Semiotics, Semiosis, Sign Relations • Discussion 4

Posted on November 7, 2019 by Jon Awbrey

Re: Semiotics, Semiosis, Sign Relations • Discussion 2

It’s a common mistake to confound infinite with unbounded.  A process can continue without end and still be “bounded in a nutshell”.  So a sign process can pass from sign to interpretant sign to next interpretant sign ad infinitum without ever leaving a finite set of signs.

The number of questions I got about that statement tells me I should have delineated the context in which it was set a little more fully.

A sign process in this context is simply a sequence of signs, of the sort we might observe in communicational, computational, or experimental settings.  For people who remember the more ancient arts of AI, cognitive science, and cybernetics, it may help to recall the orders of considerations arising in protocol analysis.

It goes with this territory to assume the formal equivalent of categorical perception.  This means we can set aside the subtleties of token haecceity — the nominal distinctiveness of every individual sign instance — along with the possibility of signs being sampled from a continuous medium.

In this setting we are left with two interpretations for infinite and bounded, depending on whether the sign domain has a quantitative measure defined on it, or not.  In the first case, bounded means the sequence never exceeds a finite bound in the relevant measure.  In the second case, bounded means the sequence never leaves a finite set.

cc: Cybernetics (1) (2) • Ontolog • Peirce (1) (2) • Structural Modeling • Systems Science

Posted in C.S. Peirce, Cybernetics, Logic, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , , | 13 Comments

Pragmatic Truth • Discussion 14

Posted on November 6, 2019 by Jon Awbrey

Re: Cybernetic Communications • Stephen Paul King

There are many conceptions of truth — linguistic, model-theoretic, proof-theoretic — for the moment I’m focused on cybernetics, systems, and experimental sciences and this is where the pragmatic conception of truth fits what we naturally do in those sciences remarkably well.

The main thing in those activities is the relationship among symbol systems, the world, and our actions, whether in thought, among ourselves, or between ourselves and the world.  So the notion of truth we want here is predicated on three dimensions:  the patch of the world we are dealing with in a given application, the systems of signs we are using to describe that domain, and the transformations of signs we find of good service in bearing information about that piece of the world.

I’ll dig up some material on the pragmatic conception of truth …

cc: Systems Science • Structural Modeling • Peirce List • Ontolog Forum • Cybernetics

Posted in Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Pragmatic Truth • Discussion 13

Posted on November 3, 2019 by Jon Awbrey

Re: FB | Charles S. Peirce Society • John Corcoran

I looked at John Corcoran’s contribution on “Formalizing Pragmatic Truth” but did not see anything near enough what I’d recognize as a pragmatic theory of truth.

Pragmatic inquiry into a candidate concept of truth would begin by applying the pragmatic maxim to clarify the concept as far as possible and a pragmatic definition of truth, should any result, would find its place within Peirce’s theory of logic as formal semiotics, in other words, stated in terms of a formal theory of triadic sign relations.

Resources

cc: Systems Science • Structural Modeling • Peirce List • Ontolog Forum • Cybernetics

Posted in Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 7 Comments

Semiotics, Semiosis, Sign Relations • Discussion 3

Posted on October 30, 2019 by Jon Awbrey

Questions about the use of “semiotic triangles” and “semiotic triskelia” to represent triadic sign relations have come up again, as they often do in the wider world, prompting me to revisit an earlier comment on the subject and to tri, tri again to render the issues as clear as I can, otherwise we appear doomed never to get off triangle one.

Re: Semiotic Triangle • (1) • (2) | John Corcoran • (1) • (2)

Concepts for Peirce are mental symbols, so they fall under the general designation of signs.  For triadic sign relations in general, then, we are dealing with a triadic relation among (1) objects of signs, (2) signs of objects, and (3) what Peirce calls interpretant signs, or interpretants for short.  It is critical to regard the three designations of objects, signs, and interpretants as relational roles not ontological essences.  It is also critical to distinguish the following things:

  • The extended sign relation L as a subset of a cartesian product O \times S \times I,
  • The elementary sign relation as an ordered triple (o, s, i) in O \times S \times I,
  • The places forming an ordered triple (o, s, i),
  • The elements o, s, i filling those places.

Triangles like the one linked above have long been used to introduce the idea of a triadic sign relation.  They have the unintended consequence, however, of leading people to miss all the points I mentioned above.  So it’s wise to move quickly on to better pictures and more detailed descriptions.

Resources

cc: Cybernetics (1) (2) • Ontolog • Peirce (1) (2) • Structural Modeling • Systems Science

Posted in C.S. Peirce, Cybernetics, Logic, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , , | 11 Comments

Survey of Semiotics, Semiosis, Sign Relations • 1

Posted on October 29, 2019 by Jon Awbrey

This is a Survey of blog and wiki resources on the theory of signs, variously known as semeiotic or semiotics, and the actions referred to as semiosis which transform signs among themselves in relation to their objects, all as based on C.S. Peirce’s concept of triadic sign relations.

Elements

Sources

Blog Series

  • Sign Relations, Triadic Relations, Relation Theory • (1)
  • C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • (1) • (2)

Blog Dialogs

References

  • Awbrey, J.L., and Awbrey, S.M. (1992), “Interpretation as Action : The Risk of Inquiry”, The Eleventh International Human Science Research Conference, Oakland University, Rochester, Michigan.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  Archive.  Journal.  Online.
Posted in C.S. Peirce, Logic, Mathematics, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , , | 15 Comments

The Difference That Makes A Difference That Peirce Makes • 32

Posted on October 27, 2019 by Jon Awbrey

Re: FB | Foundations of Mathematics • John Corcoran

There was a huge — and of course ultimately futile — discussion of truth theories back in 2005 when the Wikipediot article on Truth was under development.  Pragmatists of one stripe or another from the Peirce List ventured in vain to explain the difference between (1) “classical” correspondence theories, (2) consensus or “social” theories, and (3) Peircean pragmatic — I’m guessing what Tarski meant by “utilitarian” — theories of truth.  I’ll dig up some links and forks when I get a chance.

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science

Posted in Analogy, C.S. Peirce, Communication, Descriptive Science, Fixation of Belief, Formal Systems, Information, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Normative Science, Paradigms, Peirce, Pragmatic Maxim, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Semiotics, Semiosis, Sign Relations • Discussion 2

Posted on October 26, 2019 by Jon Awbrey

Re: Richard Coyne • Recursion Again

It’s a common mistake to confound infinite with unbounded.  A process can continue without end and still be “bounded in a nutshell”.  So a sign process can pass from sign to interpretant sign to next interpretant sign ad infinitum without ever leaving a finite set of signs.

Resources

cc: Cybernetics (1) (2) • Ontolog • Peirce (1) (2) • Structural Modeling • Systems Science

Posted in C.S. Peirce, Cybernetics, Logic, Peirce, Pragmatism, Relation Theory, Semiosis, Semiotics, Sign Relations | Tagged , , , , , , , , | 18 Comments

Peirce’s 1870 “Logic Of Relatives” • Discussion 2

Posted on October 24, 2019 by Jon Awbrey

Re: Ecology of Systems Thinking • RS • TM

My previous comment summed up my observations of a general drift toward “absolutist and dyadic ways of thinking” in various communities of inquiry of interest to me over the past 20 years.  I traced its cause to “the stubborn pull of unchecked reductionism” and a corresponding failure to grasp the relational structures of complex phenomena.

A preference for simple models and theories is natural enough so long as the chosen models and theories are up to the task of explaining the phenomena at hand, but when a preference for a particular class of structures persists in the face of steadily mounting anomalies it becomes a hidebound and dysfunctional bias.

That is my description and my diagnosis of the situation as I see it.  I could be wrong about either or both.  But the reason for addressing the case in these terms is not simply to point out a dysfunctional state of affairs.  The purpose of a diagnosis is to indicate a remedy.

cc: Systems Science • Structural Modeling • Peirce List • Ontolog Forum • Cybernetics

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Peirce’s 1870 “Logic Of Relatives” • Comment 2

Posted on October 22, 2019 by Jon Awbrey

In a recent post on a related topic I gave this assessment of our present situation:

One of the more disconcerting developments, I might say “devolutions”, I’ve observed over the past 20 years has been the general slippage back to absolutist and dyadic ways of thinking, all of it due to the stubborn pull of unchecked reductionism and a failure to comprehend the relational paradigm, especially the basic facts about triadic relations, their irreducibility, and the consequences thereof.

For anyone who sees our situation this way, and who thinks it calls for a remedy, the question becomes:  How to remediate a persistent failure to comprehend the relational paradigm, especially the basic facts about triadic relations, their irreducibility, and the consequences thereof?

My answer to that naturally brings me back to this thread, so I’ll continue from here.

cc: Systems Science • Structural Modeling • Peirce List • Ontolog Forum • Cybernetics

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Peirce’s 1870 “Logic of Relatives” • Comment 1

Posted on October 22, 2019 by Jon Awbrey

Peirce often stressed his Logic of Relatives as the key to unlocking many puzzles.  As I read him, it was Peirce’s drive to understand the Logic of Science that required the grounding of logic in the mathematical forms of triadic sign relations and this in turn demanded a leap forward in the understanding of relations in general.

My long ago encounter with Peirce’s 1870 paper, “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, was one of the events precipitating my return from the hazier heights of philosophy to the solid plains of mathematics below.  Over the years I copied out various drafts of my study notes to the web, consisting of selections from Peirce’s paper along with my running commentary.  A few years back I serialized what progress I had made so far to this blog and this Overview consists of links to those installments.

Peirce’s 1870 “Logic of Relatives”

References

  • Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.  Reprinted, Collected Papers (CP 3.45–149), Chronological Edition (CE 2, 359–429).  Online (1) (2) (3).
  • 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.  Cited as (CP volume.paragraph).
  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Cited as (CE volume, page).

Resources

cc: Cybernetics • Ontolog Forum • Peirce List • Structural Modeling • Systems Science

Posted in C.S. Peirce, Category Theory, Differential Logic, Duality, Dyadic Relations, Graph Theory, Group Theory, Logic, Logic of Relatives, Logical Graphs, Logical Matrices, Mathematics, Peirce, Peirce's Categories, Predicate Calculus, Propositional Calculus, Relation Theory, Semiotics, Sign Relations, Teridentity, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , | 6 Comments