Tag Archives: Information = Comprehension × Extension

Unknown's avatar Jon Awbrey 6:40 am on June 18, 2026
Tags: , , , , , Hypothesis, , , , Information = Comprehension × Extension, , Intension, , Peirce's Categories, Pragmatic Semiotic Information, , , ,   

Information = Comprehension × Extension • Preamble

Perhaps the best perspective from which to bring the connection between the theory of signs and the theory of inquiry into its proper focus is Peirce’s own Theory of Information, which he began setting forth in lectures at Harvard and the Lowell Institute in 1865 and 1866.  Peirce encapsulates the elements of his theory in the following formula.

Information = Comprehension × Extension

In the Resources below I link to my study of Peirce’s 1865–1866 Lectures on the Logic of Science, with selections from the lectures and my commentary on them.

Ten summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manner in which different representations stand for their objects” and the way in which different inferences transform states of information.  I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the cool of later reflection.  Now looks to be a choice moment for taking another look.

A first pass through the variations of representation and reasoning detects the axes of iconic, indexical, and symbolic manners of representation on the one hand and the axes of abductive, inductive, and deductive modes of inference on the other.  Early and often Peirce suggests a natural correspondence between the main modes of inference and the main manners of representation but his early arguments differ from his later accounts in ways deserving close examination, partly for the extra points in his line of reasoning and partly for his explanation of indices as signs constituted by convening the variant conceptions of sundry interpreters.

References

  • 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. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432.  Archive.  Online.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi
Perhaps the best perspective from which to bring the connection between the theory of signs and the theory of inquiry into its proper focus is Peirce’s own Theory of Information, which he began setting forth in lectures at Harvard and the Lowell Institute in 1865 and 1866.  Peirce encapsulates the elements of his theory in the following formula.

Information = Comprehension × Extension

In the Resources below I link to my study of Peirce’s 1865–1866 Lectures on the Logic of Science, with selections from the lectures and my commentary on them.

Ten summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manner in which different representations stand for their objects” and the way in which different inferences transform states of information.  I roughed out a sketch of my epiphany in a series of blog posts then set it aside for the cool of later reflection.  Now looks to be a choice moment for taking another look.

A first pass through the variations of representation and reasoning detects the axes of iconic, indexical, and symbolic manners of representation on the one hand and the axes of abductive, inductive, and deductive modes of inference on the other.  Early and often Peirce suggests a natural correspondence between the main modes of inference and the main manners of representation but his early arguments differ from his later accounts in ways deserving close examination, partly for the extra points in his line of reasoning and partly for his explanation of indices as signs constituted by convening the variant conceptions of sundry interpreters.

References

  • 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. (1867), “Upon Logical Comprehension and Extension”, Proceedings of the American Academy of Arts and Sciences, Vol. 7, pp. 416–432.  Archive.  Online.

Resources

cc: Academia.edu • Cybernetics • Laws of Form • Mathstodon
cc: Research Gate • Structural Modeling • Systems Science • Syscoi

#abduction, #c-s-peirce, #comprehension, #deduction, #extension, #hypothesis, #icon-index-symbol, #induction, #inference, #information-comprehension-x-extension, #inquiry, #intension, #logic, #peirces-categories, #pragmatic-semiotic-information, #pragmatism, #scientific-method, #semiotics, #sign-relations

Unknown's avatar Jon Awbrey 9:00 am on November 11, 2025
Tags: , , , , , , , , , , , , , Information = Comprehension × Extension, , , , , , , , , , , , , , , , , , , , , , , , , , , , ,   

Survey of Pragmatic Semiotic Information • 9

This is a Survey of blog and wiki posts on a theory of information which grows out of pragmatic semiotic ideas.  All my projects are exploratory in character 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 answering 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 obscuring the issue and fixed on what he called the “laws of information” as the key to solving the puzzle.

The first hints of the Information Revolution in our understanding of scientific inquiry may be traced to Peirce’s lectures of 1865–1866 at Harvard University and the Lowell Institute.  There Peirce took up “the puzzle of the validity of scientific inference” and claimed it was “entirely removed by a consideration of the laws of information”.

Fast forward to the present and I see the Big Question as follows.  Having gone through the exercise of comparing and contrasting Peirce’s theory of information, however much it yet remains in a rough‑hewn state, with Shannon’s paradigm so pervasively informing the ongoing revolution in our understanding and use of information, I have reason to believe Peirce’s idea is root and branch more general and has the potential, with due development, to resolve many mysteries still bedeviling our grasp of inference, information, and inquiry.

Inference, Information, Inquiry

Pragmatic Semiotic Information

Semiotics, Semiosis, Sign Relations

Sign Relations, Triadic Relations, Relation Theory

  • Blog Series • (1)
    • Discusssions • (1) • (2)

Excursions

Blog Dialogs

References

  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).

cc: FB | Semeiotics • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#abduction, #c-s-peirce, #communication, #control, #cybernetics, #deduction, #determination, #discovery, #doubt, #epistemology, #fixation-of-belief, #induction, #information, #information-comprehension-x-extension, #information-theory, #inquiry, #inquiry-driven-systems, #inquiry-into-inquiry, #interpretation, #invention, #knowledge, #learning-theory, #logic, #logic-of-relatives, #logic-of-science, #mathematics, #philosophy-of-science, #pragmatic-information, #probable-reasoning, #process-thinking, #relation-theory, #scientific-inquiry, #scientific-method, #semeiosis, #semiosis, #semiotic-information, #semiotics, #sign-relational-manifolds, #sign-relations, #surveys, #triadic-relations, #uncertainty, #visualization

Unknown's avatar Jon Awbrey 7:20 am on November 5, 2025
Tags: , , Constraint, , , , , Indication, , Information = Comprehension × Extension, , , , , , , Structure, Systems Theory,   

Survey of Definition and Determination • 4

In the early 1990s, “in the middle of life’s journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from signs and scientific inquiry to logic and information theory.

Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as Peirce used them in his logic and semiotics but as researchers in areas as diverse as computer science, cybernetics, physics, and systems science would find themselves forced to reconsider the concepts in later years.  That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination.  There are copies of those selections at the following sites.

What follows is a Survey of blog and wiki posts on Definition and Determination, with a focus on the part they play in Peirce’s interlinked theories of signs, information, and inquiry.  In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force when we view the overarching concept of constraint from an information-theoretic point of view, as Peirce did beginning in the 1860s.

Blog Dialogs

cc: FB | Inquiry Driven Systems • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#c-s-peirce, #comprehension, #constraint, #definition, #determination, #extension, #form, #indication, #information, #information-comprehension-x-extension, #inquiry-driven-systems, #logic, #mathematics, #scientific-method, #semiotics, #sign-relations, #structure, #systems-theory, #visualization

Unknown's avatar Jon Awbrey 12:12 pm on November 4, 2025
Tags: , , , , , , , , , , , , , Information = Comprehension × Extension, , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,   

Survey of Cybernetics • 5

Again, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors?

— Plato • Alcibiades • 135 A

This is a Survey of blog posts relating to Cybernetics.  It includes the selections from Ashby’s Introduction and the comment on them I’ve posted so far, plus two series of reflections on the governance of social systems in light of cybernetic and semiotic principles.

Anthem

Ashby’s Introduction to Cybernetics

  • Chapter 11 • Requisite Variety

Blog Series

  • Theory and Therapy of Representations • (1) • (2) • (3) • (4) • (5)

cc: FB | Inquiry Driven Systems • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#abduction, #c-s-peirce, #communication, #control, #cybernetics, #deduction, #determination, #discovery, #doubt, #epistemology, #fixation-of-belief, #induction, #information, #information-comprehension-x-extension, #information-theory, #inquiry, #inquiry-driven-systems, #inquiry-into-inquiry, #interpretation, #invention, #knowledge, #learning-theory, #logic, #logic-of-relatives, #logic-of-science, #mathematics, #peirce, #philosophy, #philosophy-of-science, #pragmatic-information, #probable-reasoning, #process-thinking, #relation-theory, #scientific-inquiry, #scientific-method, #semeiosis, #semiosis, #semiotic-information, #semiotics, #sign-relational-manifolds, #sign-relations, #surveys, #triadic-relations, #uncertainty