#triadicrelations — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #triadicrelations, aggregated by home.social.
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Reflective Interpretive Frameworks • Incident 2
• https://inquiryintoinquiry.com/2026/08/27/reflective-interpretive-frameworks-incident-2/Re: Terence Tao • Modular Arithmetic Challenge
• https://terrytao.wordpress.com/2026/06/08/modular-arithmetic-challenge/
• https://competition.sair.foundation/competitions/modular-arithmetic-challenge/overviewThe Modular Arithmetic Challenge asks a simple question:
• Can a neural network learn to do modular multiplication efficiently?
Incidental Reflection 1 —
There are alternative models of neural networks which do not depend on threshold neurons and endlessly fiddling with weights.
Incidental Reflection 2 —
The series of three blog posts linked below present a case study comparing two ways of handling a classic example from the Parallel Distributed Processing paradigm, namely, the “Jets and Sharks” database problem, first taking up the original treatment by McClelland and Rumelhart and then proceeding according to a program I developed for propositional logic modeling. The latter method makes use of ideas from Grossberg's competition‑cooperation and winner‑take‑all dynamics, but is purely propositional‑logic based, involving no extraneous weights.
Theme One Program • Jets and Sharks
(1) https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
(2) https://inquiryintoinquiry.com/2024/06/22/theme-one-program-jets-and-sharks-2-a/
(3) https://inquiryintoinquiry.com/2024/06/23/theme-one-program-jets-and-sharks-3-a/Resources —
Survey of Theme One Program
• https://inquiryintoinquiry.com/2025/05/06/survey-of-theme-one-program-7/Differential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview#Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
#Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations
#PropositionalModels #MinimalNegationOperators #DifferentialAnalyticTuringAutomata
#CactusGraphs #CactusLanguage #DifferentialLogic #NeuralNetworks #SequenceLearning -
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
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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
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Survey of Semiotics, Semiosis, Sign Relations • 6
C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play. Understanding logic as Peirce understands it thus requires a companion study of semiotics, semiosis, and sign relations.
What follows 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
Blog Series
- Sign Relations • Anthesis • Definition • Signs and Inquiry • Examples • Dyadic Aspects • Denotation • Connotation • Ennotation • Semiotic Equivalence Relations (1) (2)
Blog Dialogs
- Icon Index Symbol • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11) • (12) • (13) • (14) • (15) • (16) • (17) • (18) • (19) • (20)
- Sign Relations, Triadic Relations, Relations • (1) • (2) • (3) • (4) • (5) • (6) • (7) • (8) • (9) • (10) • (11)
Sources
- C.S. Peirce • On the Definition of Logic
- C.S. Peirce • Logic as Semiotic
- C.S. Peirce • Objective Logic
- C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • (1) • (2)
- C.S. Peirce • Algebra of Logic 1885 • Selections • (1) • (2) • (3) • (4)
Topics
- Interpreter and Interpretant
- Tone, Token, Type
- Discussions • (1)
Excursions
References
- 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. Abstract. Online.
- Awbrey, S.M., and Awbrey, J.L. (September 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.
- 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).
- 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.
cc: FB | Semeiotics • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science#CSPeirce #IconIndexSymbol #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #Semiotics #SignRelations #TriadicRelations #Triadicity #Visualization
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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.htmAwbrey, 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_InquiryResources —
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 -
❝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).
#Peirce #Logic #Semiotics #Semiosis #SignRelations #TriadicRelations
#Cybersemiotics #Interpreter #Interpretant #Hermeneutics #Hermenaut -
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 -
Peircean Semiotics and Triadic Sign Relations • 3
• https://inquiryintoinquiry.com/2024/08/23/peircean-semiotics-and-triadic-sign-relations-3-a/Having labored mightily to bring out a new edition of my primer on sign relations, including material on the pivotal concept of semiotic equivalence relations, I thought it worth the candle to post a notice of the new version here.
Sign Relations
• https://oeis.org/wiki/Sign_relationSemiotic Equivalence Relations
• https://oeis.org/wiki/Sign_relation#Semiotic_equivalence_relations#Peirce #Inquiry #Logic #LogicOfRelatives #RelationTheory
#Semiotics #Semiosis #SignRelations #TriadicRelations -
Peircean Semiotics and Triadic Sign Relations • 2
• https://inquiryintoinquiry.com/2024/08/22/peircean-semiotics-and-triadic-sign-relations-2-a/When I returned to graduate school for the third time around, this time in systems engineering, I had in mind integrating my long‑standing projects investigating the dynamics of information, inquiry, learning, and reasoning, viewing each as a process whose trajectory evolves over time through the medium which gives it concrete embodiment, namely, a triadic sign relation.
Up until that time I don't believe I'd ever given much thought to sign relations that had anything smaller than infinite domains of objects, signs, and interpretant signs. Countably infinite domains are what come natural in logic, since that is the norm for the formal languages it uses. Continuous domains come first to mind when turning to physical systems, despite the fact that systems with a discrete or quantized character often enter the fray.
So it came as a bit of a novelty to me when my advisor, following the motto of engineers the world over to “Keep It Simple, Stupid!” — affectionately known by the acronym KISS — asked me to construct the simplest non‑trivial finite example of a sign relation I could possibly come up with. The outcome of that exercise I wrote up in the following primer on sign relations.
Inquiry Driven Systems • Sign Relations : A Primer
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_1#Sign_Relations_:_A_PrimerInquiry Driven Systems • Semiotic Equivalence Relations
• https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_1#Semiotic_Equivalence_Relations#Peirce #Inquiry #Logic #LogicOfRelatives #RelationTheory
#Semiotics #Semiosis #SignRelations #TriadicRelations -
Peircean Semiotics and Triadic Sign Relations • 1
• https://inquiryintoinquiry.com/2024/08/20/peircean-semiotics-and-triadic-sign-relations-1-a/As a “guide for the perplexed”, at least when it comes to semiotics, I'll use this thread to collect a budget of resources I think have served to clarify the topic in the past.
By way of a first offering, let me recommend the following most excellent paper, which I can say with all due modesty in light of the fact all its excellence is due to my most excellent co‑author.
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.
• 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#Peirce #Inquiry #Logic #LogicOfRelatives #RelationTheory
#Semiotics #Semiosis #SignRelations #TriadicRelations -
Sign Relations, Triadic Relations, Relation Theory • Discussion 12
• https://inquiryintoinquiry.com/2024/02/24/sign-relations-triadic-relations-relation-theory-discussion-12/Re: Sign Relations, Triadic Relations, Relation Theory • 1
• https://inquiryintoinquiry.com/2024/02/18/sign-relations-triadic-relations-relation-theory-1-a/A note from a longtime correspondent points out a search of the available texts turns up no use of the plural form “semiotics” by Peirce and just one place where he uses the plural form “Semeiotics”. That prompts me to make the following excuse for my use or abuse of Peirce's terms, as the case may be.
Peirce has always been one of my chief resources in the quest to understand how logic and math and science work. There is much to be gained by getting his distinctive ideas across to active practitioners in those fields. In doing that I find it better to tweak the words a bit, if that's what it takes to preserve the idea, than to hallow the words at the risk of losing the idea.
As far as semiotics by any name goes, what seems to work best without too much clanging in modern ears is parsing “semiotics” in line with words like “mathematics” and “cybernetics”, plus we can now use the singular form as the adjective “semiotic”.
#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations -
Sign Relations, Triadic Relations, Relation Theory • 4.2
• https://inquiryintoinquiry.com/2024/02/22/sign-relations-triadic-relations-relation-theory-4/Here's an earlier draft version of Peirce's 1902 definition of a sign, which he gives in the process of defining logic.
Selections from C.S. Peirce, “Carnegie Application” (1902)
❝No. 12. On the Definition of Logic❞ [Earlier Draft]
❝Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word “formal” in the definition is also defined.❞ (NEM 4, 54).
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 ( https://cspeirce.com/menu/library/bycsp/l75/l75.htm )#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations -
Sign Relations, Triadic Relations, Relation Theory • 4.1
• https://inquiryintoinquiry.com/2024/02/22/sign-relations-triadic-relations-relation-theory-4/For ease of reference, here are two variants of Peirce's 1902 definition of a sign, which he gives in the process of defining logic.
Selections from C.S. Peirce, “Carnegie Application” (1902)
❝No. 12. On the Definition of Logic❞
❝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.❞ (NEM 4, 20–21).
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 ( https://cspeirce.com/menu/library/bycsp/l75/l75.htm )#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations -
Sign Relations, Triadic Relations, Relation Theory • 3
• https://inquiryintoinquiry.com/2024/02/20/sign-relations-triadic-relations-relation-theory-3/The middle ground between relations in general and the sign relations informing logic, inquiry, and communication is occupied by triadic relations, also called ternary or 3‑place relations.
Triadic relations are some of the most pervasive in mathematics, over and above the importance of sign relations for logic.
For a primer on triadic relations, with examples from mathematics and semiotics, see the article linked below.
Triadic Relations
• OEIS Wiki ( https://oeis.org/wiki/Triadic_relation )
• Wikiversity ( https://en.wikiversity.org/wiki/Triadic_relation )#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations -
Sign Relations, Triadic Relations, Relation Theory • 2
• https://inquiryintoinquiry.com/2024/02/19/sign-relations-triadic-relations-relation-theory-2/I always have trouble deciding whether to start with the genus and drive down to the species or begin with concrete examples and accompany Sisyphus up Mt. Abstraction.
To start at the wide end of the funnel, the following article takes up relations in general, focusing on the discrete mathematical varieties we find most useful in applications, for example, as background for empirical data sets and relational data bases.
Relation Theory
• OEIS Wiki ( https://oeis.org/wiki/Relation_theory )
• Wikiversity ( https://en.wikiversity.org/wiki/Relation_theory )#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations -
Sign Relations, Triadic Relations, Relation Theory • 1
• https://inquiryintoinquiry.com/2024/02/18/sign-relations-triadic-relations-relation-theory-1-a/To understand how signs work in Peirce's theory of triadic sign relations, or “semiotics”, we have to understand, in order of increasing generality, sign relations, triadic relations, and relations in general, each as conceived in Peirce's logic of relative terms and the corresponding mathematics of relations.
Toward that understanding, here are the current versions of articles I long ago contributed to Wikipedia and Wikiversity and continue to develop at a number of other places.
Sign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relationRelation Theory
• https://oeis.org/wiki/Relation_theory#Peirce #Logic #Mathematics #ScientificMethod #Semiotics #Semiosis
#LogicOfRelatives #RelationTheory #TriadicRelations #SignRelations