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  1. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 4
    • inquiryintoinquiry.com/2026/04

    A feature worth noting in the recursion diagram is the function traversing the square from one triadic node to the other. It preserves an image of the object n all the while its precedent p(n) is being retrieved and processed — thus it injects a measure of parallel process and a modicum of extra memory over and above that afforded by the serial composition of functions.

    Simple Recursion
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Inquiry Driven Systems • Inquiry Into Inquiry
    • oeis.org/wiki/Inquiry_Driven_S

    Reflective Interpretive Frameworks
    • oeis.org/wiki/Inquiry_Driven_S

    The Phenomenology of Reflection
    • oeis.org/wiki/Inquiry_Driven_S

    Higher Order Sign Relations
    • oeis.org/wiki/Inquiry_Driven_S

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  2. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 3
    • inquiryintoinquiry.com/2026/04

    One other feature of syntactic recursion deserves to be brought into higher relief. Evidence of it can be found in the recursion diagram by examining the places where three paths meet. On the descending side there is the point where three paths diverge. On the ascending side there is the point where the middlemost of the three divergent paths joins the upshot arrow in medias res.

    Simple Recursion
    • inquiryintoinquiry.com/wp-cont

    The arrows of the diagram represent functions, a species of dyadic relations, but nodes of degree three signify aspects of triadic relations somewhere in the mix.

    • The three arrows from the initial node represent a function F : N → N×N×N such that F(n) = (p(n), n, f(n)).

    • The three arrows at the penultimate node represent a function m : N×N → N such that m(j, k) = jk.

    For the sake of a first approach, many questions about triadic relations which might arise at this point can be safely left to later discussions, since the current level of generality is comprehensible enough in functional terms.

    Resources —

    Inquiry Driven Systems • Inquiry Into Inquiry
    • oeis.org/wiki/Inquiry_Driven_S

    Reflective Interpretive Frameworks
    • oeis.org/wiki/Inquiry_Driven_S

    The Phenomenology of Reflection
    • oeis.org/wiki/Inquiry_Driven_S

    Higher Order Sign Relations
    • oeis.org/wiki/Inquiry_Driven_S

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  3. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 2
    • inquiryintoinquiry.com/2026/04

    Turning to the form of a simple recursive function f(n) = m(n, f(p(n))), the clause we used to define it earns the title of “syntactic recursion” due to the way the function name “f” occurring in the defined phrase “f(n)” re‑occurs in the defining phrase “m(n, f(p(n)))”.

    Simple Recursion
    • inquiryintoinquiry.com/wp-cont

    It needs to be clear there is no circle in the definition — each instance of the type f is defined in terms of an instance one step simpler until the base case is reached and fixed by fiat. Instead of a circle then we have two gyres, the gyre down via the precedent function p and the gyre up via the modifier function m.

    cc: academia.edu/community/L24rvm
    cc: academia.edu/community/LE2mrr
    cc: researchgate.net/post/Reflecti

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  4. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 1.3
    • inquiryintoinquiry.com/2026/04

    Comment 5 —

    Recursion is rife in mathematics and computation, typically sporting its recursive character on its sleeve in the fashion of syntax sketched above.

    But mathematics and computation are overlearned subjects and practices, enjoying long histories of being gone over with an eye to articulating every last detail of any way they might be conceived and conducted.

    So it's fair to ask whether all that artifice truly tutors nature or only creates a rationalized reconstruction of it. Then again, even if that's all it does, is there anything of use to be learned from it?

    Comment 6 —

    The prevalence of recursion in mathematics arises from the architecture of mathematical systems.

    Mathematical systems grow from a fourfold root.

    • “Primitives” are taken as initial terms.

    • “Definitions” expound ever more complex terms in relation to the primitives.

    • “Axioms” are taken as initial truths.

    • “Theorems” follow from the axioms by way of inference rules.

    Recursive definitions of mathematical objects and inductive proofs of the corresponding theorems follow closely parallel patterns. And again, in computation, recursive programs follow the same patterns in action.

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  5. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 1.2
    • inquiryintoinquiry.com/2026/04

    Comment 3 —

    If we discard from the idea of recursion what is not of its essence, we find recursion occurs when our understanding of one situation has recourse to our understanding of other situations.

    Very typically, the object situation presents itself as complex, difficult, or unfamiliar while the resource situations are regarded as being better understood.

    It must be appreciated, however, that any ranking of situations by level of understanding is contingent on the circumstances in view and may vary radically in alternate settings.

    Comment 4 —

    Recursion occurs more markedly in “syntactic recursion”, where the recursive process shows its character as such in the symbols of its syntactic expression.

    A sense of the difference can be gained by looking at a case of “ostensible syntactic recursion”. (How much substance backs the ostentation is a subject we'll take up, maybe at length, but later …)

    Consider the following diagram for the computation of a simple recursive function.

    Simple Recursion
    • inquiryintoinquiry.com/wp-cont

    For example, the factorial function f(n) = n! has a definition in terms of the predecessor function p(n) = n-1 and the multiplier function m(j, k) = j∙k.

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  6. Jon Awbrey @[email protected] ·

    Reflection On Recursion • 1.1
    • inquiryintoinquiry.com/2026/04

    Ongoing conversations with Dan Everett on Facebook have me backtracking to recurring questions about the relationship between formal language theory (as I once learned it) and the properties of natural languages as they are found occurring in the field.

    A point of particular interest is the role of recursion in formal and natural languages, along with collateral questions about its role in the cognitive sciences at large.

    It has taken me quite a while to bring my reflections up to the threshold of minimal coherence — and the inquiry remains ongoing — but it may catalyze the thinking process if I simply share what I've thought so far …

    Comment 1 —

    Recursion is where you find it — so, myself not being a natural language researcher, when someone who is says they don't find it in a given corpus I just take them at their word …

    Comment 2 —

    The question to which I keep returning has to do with the relationship between two ways we find recursion occurring.

    One way I'd call “pragmatic recursion” — if I wanted to be precise and cover its full scope — since so many of its operations occur without conscious direction, but for now I'll defer to more familiar language, calling it “cognitive” or “conceptual” recursion.

    Resources —

    Inquiry Driven Systems • Inquiry Into Inquiry
    • oeis.org/wiki/Inquiry_Driven_S

    Reflective Interpretive Frameworks
    • oeis.org/wiki/Inquiry_Driven_S

    The Phenomenology of Reflection
    • oeis.org/wiki/Inquiry_Driven_S

    Higher Order Sign Relations
    • oeis.org/wiki/Inquiry_Driven_S

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  7. Jon Awbrey @[email protected] ·

    Reflective Interpretive Frameworks • Incident 1
    • inquiryintoinquiry.com/2026/03

    Re: William Waites • The Agent That Doesn't Know Itself
    • johncarlosbaez.wordpress.com/2

    WW: ❝Why Has Nobody Done This?❞

    People who study C.S. Peirce would say reflective reasoning requires triadic relations at core and there is work being done on that. One of the challenges is clarifying the role of triadic relations in category theory and raising them into higher relief as fundamental operations.

    Note. I was looking for a word to describe a random encounter with something that jogs one's memory of a recurring theme — “incident” plays into the “reflection” theme and looked worth trying for now.

    Resources —

    Inquiry Driven Systems • Inquiry Into Inquiry
    • oeis.org/wiki/Inquiry_Driven_S

    Reflective Interpretive Frameworks
    • oeis.org/wiki/Inquiry_Driven_S

    The Phenomenology of Reflection
    • oeis.org/wiki/Inquiry_Driven_S

    Higher Order Sign Relations
    • oeis.org/wiki/Inquiry_Driven_S

    Notes On Categories
    • inquiryintoinquiry.com/2013/02
    • inquiryintoinquiry.com/2021/07

    #Peirce #HigherOrderSignRelations #Inquiry #InquiryIntoInquiry #Logic #Mathematics
    #Recursion #Reflection #RelationTheory #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #relationtheory #reflection #recursion
  8. Jon Awbrey @[email protected] ·

    Propositions As Types Analogy • 1
    • inquiryintoinquiry.com/2013/01

    One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

    Proof Hint ∶ Proof ∶ Proposition
    ∷
    Untyped Term ∶ Typed Term ∶ Type

    or

    Proof Hint ∶ Untyped Term
    ∷
    Proof ∶ Typed Term
    ∷
    Proposition ∶ Type

    See my working notes on the Propositions As Types Analogy —
    • oeis.org/wiki/Propositions_As_

    #Mathematics #CategoryTheory #ProofTheory #TypeTheory
    #Logic #Analogy #Isomorphism #PropositionalCalculus
    #CombinatorCalculus #CombinatoryLogic #LambdaCalculus
    #Peirce #LogicalGraphs #GraphTheory #RelationTheory

    #relationtheory #graphtheory #logicalgraphs #peirce #lambdacalculus #combinatorylogic
  9. Jon Awbrey @[email protected] ·

    Sign Relations • Semiotic Equivalence Relations 2.3
    • inquiryintoinquiry.com/2025/12

    The semiotic equivalence relation for interpreter A yields the following semiotic equations.

    • [“A”]_A = [“i”]_A

    • [“B”]_A = [“u”]_A

    Display 4
    • inquiryintoinquiry.com/wp-cont

    or

    • “A” =_A “i”

    • “B” =_A “u”

    Display 5
    • inquiryintoinquiry.com/wp-cont

    In this way the SER for A induces the following semiotic partition.

    • {{“A”, “i”}, {“B”, “u”}}.

    Display 6
    • inquiryintoinquiry.com/wp-cont

    The semiotic equivalence relation for interpreter B yields the following semiotic equations.

    • [“A”]_B = [“u”]_B

    • [“B”]_B = [“i”]_B

    Display 7
    • inquiryintoinquiry.com/wp-cont

    or

    • “A” =_B “u”

    • “B” =_B “i”

    Display 8
    • inquiryintoinquiry.com/wp-cont

    In this way the SER for B induces the following semiotic partition.

    • {{“A”, “u”}, {“B”, “i”}}.

    Display 9
    • inquiryintoinquiry.com/wp-cont

    Taken all together we have the following picture.

    Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VBAXbj
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2026/01/01/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  10. Jon Awbrey @[email protected] ·

    Sign Relations • Semiotic Equivalence Relations 2.2
    • inquiryintoinquiry.com/2025/12

    In the application to sign relations it is useful to extend the square bracket notation in the following ways. If L is a sign relation whose connotative component L_SI is an equivalence relation on S = I, let [s]_L be the equivalence class of s under L_SI. In short, [s]_L = [s]_{L_{SI}}.

    A statement that the signs x and y belong to the same equivalence class under a semiotic equivalence relation L_SI is called a “semiotic equation” (SEQ) and may be written in either of the following forms.

    • [x]_L = [y]_L

    • x =_L y

    Display 3
    • inquiryintoinquiry.com/wp-cont

    In many situations there is one further adaptation of the square bracket notation for semiotic equivalence classes that can be useful. Namely, when there is known to exist a particular triple (o, s, i) in a sign relation L, it is permissible to let [o]_L be defined as [s]_L. This modifications is designed to make the notation for semiotic equivalence classes harmonize as well as possible with the frequent use of similar devices for the denotations of signs and expressions.

    Applying the array of equivalence notations to the sign relations for A and B will serve to illustrate their use and utility.

    Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VBAXbj
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2026/01/01/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  11. Jon Awbrey @[email protected] ·

    Sign Relations • Semiotic Equivalence Relations 2.1
    • inquiryintoinquiry.com/2025/12

    A few items of notation are useful in discussing equivalence relations in general and semiotic equivalence relations in particular.

    In general, if E is an equivalence relation on a set X then every element x of X belongs to a unique equivalence class under E called “the equivalence class of x under E”. Convention provides the “square bracket notation” for denoting such equivalence classes, in either the form [x]_E or the simpler form [x] when the subscript E is understood.

    A statement that the elements x and y are equivalent under E is called an “equation” or an “equivalence” and may be expressed in any of the following ways.

    • (x, y) ∈ E

    • x ∈ [y]_E

    • y ∈ [x]_E

    • [x]_E = [y]_E

    • x =_E y

    Display 1
    • inquiryintoinquiry.com/wp-cont

    Thus we have the following definitions.

    • [x]_E = {y ∈ X : (x, y) ∈ E}

    • x =_E y ⇔ (x, y) ∈ E

    Display 2
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VBAXbj
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2026/01/01/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  12. Jon Awbrey @[email protected] ·

    Sign Relations • Semiotic Equivalence Relations 1.2
    • inquiryintoinquiry.com/2025/12

    A nice property of the sign relations L_A and L_B is that their connotative components Con(L_A) and Con(L_B) form a pair of equivalence relations on their common syntactic domain S = I. This type of equivalence relation is called a “semiotic equivalence relation” (SER) because it equates signs having the same meaning to some interpreter.

    Each of the semiotic equivalence relations, Con(L_A), Con(L_B) ⊆ S×I ≅ S×S partitions the collection of signs into semiotic equivalence classes. This constitutes a strong form of representation in that the structure of the interpreters' common object domain {A, B} is reflected or reconstructed, part for part, in the structure of each one's semiotic partition of the syntactic domain {“A”, “B”, “i”, “u”}.

    It's important to observe the semiotic partitions for interpreters A and B are not identical, indeed, they are “orthogonal” to each other. Thus we may regard the “form” of the partitions as corresponding to an objective structure or invariant reality, but not the literal sets of signs themselves, independent of the individual interpreter's point of view.

    Information about the contrasting patterns of semiotic equivalence corresponding to the interpreters A and B is summarized in Tables 7a and 7b. The form of the Tables serves to explain what is meant by saying the SEPs for A and B are “orthogonal” to each other.

    Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
    • inquiryintoinquiry.com/wp-cont

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  13. Jon Awbrey @[email protected] ·

    Sign Relations • Semiotic Equivalence Relations 1.1
    • inquiryintoinquiry.com/2025/12

    A “semiotic equivalence relation” (SER) is a special type of equivalence relation arising in the analysis of sign relations. Generally speaking, any equivalence relation induces a partition of the underlying set of elements, known as the “domain” or “space” of the relation, into a family of equivalence classes. In the case of a SER the equivalence classes are called “semiotic equivalence classes” (SECs) and the partition is called a “semiotic partition” (SEP).

    The sign relations L_A and L_B have many interesting properties over and above those possessed by sign relations in general. Some of those properties have to do with the relation between signs and their interpretant signs, as reflected in the projections of L_A and L_B on the SI‑plane, notated as proj_{SI} L_A and proj_{SI} L_B, respectively. The dyadic relations on S×I induced by those projections are also referred to as the “connotative components” of the corresponding sign relations, notated as Con(L_A) and Con(L_B), respectively. Tables 6a and 6b show the corresponding connotative components.

    Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/Lm48yP
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/30/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  14. Jon Awbrey @[email protected] ·

    Sign Relations • Ennotation • Part 2
    • inquiryintoinquiry.com/2025/12

    As it happens, the sign relations L_A and L_B are fully symmetric with respect to exchanging signs and interpretants, so all the data of proj_{OS} L_A is echoed unchanged in proj_{OI} L_A and all the data of proj_{OS} L_B is echoed unchanged in proj_{OI} L_B.

    Tables 5a and 5b show the ennotative components of the sign relations associated with the interpreters A and B, respectively. The rows of each Table list the ordered pairs (o, i) in the corresponding projections, Enn(L_A), Enn(L_B) ⊆ O×I.

    • Tables 5a and 5b. Ennotative Components Enn(L_A) and Enn(L_B)
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation • OEIS • MyWikiBiz • Wikiversity
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/V0rbOx
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/29/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  15. Jon Awbrey @[email protected] ·

    Sign Relations • Ennotation • Part 1
    • inquiryintoinquiry.com/2025/12

    A third aspect of a sign's complete meaning concerns the relation between its objects and its interpretants, which has no standard name in semiotics. It would be called an “induced relation” in graph theory or the result of “relational composition” in relation theory. If an interpretant is recognized as a sign in its own right then its independent reference to an object can be taken as belonging to another moment of denotation, but this neglects the mediational character of the whole transaction in which this occurs. Denotation and connotation have to do with dyadic relations in which the sign plays an active role but here we are dealing with a dyadic relation between objects and interpretants mediated by the sign from an off‑stage position, as it were.

    As a relation between objects and interpretants mediated by a sign, this third aspect of meaning may be referred to as the “ennotation” of a sign and the dyadic relation making up the ennotative aspect of a sign relation L may be notated as Enn(L). Information about the ennotative aspect of meaning is obtained from L by taking its projection on the object‑interpretant plane and visualized as the “shadow” L casts on the 2‑dimensional space whose axes are the object domain O and the interpretant domain I. The ennotative component of a sign relation L, variously written as proj_{OI} L, L_OI, proj₁₃ L, or L₁₃, is defined as follows.

    • Enn(L) = proj_{OI} L = {(o, i) ∈ O × I : (o, s, i) ∈ L for some s ∈ S}.
    • inquiryintoinquiry.com/wp-cont

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  16. Jon Awbrey @[email protected] ·

    Sign Relations • Connotation • Part 2
    • inquiryintoinquiry.com/2025/12

    Formally speaking, however, the connotative aspect of meaning presents no additional difficulty. The dyadic relation making up the connotative aspect of a sign relation L is notated as Con(L). Information about the connotative aspect of meaning is obtained from L by taking its projection on the sign‑interpretant plane and visualized as the “shadow” L casts on the 2‑dimensional space whose axes are the sign domain S and the interpretant domain I. The connotative component of a sign relation L, variously written as proj_{SI} L, L_SI, proj₂₃ L, or L₂₃, is defined as follows.

    • Con(L) = proj_{SI} L = {(s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O}.
    • inquiryintoinquiry.com/wp-cont

    Tables 4a and 4b show the connotative components of the sign relations associated with the interpreters A and B, respectively. The rows of each Table list the ordered pairs (s, i) in the corresponding projections, Con(L_A), Con(L_B) ⊆ S×I.

    • Tables 4a and 4b. Connotative Components Con(L_A) and Con(L_B)
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VqeB0k
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/28/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  17. Jon Awbrey @[email protected] ·

    Sign Relations • Connotation • Part 1
    • inquiryintoinquiry.com/2025/12

    Another aspect of a sign's complete meaning concerns the reference a sign has to its interpretants, which interpretants are collectively known as the “connotation” of the sign. In the pragmatic theory of sign relations, connotative references fall within the projection of the sign relation on the plane spanned by its sign domain and its interpretant domain.

    In the full theory of sign relations the connotative aspect of meaning includes the links a sign has to affects, concepts, ideas, impressions, intentions, and the whole realm of an interpretive agent's mental states and allied activities, broadly encompassing intellectual associations, emotional impressions, motivational impulses, and real conduct.

    Taken at the full, in the natural setting of semiotic phenomena, this complex system of references is unlikely ever to find itself mapped in much detail, much less completely formalized, but the tangible warp of its accumulated mass is commonly alluded to as the connotative import of language.

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/VqeB0k
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/28/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  18. Jon Awbrey @[email protected] ·

    Sign Relations • Denotation
    • inquiryintoinquiry.com/2025/12

    One aspect of a sign's complete meaning concerns the reference a sign has to its objects, which objects are collectively known as the “denotation” of the sign. In the pragmatic theory of sign relations, denotative references fall within the projection of the sign relation on the plane spanned by its object domain and its sign domain.

    The dyadic relation making up the “denotative”, “referent”, or “semantic” aspect of a sign relation L is notated as Den(L). Information about the denotative aspect of meaning is obtained from L by taking its projection on the object‑sign plane. The result may be visualized as the “shadow” L casts on the 2‑dimensional space whose axes are the object domain O and the sign domain S. The denotative component of a sign relation L, variously written as proj_{OS} L, L_OS, proj₁₂ L, or L₁₂, is defined as follows.

    • Den(L) = proj_{OS} L = {(o, s) ∈ O × S : (o, s, i) ∈ L for some i ∈ I}.
    • inquiryintoinquiry.com/wp-cont

    Tables 3a and 3b show the denotative components of the sign relations associated with the interpreters A and B, respectively. The rows of each Table list the ordered pairs (o, s) in the corresponding projections, Den(L_A), Den(L_B) ⊆ O×S.

    • Tables 3a and 3b. Denotative Components Den(L_A) and Den(L_B)
    • inquiryintoinquiry.com/wp-cont

    Looking to the denotative aspects of L_A and L_B, various rows of the Tables specify, for example, that A uses “i” to denote A and “u” to denote B, while B uses “i” to denote B and “u” to denote A.

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  19. Jon Awbrey @[email protected] ·

    Relational Arrows ⟿

    Relations have types.
    Types are functions.
    Functions are relations.

    Relation Theory
    • ncatlab.org/nlab/revision/rela

    Relational Arrows
    • ncatlab.org/nlab/revision/rela

    #CategoryTheory #Mathematics
    #RelationTheory #RelationalArrows

    #mathematics #relationalarrows #relationtheory #categorytheory
  20. Jon Awbrey @[email protected] ·

    Sign Relations • Dyadic Aspects
    • inquiryintoinquiry.com/2025/12

    For an arbitrary triadic relation L ⊆ O×S×I, whether it happens to be a sign relation or not, there are six dyadic relations obtained by “projecting” L on one of the planes of the OSI‑space O×S×I. The six dyadic projections of a triadic relation L are defined and notated as shown in Table 2.

    Table 2. Dyadic Aspects of Triadic Relations
    • inquiryintoinquiry.com/wp-cont

    By way of unpacking the set‑theoretic notation, here is what the first definition says in ordinary language.

    • The dyadic relation resulting from the projection of L on the OS‑plane O×S is written briefly as L₁₂ or written more fully as proj₁₂(L) and is defined as the set of all ordered pairs (o, s) in the cartesian product O×S for which there exists an ordered triple (o, s, i) in L for some element i in the set I.

    In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of L can be recognized as formalizing aspects of sign meaning which have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology.

    Of course, traditions vary with respect to the precise formation and usage of such concepts and terms. Other aspects of meaning have not received their fair share of attention and thus remain innominate in current anatomies of sign relations.

    Resources —

    Sign Relation
    • oeis.org/wiki/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  21. Jon Awbrey @[email protected] ·

    Sign Relations • Examples • Part 3
    • inquiryintoinquiry.com/2025/12

    Introducing a few abbreviations for use in the Example, we have the following data.

    • O = {Ann, Bob} = {A, B}
    • S = {“Ann”, “Bob”, “I”, “you”} = {“A”, “B”, “i”, “u”}
    • I = {“Ann”, “Bob”, “I”, “you”} = {“A”, “B”, “i”, “u”}

    Display 2 • Domains and Elements of Two Sign Relation Examples
    • inquiryintoinquiry.com/wp-cont

    In the present example, S = I = Syntactic Domain.

    Tables 1a and 1b show the sign relations associated with the interpreters A and B, respectively. In this arrangement the rows of each Table list the ordered triples of the form (o, s, i) belonging to the corresponding sign relations, L(A), L(B) ⊆ O×S×I.

    Sign Relation Tables L(A) and L(B)
    • inquiryintoinquiry.com/wp-cont

    The Tables codify a rudimentary level of interpretive practice for the agents A and B and provide a basis for formalizing the initial semantics appropriate to their common syntactic domain. Each row of a Table lists an object and two co‑referent signs, together forming an ordered triple (o, s, i) called an “elementary sign relation”, in other words, one element of the relation's set‑theoretic extension.

    Already in this elementary context, there are several meanings which might attach to the project of a formal semiotics, or a formal theory of meaning for signs. In the process of discussing the alternatives, it is useful to introduce a few terms occasionally used in the philosophy of language to point out the needed distinctions. That is the task we'll turn to next.

    Resources —

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  22. Jon Awbrey @[email protected] ·

    Sign Relations • Examples • Part 2
    • inquiryintoinquiry.com/2025/12

    In terms of its set‑theoretic extension, a sign relation L is a subset of a cartesian product O×S×I. The three sets O, S, I are known as the “object domain”, the “sign domain”, and the “interpretant domain”, respectively, of the sign relation L ⊆ O×S×I.

    Broadly speaking, the three domains of a sign relation may be any sets at all but the types of sign relations contemplated in formal settings are usually constrained to having I ⊆ S. In those cases it becomes convenient to lump signs and interpretants together in a single class called a “sign system” or “syntactic domain”. In the forthcoming examples S and I are identical as sets, so the same elements manifest themselves in two different roles of the sign relations in question.

    When it becomes necessary to refer to the whole set of objects and signs in the union of the domains O, S, I for a given sign relation L, we will call this set the “World” of L and write W = W(L) = O ∪ S ∪ I.

    To facilitate an interest in the formal structures of sign relations and to keep notations as simple as possible as the examples become more complicated, it serves to introduce the following general notations.

    • O = Object Domain
    • S = Sign Domain
    • I = Interpretant Domain

    Display 1 • Domains of a Triadic Sign Relation
    • inquiryintoinquiry.com/wp-cont

    Resources —

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/lan2Bx
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/19/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  23. Jon Awbrey @[email protected] ·

    Sign Relations • Examples • Part 1
    • inquiryintoinquiry.com/2025/12

    Soon after I made my third foray into grad school, this time in Systems Engineering, I was trying to explain sign relations to my advisor and he, being the very model of a modern systems engineer, asked me to give a concrete example of a sign relation, as simple as possible without being trivial. After much cudgeling of the grey matter I came up with a pair of examples which had the added benefit of bearing instructive relationships to each other. Despite their simplicity, the examples to follow have subtleties of their own and their careful treatment serves to illustrate important issues in the general theory of signs.

    Imagine a discussion between two people, Ann and Bob, and attend only to the aspects of their interpretive practice involving the use of the following nouns and pronouns.

    • {“Ann”, “Bob”, “I”, “you”}

    • The “object domain” of their discussion is the set of two people {Ann, Bob}.

    • The “sign domain” of their discussion is the set of four signs {“Ann”, “Bob”, “I”, “you”}.

    Ann and Bob are not only the passive objects of linguistic references but also the active interpreters of the language they use. The “system of interpretation” associated with each language user can be represented in the form of an individual three‑place relation known as the “sign relation” of that interpreter.

    Resources —

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/lan2Bx
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/19/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  24. Jon Awbrey @[email protected] ·

    Sign Relations • Signs and Inquiry
    • inquiryintoinquiry.com/2025/12

    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.
    • gutenberg.org/files/37423/3742

    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.
    • web.archive.org/web/2000121016
    • pdcnet.org/inquiryct/content/i
    • academia.edu/1266493/Interpret
    • academia.edu/57812482/Interpre

    Resources —

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    Survey of Inquiry Driven Systems
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/lQk7Z2
    cc: stream.syscoi.com/2025/12/16/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  25. Jon Awbrey @[email protected] ·

    Sign Relations • Definition
    • inquiryintoinquiry.com/2025/12

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  26. Jon Awbrey @[email protected] ·

    Sign Relations • Anthesis
    • inquiryintoinquiry.com/2025/12

    ❝Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun.❞

    — C.S. Peirce, Collected Papers, CP 2.274

    In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or “semiosis”, Peirce uses the technical term “representamen” for his concept of a sign, but the shorter word is precise enough, so long as one recognizes its meaning in a particular theory of signs is given by a specific definition of what it means to be a sign.

    Resources —

    Sign Relation • OEIS • MyWikiBiz • Wikiversity
    • oeis.org/wiki/Sign_relation
    • mywikibiz.com/Sign_relation
    • en.wikiversity.org/wiki/Sign_r

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/LGxrpW
    cc: researchgate.net/post/Sign_Rel
    cc: stream.syscoi.com/2025/12/14/s

    #Peirce #Inquiry #Logic #Mathematics #RelationTheory
    #Semiosis #Semiotics #SignRelations #TriadicRelations

    #triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics
  27. Jon Awbrey @[email protected] ·

    Survey of Precursors Of Category Theory • 6
    • inquiryintoinquiry.com/2025/05

    A few years ago I began a sketch on the “Precursors of Category Theory”, tracing the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. A Survey of resources on the topic is given below, still very rough and incomplete, but perhaps a few will find it of use.

    Background —

    Precursors Of Category Theory
    • oeis.org/wiki/Precursors_Of_Ca

    Propositions As Types Analogy
    • oeis.org/wiki/Propositions_As_

    Blog Series —

    Notes On Categories
    • inquiryintoinquiry.com/2013/02

    Precursors Of Category Theory
    1. inquiryintoinquiry.com/2024/05
    2. inquiryintoinquiry.com/2024/05
    3. inquiryintoinquiry.com/2024/05
    4. inquiryintoinquiry.com/2024/05
    5. inquiryintoinquiry.com/2024/05
    6. inquiryintoinquiry.com/2024/05

    Precursors Of Category Theory • Discussion
    1. inquiryintoinquiry.com/2020/09
    2. inquiryintoinquiry.com/2020/09
    3. inquiryintoinquiry.com/2020/09

    Categories à la Peirce —

    C.S. Peirce • A Guess at the Riddle
    • inquiryintoinquiry.com/2012/03

    Peirce's Categories
    1. inquiryintoinquiry.com/2015/10
    2. inquiryintoinquiry.com/2015/10
    3. inquiryintoinquiry.com/2015/11
    •••
    19. inquiryintoinquiry.com/2020/05
    20. inquiryintoinquiry.com/2020/05
    21. inquiryintoinquiry.com/2020/06

    C.S. Peirce and Category Theory
    1. inquiryintoinquiry.com/2021/06
    2. inquiryintoinquiry.com/2021/06
    3. inquiryintoinquiry.com/2021/06
    4. inquiryintoinquiry.com/2021/06
    5. inquiryintoinquiry.com/2021/06
    6. inquiryintoinquiry.com/2021/06
    7. inquiryintoinquiry.com/2021/07
    8. inquiryintoinquiry.com/2021/07

    #Aristotle #Peirce #Kant #Carnap #Hilbert #Ackermann #SaundersMacLane
    #Abstraction #Analogy #CategoryTheory #FunctionalLogic #RelationTheory
    #PrecursorsOfCategoryTheory #PropositionsAsTypes #Semiotics #TypeTheory

    #typetheory #propositionsastypes #relationtheory #functionallogic #categorytheory #analogy
  28. Inquiry Into Inquiry @[email protected] ·

    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

    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

    #cspeirce #connotation #denotation #inquiry #logic #logicofrelatives
  29. Inquiry Into Inquiry @[email protected] ·

    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

    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

    #cspeirce #connotation #denotation #inquiry #logic #logicofrelatives
  30. Inquiry Into Inquiry @[email protected] ·

    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

    • Peircean Semiotics and Triadic Sign Relations • (1) • (2) • (3)

    Blog Dialogs

    Sources

    • C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • (1) • (2)
    • C.S. Peirce • Algebra of Logic 1885 • Selections • (1) • (2) • (3) • (4)

    Topics

    Excursions

    • Semiositis • (1)
    • Signspiel • (1)
    • Skiourosemiosis • (1)

    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

    #cspeirce #iconindexsymbol #inquiry #logic #logicofrelatives #mathematics