Inquiry Driven Systems • Comment 2

I just got reminded of an earlier blog post that more or less fits here.  It links to the bibliography I had in hand and mind when I went back to graduate school in systems engineering to synthesize all the unfinished projects I had been accumulating over the years and dedicated myself to the systems aspects of Peirce’s theory of inquiry in a more applied way.

I finally finished retyping the bibliography to my systems engineering proposal that had gotten lost in a move between computers, so here is a link to the InterSciWiki copy:

This may be of interest to people working towards applications of Peirce’s theory of inquiry, especially the design of intelligent systems with a capacity for supporting scientific inquiry.

Posted in C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Knowledge Bases, Knowledge Representation, Learning, Logic, Peirce, Reasoning, Semiotics, Sign Relations, Systems Theory | Tagged , , , , , , , , , , , , , , | Leave a comment

Inquiry Driven Systems • Comment 1

Re: Peirce List DiscussionDEET

The role of acquired knowledge bases in inquiry, learning, and reasoning is discussed in the following article and sections.

Posted in C.S. Peirce, Cybernetics, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Knowledge Bases, Knowledge Representation, Learning, Logic, Peirce, Reasoning, Semiotics, Sign Relations, Systems Theory | Tagged , , , , , , , , , , , , , , | Leave a comment

Sign Relations • Comment 12

Re: Ontolog DiscussionHP

In the Peirce universe “the role that human institutions play in establishing grounding and associated frames of reference and standards” (Hans Polzer) is articulated by reference to “communities of inquiry” and “communities of interpretation”.  Invoking communities as extended agents of inquiry and interpretation equips us with a better handle on “contexts of interpretation” and the structures involved in this array of constructs are found to be of triadic sign relations all compact.

Over the years I have found the hardest thing to convey about sign relations has been what it’s like to think and work within an extended sign relational environment.  A “setting” like that consists of a large number of individual sign-relational triples called “elementary sign relations”, each having the form (o, s, i), where o is the object, s is the sign, and i is the interpretant sign of the triple.

This means that any given sign relation L is a subset of a cartesian product O \times S \times I, where O is the object domain, S is the sign domain, and I is the interpretant sign domain of the sign relation L in view.

Taking this point of view on sign relations makes a big difference in the conjoined theories of inquiry and interpretation that develop from this point on.

Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | Leave a comment

Sign Relations • Comment 11

Re: Peirce List DiscussionJAS

When you ask a question about what something is, you are asking a question about its ontology.  But signhood is not a matter of ontology, it is a form of relation.

Re: Peirce List DiscussionETHRNB

Here again is that budget of excerpts on Determination, mostly Peirce with a few others before and after his time, all of which I collected back when I was turning my hand to the cybernetic and intelligent systems engineering prospects of Peirce’s theories of information, inquiry, and signs.

Contemporary conceptions of determination and determinacy in mathematics, physics, computer science, and engineering are covered by the concept of constraint and generalize beyond absolute determinism to degrees and measures of determination, ranging from none at all to totality.

Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | Leave a comment

Sign Relations • Comment 10

Re: Peirce List DiscussionJFS

Three-Headed Dogs and Triadic Sign Relations

Peirce’s “Sop to Cerberus” got tossed about quite a bit in our discussions across the Web this millennium.  Here’s a record of one occasion from the days when our discussions bridged over multiple perspectives, in this instance the Peirce List and its parallel Arisbe List, the French SemioCom, and the Standard Upper Ontology Working Group:

There is a critical passage where Peirce explains the relationship between his popular illustrations and his technical theory of signs.

It is clearly indispensable to start with an accurate and broad analysis of the nature of a Sign.  I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former.  My insertion of “upon a person” is a sop to Cerberus, because I despair of making my own broader conception understood.  (Peirce 1908, Selected Writings, p. 404).

I have long connected this passage with Peirce’s much earlier “metaphorical argument” where he changes the addressee of a word — that to which it stands for something — from a person, to that person’s memory, to “a particular remembrance or image in that memory”, to wit, “the one which is the mental equivalent of the word … in short, its interpretant.”

Here is a passage from Peirce that is decisive in clearing up the relationship between the interpreter and the interpretant …

I think we need to reflect upon the circumstance that every word implies some proposition or, what is the same thing, every word, concept, symbol has an equivalent term — or one which has become identified with it, — in short, has an interpretant.

Consider, what a word or symbol is;  it is a sort of representation.  Now a representation is something which stands for something.  I will not undertake to analyze, this evening, this conception of standing for something — but, it is sufficiently plain that it involves the standing to something for something.  A thing cannot stand for something without standing to something for that something.  Now, what is this that a word stands to?  Is it a person?

We usually say that the word homme stands to a Frenchman for man.  It would be a little more precise to say that it stands to the Frenchman’s mind — to his memory.  It is still more accurate to say that it addresses a particular remembrance or image in that memory.  And what image, what remembrance?  Plainly, the one which is the mental equivalent of the word homme — in short, its interpretant.  Whatever a word addresses then or stands to, is its interpretant or identified symbol.  …

The interpretant of a term, then, and that which it stands to are identical.  Hence, since it is of the very essence of a symbol that it should stand to something, every symbol — every word and every conception — must have an interpretant — or what is the same thing, must have information or implication.  (Peirce 1866, Chronological Edition 1, pp. 466–467).

As I read the long arc of Peirce’s work, the greater significance of the transformation he suggests at these points is not the shift from one type of interpreter to another, however compelling the consideration of life-forms in general as sign-processing agents may be, but the change of perspective that pulls our exclusive focus on representative agents of semiosis back to a properly relational point of view and the triadic sign relations that generate competent semiotic conduct.  But Peirce made this transformation early on in his work, and even more strikingly in its first trials.  Viewed in that light I think I share Peirce’s despair that its full impact has yet to be felt.


  • Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
  • Peirce, C.S. (1908), “Letters to Lady Welby”, Chapter 24, pp. 380–432 in Charles S. Peirce : Selected Writings (Values in a Universe of Chance), Edited with Introduction and Notes by Philip P. Wiener, Dover Publications, New York, NY, 1966.


Posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations | Tagged , , , , , , | Leave a comment

{ Information = Comprehension × Extension } • Discussion 7

Re: Joselle DiNunzio KehoeInformation and Questions of Consciousness

C.S. Peirce put forth the idea that what he called “the laws of information” were key to solving “the puzzle of the validity of scientific inference” and thus to understanding the “logic of science”.  See my notes on his notorious formula:

Posted in Abduction, C.S. Peirce, Comprehension, Consciousness, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Intension, Logic, Logic of Science, Mathematics, Peirce, Scientific Method, Semiotic Information, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs : 12

Re: Facebook DiscussionMBM

I’ve always been fond of picture proofs — it was one of the things that drew me to graph theory, topology, and the logical graphs of C.S. Peirce and Spencer Brown in the first place.  Sue was transitioning from Chemistry to Instructional Media when we first met and we often talked of crafting visual media for teaching mathematics from the ground up.

But the more I programmed the basal learning and reasoning modules the more I ran up against the limitations of the CSP–GSB calculi in their handed down forms and the limits of iconic representations in general.  Changes had to be made.  Curiously enough, many of the needed changes could be gleaned by looking more closely at the steps CSP and GSB used to arrive at their systems, by self-applying, iterating, and then taking those steps to the limit.


Posted in Abstraction, Amphecks, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Complementarity, Computational Complexity, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Graph Theory, Iconicity, Interpretation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment