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#inquiry — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #inquiry, aggregated by home.social.

  1. University of Newcastle academic with terminal cancer risks job to speak out about ‘unsafe’ workloads

    Associate professor Trisha Pender has terminal cancer but it has not stopped the University of Newcastle intensifying her…
    #NewsBeep #News #Australia #AU #Education #Governance #inquiry #nsw #professors #teachers #teachingworkload #tertiaryeducation #Universities #UniversityofNewcastle #universitystaff
    newsbeep.com/au/664484/

  2. University of Newcastle academic with terminal cancer risks job to speak out about ‘unsafe’ workloads

    Associate professor Trisha Pender has terminal cancer but it has not stopped the University of Newcastle intensifying her…
    #NewsBeep #News #Australia #AU #Education #Governance #inquiry #nsw #professors #teachers #teachingworkload #tertiaryeducation #Universities #UniversityofNewcastle #universitystaff
    newsbeep.com/au/664484/

  3. LIVE: Former UK foreign office official Olly Robbins questioned over Mandelson vetting

    Former foreign office official Olly Robbins, who was sacked over his role in the Peter Mandelson vetting scandal, gives evidence to parliament's Foreign Affairs Committee. #UK #Politics #OllyRobbins #Mandelson #Parliament #ForeignAffairs #Vetting #Inquiry #live #Reuters #News Keep up with the latest news from around the world:

    fllics.com/en/video/live-forme

  4. LIVE: Former UK foreign office official Olly Robbins questioned over Mandelson vetting

    Former foreign office official Olly Robbins, who was sacked over his role in the Peter Mandelson vetting scandal, gives evidence to parliament's Foreign Affairs Committee. #UK #Politics #OllyRobbins #Mandelson #Parliament #ForeignAffairs #Vetting #Inquiry #live #Reuters #News Keep up with the latest news from around the world:

    fllics.com/en/video/live-forme

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. theguardian.com/uk-news/2026/a. "Ministers are 'failing to learn the lessons' from the #Southport attack & allowing violence-obsessed #teenagers to remain a 'catastrophic' threat to #society, #lawyers for #victims of the #atrocity have said ahead of the findings of an official #inquiry. A report on the July 2024 attack by the judge Sir Adrian Fulford, to be released on Monday, is expected to strongly criticise failings by a series of agencies, including the counter-terrorism programme #Prevent."

  16. 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

  17. 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. A quotation from Hyman Rickover

    Always use the chain of command to issue orders, but if you use the chain of command for information, you’re dead.

    Hyman Rickover (1900-1986) Polish-American naval engineer, admiral [b. Chaim Gdala Rykower]
    (Attributed)

    More about this quote: wist.info/rickover-hyman/6924/

    #quote #quotes #quotation #qotd #rickover #hymanrickover #chainofcommand #command #information #inquiry #investigation #misinformation #order #procedure #subordinates #networking

  37. A quotation from Hyman Rickover

    Always use the chain of command to issue orders, but if you use the chain of command for information, you’re dead.

    Hyman Rickover (1900-1986) Polish-American naval engineer, admiral [b. Chaim Gdala Rykower]
    (Attributed)

    More about this quote: wist.info/rickover-hyman/6924/

    #quote #quotes #quotation #qotd #rickover #hymanrickover #chainofcommand #command #information #inquiry #investigation #misinformation #order #procedure #subordinates #networking

  38. A quotation from Hyman Rickover

    Always use the chain of command to issue orders, but if you use the chain of command for information, you’re dead.

    Hyman Rickover (1900-1986) Polish-American naval engineer, admiral [b. Chaim Gdala Rykower]
    (Attributed)

    More about this quote: wist.info/rickover-hyman/6924/

    #quote #quotes #quotation #qotd #rickover #hymanrickover #chainofcommand #command #information #inquiry #investigation #misinformation #order #procedure #subordinates #networking

  39. A quotation from Hyman Rickover

    Always use the chain of command to issue orders, but if you use the chain of command for information, you’re dead.

    Hyman Rickover (1900-1986) Polish-American naval engineer, admiral [b. Chaim Gdala Rykower]
    (Attributed)

    More about this quote: wist.info/rickover-hyman/6924/

    #quote #quotes #quotation #qotd #rickover #hymanrickover #chainofcommand #command #information #inquiry #investigation #misinformation #order #procedure #subordinates #networking

  40. A quotation from Hyman Rickover

    Always use the chain of command to issue orders, but if you use the chain of command for information, you’re dead.

    Hyman Rickover (1900-1986) Polish-American naval engineer, admiral [b. Chaim Gdala Rykower]
    (Attributed)

    More about this quote: wist.info/rickover-hyman/6924/

    #quote #quotes #quotation #qotd #rickover #hymanrickover #chainofcommand #command #information #inquiry #investigation #misinformation #order #procedure #subordinates #networking

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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