## Theme One Program • Discussion 5

JC:
This post [Theme One Program • Motivation 1] is so muddled
that I gave up on a meaningful scientific interpretation of it.

Dear Jerry,

Thanks for the response.

I heartily agree with the sentiment we need to pay more attention to
Mathematical And Scientific Substance (MASS) and boggle our brains
less about Purity Of Orthodox Faith (POOF).

That is what I hope to do here, on the one hand giving a realistic account of real‑world problems I encountered through the years and along the way describing how the logic of science and the tools of mathematics, especially as articulated by C.S. Peirce and tested in computational experiment, helped to address them or at least to clarify my understanding of their nature.

But that first post is only a preamble, so I hope you’ll stay tuned …

Regards,

Jon

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## Theme One Program • Discussion 4

I’ve been going back and looking again at the problems and questions which nudged me into the computational sphere as a way of building our human capacities for inquiry, learning, and reasoning.

One critical issue, you might even say bifurcation point, came up again on the Peirce List almost a decade ago in discussing the so-called “Symbol Grounding Problem”, a problem I thought had long been laid to rest, at least, among readers of Peirce, who ought to have no trouble grasping how the problem dissolves as soon as placed in the medium of Peirce’s sign relations.

Here is how the ghost of a problem returned to haunt us on that occasion …

All of which led me to recall the problems I worked on all through the ’80s …

I spent one of my parallel lives in the 1980s earning a Master’s degree in psychology, concentrating on the quantitative-statistical branch with courses in systems theory, simulation, and mathematical models, plus a healthy diet of courses and seminars in cognitive science and counseling psychology.  Instead of the usual thesis I submitted a computer program which integrated a module for multi-level sequential learning with a module for propositional constraint satisfaction, the latter based on an extension of Peirce’s logical graphs.

All the hottest topics of artificial intelligence and cognitive science from those days enjoy no end of periodic revivals, and though it brings me a twinge of nostalgia to see those old chestnuts being fired up again, those problems now seem to me as problems existing only for a peculiar tradition of thought, a tradition ever occupied with chasing will o’ th’ wisps Peirce dispersed long before the chase began.

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## Logical Graphs, Iconicity, Interpretation • Discussion 1

JM:
I’m impressed that you have read Ricoeur — my impression is that Americans don’t have much time for Continental philosophy (a huge generalisation of course).

Have you looked at Habermas?  He uses Peirce’s work as well as hermeneutics (mainly Gadamer) and critical theory to come up with what he calls a theory of communicative action.  He also called it “universal pragmatics” at one time as a nod to both Chomsky and semiotics.

Dear John,

That observation from Ricoeur’s Conflict of Interpretations comes from a time when Susan Awbrey and I were exploring the synergies of action research, critical thinking, classical and post-modern hermeneutics, and C.S. Peirce’s triadic relational semiotics.  We benefited greatly from our study of Gadamer, Habermas, Ricoeur and a little more from Derrida, Foucault, Lyotard, aided by the panoramic surveys of Richard J. Bernstein.  All that led to a paper we gave at a conference on Hermeneutics and the Human Sciences, subsequently published as “Interpretation as Action : The Risk of Inquiry” (doc) (pdf).

I found Ricoeur’s comment fitting in the present connection because it speaks to the way identical modulations of a medium may convey different messages to different cultures and contexts of communication.  Conversely, conveying the same message to different cultures and contexts of communication may require different modulations of the same medium.

That is precisely the situation we observe in the Table from Episode 1, for ease of reference repeated below.  The objects to be conveyed are the 16 boolean functions on 2 variables, whose venn diagrams appear in Column 1.  And we have the two cultures of interpreters, Entitative and Existential, whose graphical and parenthetical forms of expression for the boolean functions are shown in Column 2 and Column 3, respectively.

$\text{Boolean Functions and Logical Graphs on Two Variables}$

### References

• Awbrey, J.L., and Awbrey, S.M. (Autumn 1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  ArchiveJournal.  Online (doc) (pdf).
• Awbrey, J.L., and Awbrey, S.M. (June 1992), “Interpretation as Action : The Risk of Inquiry”, The Eleventh International Human Science Research Conference, Oakland University, Rochester, Michigan.

## Conceptual Barriers • 4

Re: Conceptual Barriers • (1)(2)(3)
Re: Peirce ListJohn SowaGary RichmondRobert Marty

Dear Robert,

I believe you have pointed to the crux of the matter.

When I arrived on the campus of my first university in the late ’60s there was already in progress some sort of year-long cross-campus “Colloquium” or “Dialogue” going on — with many invited speakers and representatives from all the colleges and departments, springing from the issues raised by C.P. Snow’s 1959 lecture on “The Two Cultures”.  About the same time the University instituted three new residential colleges in cross-cultural liberal arts, “statecraft” (a mix of history, law, and political science), and the bridge between science and society.

I confess it was all over the head of a first year student with his brain buried in math and physics with a minor in beer but I did get a whiff now and then of a sea change in the air.  A Möbius twist of fate and my room-mate’s hankering to find a dorm with a reputation for better food soon led me to relocate to the residence hall housing the “relevant science” people.  They all took courses with titles like “Third Cultural Rhetoric” and so I osmoted some of that synthesis from my brushes with the crew of that Enterprise.  Plus I met my future wife.

Poking around the web I see I already began this story two years ago, in connection with remarks John Sowa made in the Ontolog Forum as to “Why A Single Unified Ontology Is Impossible”.  I’ve also just realized how one of the main themes of the present discussion links up with what I wrote earlier about the “Immune System Metaphor” — so I can save myself the effort of crafting new syntax by continuing the story as I did before under the heading of Conceptual Barriers.

Long time passing, I found myself returning to these questions around the turn of the millennium, addressing the “problem of silos” and the “scholarship of integration” from the perspective of Peirce’s and Dewey’s pragmatism and semiotics.  Here’s a couple of contributions Susan Awbrey and I made to the area.

#### 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.  AbstractOnline.

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## C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • 2

### Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885)

#### §1.  Three Kinds Of Signs (cont.)

I have taken pains to make my distinction of icons, indices, and tokens clear, in order to enunciate this proposition:  in a perfect system of logical notation signs of these several kinds must all be employed.  Without tokens there would be no generality in the statements, for they are the only general signs;  and generality is essential to reasoning.  Take, for example, the circles by which Euler represents the relations of terms.  They well fulfill the function of icons, but their want of generality and their incompetence to express propositions must have been felt by everybody who has used them.  Mr. Venn has, therefore, been led to add shading to them;  and this shading is a conventional sign of the nature of a token.  In algebra, the letters, both quantitative and functional, are of this nature.

But tokens alone do not state what is the subject of discourse;  and this can, in fact, not be described in general terms;  it can only be indicated.  The actual world cannot be distinguished from a world of imagination by any description.  Hence the need of pronouns and indices, and the more complicated the subject the greater the need of them.  The introduction of indices into the algebra of logic is the greatest merit of Mr. Mitchell’s system.  He writes $F_1$ to mean that the proposition $F$ is true of every object in the universe, and $F_u$ to mean that the same is true of some object.  This distinction can only be made in some such way as this.  Indices are also required to show in what manner other signs are connected together.

With these two kinds of signs alone any proposition can be expressed;  but it cannot be reasoned upon, for reasoning consists in the observation that where certain relations subsist certain others are found, and it accordingly requires the exhibition of the relations reasoned with in an icon.  It has long been a puzzle how it could be that, on the one hand, mathematics is purely deductive in its nature, and draws its conclusions apodictically, while on the other hand, it presents as rich and apparently unending a series of surprising discoveries as any observational science.  Various have been the attempts to solve the paradox by breaking down one or other of these assertions, but without success.  The truth, however, appears to be that all deductive reasoning, even simple syllogism, involves an element of observation;  namely, deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts.  (3.363).

### References

• Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
• 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 3 : Exact Logic (Published Papers), 1933.  CP 3.359–403.
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Volume 5 (1884–1886), 1993.  Item 30, 162–190.

## C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • 1

### Selection from C.S. Peirce, “On the Algebra of Logic : A Contribution to the Philosophy of Notation” (1885)

#### §1.  Three Kinds Of Signs

Any character or proposition either concerns one subject, two subjects, or a plurality of subjects.  For example, one particle has mass, two particles attract one another, a particle revolves about the line joining two others.  A fact concerning two subjects is a dual character or relation;  but a relation which is a mere combination of two independent facts concerning the two subjects may be called degenerate, just as two lines are called a degenerate conic.  In like manner a plural character or conjoint relation is to be called degenerate if it is a mere compound of dual characters.  (3.359).

A sign is in a conjoint relation to the thing denoted and to the mind.  If this triple relation is not of a degenerate species, the sign is related to its object only in consequence of a mental association, and depends upon a habit.  Such signs are always abstract and general, because habits are general rules to which the organism has become subjected.  They are, for the most part, conventional or arbitrary.  They include all general words, the main body of speech, and any mode of conveying a judgment.  For the sake of brevity I will call them tokens.  (3.360).

But if the triple relation between the sign, its object, and the mind, is degenerate, then of the three pairs

$\begin{array}{lll} \text{sign} & & \text{object} \\ \text{sign} & & \text{mind} \\ \text{object} & & \text{mind} \end{array}$

two at least are in dual relations which constitute the triple relation.  One of the connected pairs must consist of the sign and its object, for if the sign were not related to its object except by the mind thinking of them separately, it would not fulfill the function of a sign at all.  Supposing, then, the relation of the sign to its object does not lie in a mental association, there must be a direct dual relation of the sign to its object independent of the mind using the sign.  In the second of the three cases just spoken of, this dual relation is not degenerate, and the sign signifies its object solely by virtue of being really connected with it.  Of this nature are all natural signs and physical symptoms.  I call such a sign an index, a pointing finger being the type of this class.

The index asserts nothing;  it only says “There!”  It takes hold of our eyes, as it were, and forcibly directs them to a particular object, and there it stops.  Demonstrative and relative pronouns are nearly pure indices, because they denote things without describing them;  so are the letters on a geometrical diagram, and the subscript numbers which in algebra distinguish one value from another without saying what those values are.  (3.361).

The third case is where the dual relation between the sign and its object is degenerate and consists in a mere resemblance between them.  I call a sign which stands for something merely because it resembles it, an icon.  Icons are so completely substituted for their objects as hardly to be distinguished from them.  Such are the diagrams of geometry.  A diagram, indeed, so far as it has a general signification, is not a pure icon;  but in the middle part of our reasonings we forget that abstractness in great measure, and the diagram is for us the very thing.  So in contemplating a painting, there is a moment when we lose consciousness that it is not the thing, the distinction of the real and the copy disappears, and it is for the moment a pure dream — not any particular existence, and yet not general.  At that moment we are contemplating an icon.  (3.362).

### References

• Peirce, C.S. (1885), “On the Algebra of Logic : A Contribution to the Philosophy of Notation”, American Journal of Mathematics 7, 180–202.
• 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 3 : Exact Logic (Published Papers), 1933.  CP 3.359–403.
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Volume 5 (1884–1886), 1993.  Item 30, 162–190.

## Semiotics, Semiosis, Sign Relations • Discussion 19

Normative science rests largely on phenomenology and on mathematics;
metaphysics on phenomenology and on normative science.

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)

JS:
Questions for everybody to consider:  In the 1903 classification of the sciences, Peirce did not mention semeiotic, the most important science that he introduced.  Why not?  Where does it belong in the classification?

The short schrift on this subject may be summed up in the following syllogism.

• Logic = Formal Semiotic
• Conclusion.  Logic = Normative Semiotic.
• Corollary.  This leaves room for Descriptive Semiotic.

• Definition and Determination • (4)(5)

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## Logical Graphs, Iconicity, Interpretation • 2

In the first place there are likenesses or copies — such as statues, pictures, emblems, hieroglyphics, and the like.  Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters. The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less;  for they stand for whatever they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men or a decree of God.  Such are tallies, proper names, &c.  The peculiarity of these conventional signs is that they represent no character of their objects.  Likenesses denote nothing in particular;  conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations.  They connote attributes and so connote them as to determine what they denote.  To this class belong all words and all conceptions.  Most combinations of words are also symbols.  A proposition, an argument, even a whole book may be, and should be, a single symbol.

The Table in the previous post can now be sorted to bring out the “family resemblances”, likenesses, or symmetries among logical graphs and the boolean functions they denote, where the “orbits” or similarity classes are determined by the dual interpretation of logical graphs.  Performing the sort produces the following Table.  As we have seen in previous discussions, there are 10 orbits in all, 4 orbits of 1 point each and 6 orbits of 2 points each.

$\text{Boolean Functions and Logical Graphs on Two Variables} \stackrel{_\bullet}{} \text{Orbit Order}$

## Logical Graphs, Iconicity, Interpretation • 1

If exegesis raised a hermeneutic problem, that is, a problem of interpretation, it is because every reading of a text always takes place within a community, a tradition, or a living current of thought, all of which display presuppositions and exigencies — regardless of how closely a reading may be tied to the quid, to “that in view of which” the text was written.

If a picture is worth a thousand words, here’s my 48,000 words worth on the recurring question of logical graphs, their iconicity, and their interpretation, at least as concerns Peirce’s alpha graphs interpreted for propositional logic.  A few more actual words, literally speaking, may be called for.  I’ll return to that anon.

Referring to the Table —

• Column 1 shows a conventional name $f_{i}$ and a venn diagram for each of the sixteen boolean functions on two variables.
• Column 2 shows the logical graph canonically representing the boolean function in Column 1 under the entitative interpretation.  This is the interpretation C.S. Peirce used in his earlier work on entitative graphs and the one Spencer Brown used in his book Laws of Form.
• Column 3 shows the logical graph canonically representing the boolean function in Column 1 under the existential interpretation.  This is the interpretation C.S. Peirce used in his later work on existential graphs.

$\text{Boolean Functions and Logical Graphs on Two Variables}$

## Minimal Negation Operators • Discussion 2

Re: Minimal Negation Operators • (1)(2)(3)(4)
Re: Peirce List (1) (2) (3)Jerry Chandler

JC:
As a chemist, CSP often inscended hyle terminology into his logical corpse as he sought to extend the 15–17th century historical usages of the meaning of the concept of a “term”.

One particularity of chemical synthesis is the absence of the “negative” operators on the chemical elements.  Each element is a logical constant in the language of chemistry and hence can not be negated.  Yet, in the notation for chemistry it is necessary to assert and signify the absence of a chemical unit in a logical product.  This could be referred to as a minimal negation in a logically consistent semantics of a chemical syntax.

I have no information, either positive or negative, of the meaning Jon intends to infer logically with his usage of this non-standard semantics.  However, this semantics is obviously useful in attempting to give a logical semantics for the well‑established semiosis of hyle.

Dear Jerry,

I’ve been spending a lot of time lately thinking about how I first got into all the things I’ve gotten into over the years.  The thing that surprised me the most was how much of my life I’ve been immersed in raw data despite my best efforts to rise above it in flights of theory and just plain fancy.  The honors chemistry course I took my first year in college was pretty advanced — we “hit the ground running” as my Dad used to say from his paratroop days — moving from covalent bonding theory the first term to molecular orbital theory the second.

It was there I first encountered the triple interaction of theory, experiment, and electronic computation.  Aside from the routine programs we ran to analyze our data, drawing least squares lines through experimental scatterplots and all that, I began my first attempts to compute with symbolic forms, trying to get Fortran to place the electron dots around and between chemical symbols in various molecular combinations.  Mostly I learned to dislike Fortran — wrong tool for the job, I guess — and it would be years before I woke to Lisp.

At any rate, let me beg off on chemical logic or logical chemistry.  My experiences in that borderland are more a tale of fits and starts than anything conclusive and reconstructing the details would take a search through the darker corners of my basement archives.

The matter of “non-standard semantics”, however, is a timely and topical subject to address, one it would dispel a mass of obscurities about the link between logic and semiotics to clarify as much as we can.

To begin, we may pose the question as follows.

• In what way does a propositional calculus based on minimal negation operators deviate from standard semantics?

I will take that up next time, perhaps under a different heading.

Regards,

Jon