conference in 1990.

Information as a Matter of Form, Not a Form of Matter

Information is the property of a message or sign by virtue of which it can reduce the uncertainty of an interpreter about the state of an object. This property has the alternate aspect of acting to increase the control of an interpreter with respect to achieving a goal.

In Aristotle’s Psychology [1], two important distinctions were drawn which we would like to adapt to our discussion of information.

First, he distinguished form and matter, saying that matter is the potentiality, while form is the actuality of the mind. Although it combines both, the essential nature of the mind is found in its form. Applied to the mind in its aspect of information processing system, this proposition foreshadows a point that was often emphasized at the beginning of the information revolution, that information is a formal entity, not a material one.

Next, Aristotle drew a distinction between the possession and the exercise of knowledge. A corresponding distinction may be drawn between the information that a system possesses by virtue of being in a certain state and the information that a self-informed or intelligent system may exercise with respect to its own states. It is not a distinction in the kind or essence of information, but a pragmatic difference in the role a system plays within the relation of sign, object, and interpreter. In the first case, the state of a system serves as a sign to others, reducing the uncertainty of these interpreters about the state of an object system. In the second case, the state of a system serves as information to itself in its role as interpreter. This is one of the marks of an intelligent system.

Reference

1. Aristotle, “On the Soul” (De Anima), W.S. Hett (trans.), in Aristotle, Volume 8, Loeb Classical Library, William Heinemann, London, 1986.

I continued to make use of the frame introduced in Aristotle’s sketch of the soul in my work on Inquiry Driven Systems, for instance, here:

To be continued …

Semiotic Theory Of Information : 4

2014 Oct 08

Let us now return to the information.” To coin a phrase. This time around we come to Peirce’s notion of information in a critical and recurring passage that Frederik Stjernfelt takes as the next stepping stone from propositions through dicisigns to the information they convey:

This maybe surprising definition of the Dicisign is closely connected, however, to the basic function of the Dicisign, namely to convey information — to relay claims, assert statements, true or false. Only by separately indicating an object does it become possible for a sign to convey information about that object, correctly or not:

“… the essential nature of the Dicisign, in general, that is, the kind of sign that conveys information, in contradistinction to a sign from which information may be derived. The readiest characteristic test showing whether a sign is a Dicisign or not, is that a Dicisign is either true or false, but does not directly furnish reasons for its being so.” (Syllabus, 1903, EP2, 276).

(Frederik Stjernfelt, Natural Propositions, 54)

In working through the argument of this series of texts I found it worth my trouble to copy out a longer excerpt from the 1903 Syllabus to my blog:

To be continued …

Semiotic Theory Of Information : 3

2014 Oct 08

Re: Resources On Peircean Information Theory • (1)(2)

In trying to remember why I started this thread, I traced it back to the point when various notions of information came up in Chapter 3.3 of Frederik Stjernfelt’s book, Natural Propositions.

So let us review …

First we have the eureka moment in Kaina Stoicheia where Peirce declares a “true definition of a proposition”, namely, “A proposition is a sign which separately, or independently, indicates its object.” And we know that Peirce attaches the label of a “Dicisign” to the definiens of that definition.

3.3. Dicisigns : Signs Separately Indicating Their Object

True to Peirce’s general way of investigating sign types, he describes Dicisigns
compositionally, functionally, and systematically. As Hilpinen (1992) says,
Peirce’s recurrent and “standard” definition of Dicisigns is given in the
following italicized passage from “Kaina stoicheia”:

“It is remarkable that while neither a pure icon or a pure index can assert anything, an index which forces something to be an icon, as a weathercock does, or which forces us to regard it as an icon, as the legend under the portrait does, does make an assertion, and forms a proposition. This suggests a true definition of a proposition, which is a question in much dispute at the moment. A proposition is a sign which separately, or independently, indicates its object.” (EP2, 307, emphasis Hilpinen’s)

(Frederik Stjernfelt, Natural Propositions, 53–54)

To be continued …

Semiotic Theory Of Information : 2

2014 Oct 06

Some portions of a paper Susan Awbrey and I presented at a Society for Applied Learning Technology conference in 1990 may be relevant at this juncture.

How do we, and how should we, integrate the empirical and rational sources of information that make up our putative knowledge of the actual world we observe and the possible worlds we contemplate? That is the question we sought to address in this line of research.

Those are hardly new questions, of course, but it’s my firm opinion to this day that Peirce set out new ideas, and intrinsically integral ideas, if you will, when it comes to answering them.

One way to explore the problem domain is to write computer programs that tackle the task of integrating learning and reasoning faculties, starting with simple but non-trivial functions of those types, and to see what one can see from the trials of doing that.

Here is our overture:

Abstract

If computer programs were smarter, they would, like people, recognize sequences of events, form models of their environment, and formulate rules based on experience. This paper describes the development of a program designed to address the difficult computational problems involved in integrating the inductive and deductive reasoning necessary to perform such tasks. Theme One is a prototype program composed of Index, a learning algorithm for sequential data, and Study, an algorithm for building logical models. The project goal is an interactive research tool that assists students and investigators in the exploration of qualitative data using artificial intelligence.

To be continued …

Semiotic Theory Of Information : 1

2014 Oct 06

Peircers & Others,

On the subject of Peirce’s laws of information — or the semiotic theory of information — here are just a few links that come to mind for possible future reference:

I highly recommend looking into the early lectures on the ”Logic of Science”.  The bare, spare, and rather vague allusions that Peirce makes to information in his late manuscripts can scarcely be understood without the aid of these early, more concrete, and more detailed discussions, however undeveloped their full potential may yet be.

Regards,

Jon

C.S. Peirce • Syllabus • Selection 2

But round about the castle there began to grow a hedge of thorns, which every year became higher, and at last grew close up round the castle and all over it, so that there was nothing of it to be seen, not even the flag upon the roof.

Grimm’s Fairy Tales • Little Briar-Rose

Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903)

Section “Sundry Logical Conceptions”  •  Subsection “Speculative Grammar”

The second trichotomy of representamens is [divided] into:

• first, simple signs, substitutive signs, or Sumisigns;
• second, double signs, informational signs, quasi-propositions, or Dicisigns;
• third, triple signs, rationally persuasive signs, arguments, or Suadisigns.

Of these three classes, the one whose nature is, by all odds, the easiest to comprehend, is the second, that of quasi-propositions, despite the fact that the question of the essential nature of the “judgment” is today quite the most vexed of all questions of logic.

The truth is that all these classes are of very intricate natures;  but the problem of the day is needlessly complicated by the attention of most logicians, instead of extending to propositions in general, being confined to “judgments”, or acts of mental acceptance of propositions, which not only involve characters additional to those of propositions in general, — characters required to differentiate them as propositions of a particular kind, — but which further involve, beside the mental proposition itself, the peculiar act of assent.

The problem is difficult enough, when we merely seek to analyze the essential nature of the Dicisign, in general, that is, the kind of sign that conveys information, in contradistinction to a sign from which information may be derived.

The readiest characteristic test showing whether a sign is a Dicisign or not, is that a Dicisign is either true or false, but does not directly furnish reasons for its being so.

This shows that a Dicisign must profess to refer or relate to something as having a real being independently of the representation of it as such, and further that this reference or relation must not be shown as rational, but must appear as a blind Secondness.  But the only kind of sign whose Object is necessarily existent is the genuine Index.  This Index might, indeed, be part of a Symbol;  but in that case the relation would appear as rational.  Consequently a Dicisign necessarily represents itself to be a genuine Index, and to be nothing more.

At this point let us discard all other considerations, and see what sort of a sign a sign must be that in any way represents itself to be a genuine Index of its Object, and nothing more.

Substituting for “represents_____to be” a clearer interpretation, the statement is that the Dicisign’s Interpretant represents an identity of the Dicisign with a genuine Index of the Dicisign’s real Object.  That is, the Interpretant represents a real existential relation, or genuine Secondness, as subsisting between the Dicisign and its real Object.

But the Interpretant of a Sign can represent no other Object than that of the Sign itself.

Hence, this same existential relation must be an Object of the Dicisign, if the latter have any real Object.

This represented existential relation, in being an Object of the Dicisign, makes that real Object which is the correlate of this relation also an Object of the Dicisign.  This latter Object may be distinguished as the Primary Object, the other being termed the Secondary Object.

The Dicisign, in so far as it is the relate of the existential relation which is the Secondary Object of the Dicisign, can evidently not be the entire Dicisign.  It is at once a part of the Object and a part of the Interpretant of the Dicisign.

Since the Dicisign is represented in its Interpretant to be an Index of a complexus as such, it must be represented in that same Interpretant to be composed of two parts, corresponding respectively to its Object and to itself.

That is to say, in order to understand the Dicisign, it must be regarded as composed of two such parts whether it be in itself so composed or not.  It is difficult to see how this can be, unless it really have two such parts;  but perhaps this may be possible.

Let us consider these two represented parts separately.

The part which is represented to represent the Primary Object, since the Dicisign is represented to be an Index of its Object, must be represented as an Index, or some Representamen of an Index, of the Primary Object.

The part which is represented to represent a part of the Dicisign, is represented as at once part of the Interpretant and part of the Object.  It must, therefore, be represented as such a sort of Representamen (or to represent such a sort) as can have its Object and its Interpretant the same.

Now, a Symbol cannot even have itself as its Object;  for it is a law governing its Object.

For example, if I say “This proposition conveys information about itself”, or “Let the term ‘sphinx’ be a general term to denote any thing of the nature of a symbol that is applicable to every ‘sphinx’ and to nothing else”, I shall talk unadulterated nonsense.

But a Representamen mediates between its Interpretant and its Object, and that which cannot be the Object of the Representamen cannot be the Object of the Interpretant.

Hence, a fortiori, it is impossible that a Symbol should have its Object as its Interpretant.

An Index can very well represent itself.

Thus, every number has a double;  and thus the entire collection of even numbers is an Index of the entire collection of numbers, and so this collection of even numbers contains an Index of itself.

But it is impossible for an Index to be its own Interpretant, since an Index is nothing but an individual existence in a Secondness with something;  and it only becomes an Index by being capable of being represented by some Representamen as being in that relation.  Could this Interpretant be itself, there would be no difference between an Index and a Second.

An Icon, however, is strictly a possibility, involving a possibility, and thus the possibility of its being represented as a possibility is the possibility of the involved possibility.  In this kind of Representamen alone, then, the Interpretant may be the Object.  Consequently, that constituent of the Dicisign which is represented in the Interpretant as being a part of the Object, must be represented by an Icon or by a Representamen of an Icon.

The Dicisign, as it must be understood in order to be understood at all, must contain those two parts.  But the Dicisign is represented to be an Index of the Object, in that the latter involves something corresponding to these parts;  and it is this Secondness that the Dicisign is represented to be the Index of.

Hence the Dicisign must exhibit a connection between these parts of itself, and must represent this connection to correspond to a connection in the Object between the Secundal Primary Object and Firstness indicated by the part corresponding to the Dicisign.

We conclude, then, that, if we have succeeded in threading our way through the maze of these abstractions, a Dicisign, defined as a Representamen whose Interpretant represents it as an Index of its Object, must have the following characters.

First, it must, in order to be understood, be considered as containing two parts.  Of these, the one, which may be called the Subject, is or represents an Index of a Second existing independently of its being represented, while the other, which may be called the Predicate, is or represents an Icon of a Firstness.

Second, these two parts must be represented as connected;  and that in such a way that if the Dicisign has any Object, it must be an Index of a Secondness subsisting between the real Object represented in one represented part of the Dicisign to be indicated, and a Firstness represented in the other represented part of the Dicisign to be iconized.

Let us now examine whether these conclusions, together with the assumption from which they proceed, hold good of all signs which profess to convey information without furnishing any rational persuasion of it;  and whether they fail alike for all signs which do not convey information as well as for all those which furnish evidence of the truth of their information, or reasons for believing it.  If our analysis sustains these tests, we may infer that the definition of the Dicisign on which they are founded, holding, at least, within the sphere of signs, is presumably sound beyond that sphere.

(Peirce, EP 2.275–277, CP 2.309–313)

Notes

Collected Papers 1

• A Syllabus of Certain Topics of Logic, 1903, Alfred Mudge & Son, Boston, bearing the following preface:  “This syllabus has for its object to supplement a course of eight lectures to be delivered at the Lowell Institute, by some statements for which there will not be time in the lectures, and by some others not easily carried away from one hearing.  It is to be a help to those who wish seriously to study the subject, and to show others what the style of thought is that is required in such study.  Like the lectures themselves, this syllabus is intended chiefly to convey results that have never appeared in print;  and much is omitted because it can be found elsewhere.”

References

• Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958.  Volume 2 : Elements of Logic, 1932.
• Peirce Edition Project (eds., 1998), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington and Indianapolis, IN.