#triadicrelations — Public Fediverse posts

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry.  In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject.  In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve.  In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation.  Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

• Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA.  Reprinted (1991), Prometheus Books, Buffalo, NY.  Online.
• 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 (doc) (pdf).

Resources

• Sign Relation • OEIS • MyWikiBiz • Wikiversity
• Survey of Semiotics, Semiosis, Sign Relations
• Survey of Inquiry Driven Systems

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

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.  Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places.  In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

• Correspondence.  From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself.  In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

• Determination.  Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes.  First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms.  Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

• Non‑psychological.  Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism.  He was quite interested in matters of psychology and had much of import to say about them.  But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

• Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.

Resources

• Sign Relation • OEIS • MyWikiBiz • Wikiversity
• Survey of Semiotics, Semiosis, Sign Relations

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

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

Interpreter and Interpretant • Selection 7
• https://inquiryintoinquiry.com/2025/01/15/interpreter-and-interpretant-selection-7-a/

Learning —

Rules in a knowledge base, as far as their effective content goes, can be obtained by any mode of inference. For example, consider a proposition of the following form.

• B ⇒ A, Just Before it rains, the Air is cool.

Such a proposition is usually induced from a consideration of many past events. The inductive inference may be observed to fit the following pattern.

• Case : C ⇒ B, In Certain events, it is just Before it rains.
• Fact : C ⇒ A, In Certain events, the Air is cool.
────────────────────────────────────
• Rule : B ⇒ A, Just Before it rains, the Air is cool.

However, the same proposition could also be abduced as an explanation of a singular occurrence or deduced as a conclusion of a prior theory.

References —

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.
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

Resources —

Survey of Abduction, Deduction, Induction, Analogy, Inquiry
• https://inquiryintoinquiry.com/2024/02/27/survey-of-abduction-deduction-induction-analogy-inquiry-4/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Logic #Semiotics #SignRelations #TriadicRelations
#Interpretation #Interpreter #Interpretant #Hermeneutics
#JohnDewey #Inquiry #Abduction #Deduction #Induction
#Abstraction #HypostaticAbstraction #Reflection

Interpreter and Interpretant • Selection 6
• https://inquiryintoinquiry.com/2025/01/13/interpreter-and-interpretant-selection-6-a/

Inquiry and Induction —

To understand the bearing of inductive reasoning on the closing phases of inquiry there are a couple of observations we should make.

• Smaller inquiries are typically woven into larger inquiries, whether the whole pattern of inquiry is carried on by a single agent or by a complex community.

• There are several ways particular instances of inquiry are related to ongoing inquiries at larger scales. Three modes of interaction between component inquiries and compound inquiries may be described under the headings of Learning, Transfer, and Testing of Rules.

#Peirce #Logic #Semiotics #SignRelations #TriadicRelations
#Interpretation #Interpreter #Interpretant #Hermeneutics
#JohnDewey #Inquiry #Abduction #Deduction #Induction
#Abstraction #HypostaticAbstraction #Reflection

Interpreter and Interpretant • Selection 5
• https://inquiryintoinquiry.com/2025/01/11/interpreter-and-interpretant-selection-5-a/

Inquiry and Inference —

If we follow Dewey's “Sign of Rain” story far enough to consider the import of thought for action, we realize the subsequent conduct of the interpreter, progressing up through the natural conclusion of the episode — the quickening steps, the seeking of shelter in time to escape the rain — all those acts amount to a series of further interpretants for the initially recognized signs of rain and the first impressions of the actual case. Just as critical reflection develops the positive and negative signs which gather about an idea, pragmatic interpretation explores the consequential and contrasting actions which give effective and testable meaning to a person's belief in it.

#Peirce #Logic #Semiotics #SignRelations #TriadicRelations
#Interpretation #Interpreter #Interpretant #Hermeneutics
#JohnDewey #Inquiry #Abduction #Deduction #Induction
#Abstraction #HypostaticAbstraction #Reflection

References —

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

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.
• https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Resources —

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2024/02/28/survey-of-inquiry-driven-systems-6/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut
#JohnDewey #HowWeThink #Inquiry #Abduction #Deduction #Induction
#Abstraction #HypostaticAbstraction #Reflection #Interpretation

Interpreter and Interpretant • Selection 4
• https://inquiryintoinquiry.com/2025/01/09/interpreter-and-interpretant-selection-4-a/

Interpretation and Inquiry —

To illustrate the role of sign relations in inquiry we begin with Dewey's elegant and simple example of reflective thinking in everyday life.

❝A man is walking on a warm day. The sky was clear the last time he observed it; but presently he notes, while occupied primarily with other things, that the air is cooler. It occurs to him that it is probably going to rain; looking up, he sees a dark cloud between him and the sun, and he then quickens his steps. What, if anything, in such a situation can be called thought? Neither the act of walking nor the noting of the cold is a thought. Walking is one direction of activity; looking and noting are other modes of activity. The likelihood that it will rain is, however, something suggested. The pedestrian feels the cold; he thinks of clouds and a coming shower.❞ (John Dewey, How We Think, 6–7).

#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut
#JohnDewey #HowWeThink #Inquiry #Abduction #Deduction #Induction
#Abstraction #HypostaticAbstraction #Reflection #Interpretation

Reference —

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.

Resources —

Hypostatic Abstraction
• https://inquiryintoinquiry.com/2008/08/08/hypostatic-abstraction/

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/

#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut
#Abstraction #HypostaticAbstraction #SopToCerberus #Interpretation

Interpreter and Interpretant • Selection 3
• https://inquiryintoinquiry.com/2025/01/08/interpreter-and-interpretant-selection-3-a/

The following selection from Peirce's “Lowell Lectures on the Logic of Science” (1866) lays out in detail his “metaphorical argument” for the relationship between interpreters and interpretant signs.

#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut
#Abstraction #HypostaticAbstraction #SopToCerberus #Interpretation

Interpreter and Interpretant • Selection 2
• https://inquiryintoinquiry.com/2025/01/07/interpreter-and-interpretant-selection-2-a/

A idea of what Peirce means by an Interpretant and the part it plays in a triadic sign relation is given by the following passage.

❝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).

According to his custom of clarifying ideas in terms of their effects, Peirce tells us what a sign is in terms of what it does, the effect it brings to bear on a “person”. That effect he calls the interpretant of the sign. And what of that person? Peirce finesses that question for the moment, resorting to a “Sop to Cerberus”, in other words, a rhetorical gambit used to side‑step a persistent difficulty of exposition. In doing so, Peirce invokes the hypostatic abstraction of a “person” who conducts the movement of signs and embodies the ongoing process of semiosis.

Reference —

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.

#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut
#Abstraction #HypostaticAbstraction #Interpretation

Interpreter and Interpretant • Discussion 1
• http://inquiryintoinquiry.com/2024/02/01/interpreter-and-interpretant-discussion-1/

Re: Conceptual Graphs
• https://lists.cs.uni-kassel.de/hyperkitty/list/[email protected]/thread/TC5YDO4NC42TFUNQ2QAIE4RFLJNQVVH2/

Helmut Raulien:
❝I find it a bit problematic to say, that the sign determines the interpretant, because the sign doesn't infer, it is the interpreter, who does the inference. But ok, I guess we might say, that Peirce prescinds the semiosis from the interpreter, so, ok, the flow of determination goes from the sign to the interpretant, because it is the interpreter, who receives the sign, and then forms the interpretant […]❞

Helmut,

Thanks for this. Something about the way you expressed the question led me to think of a new angle on it.

What makes an interpretant is fairly simple, at least, here's the catch, once you have the appropriate mathematical framework in place — An interpretant is whatever appears in the third place of a sign‑relational triple (o, s, i).

What makes an interpreter is more complex. I'll take that up as I get more time.

Resources —

Pragmatic Maxim
• https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-a/

Hypostatic Abstraction
• https://inquiryintoinquiry.com/2008/08/08/hypostatic-abstraction/

#Peirce #Logic #Semiotics #SignRelations #TriadicRelations
#Inference #Information #Inquiry #Interpreter #Interpretant
#Abstraction #HypostaticAbstraction #PrescissiveAbstraction
#Pragma #Pragmata #Pragmatism #PragmaticMaxim #Determination

Interpreter and Interpretant • Selection 2
• https://inquiryintoinquiry.com/2024/01/28/interpreter-and-interpretant-selection-2/

In the next passage up for review the hypostatic abstraction of a person to conduct the movement of signs is described by Peirce as a Sop to Cerberus, a rhetorical gambit set to side‑step a persistent difficulty of exposition.

❝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).

Reference —

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.

Resource —

Hypostatic Abstraction
• https://inquiryintoinquiry.com/2008/08/08/hypostatic-abstraction/

#Peirce #Logic #Semiotics #SignRelations #TriadicRelations
#Aristotle #Interpretation #Hermeneutics #InterpretantSign
#Abstraction #HypostaticAbstraction #SopToCerberus #Pragma