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#peirce — Public Fediverse posts

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

  1. Błażej Gruszka @[email protected] ·

    Semiotics - why an LLM doesn't

    Saussure, Peirce and Derrida as the key to understanding LLMs. Why a model is not a mind, but a mach...

    gruszka.dev/en/semiotics-and-l
    #llm #ai #semiotics #signs #linguistics #languagemodels #saussure #peirce #derrida

    #llm #ai #semiotics #signs #linguistics #languagemodels
  2. Błażej Gruszka @[email protected] ·

    Semiotics - why an LLM doesn't

    Saussure, Peirce and Derrida as the key to understanding LLMs. Why a model is not a mind, but a mach...

    gruszka.dev/en/semiotics-and-l
    #llm #ai #semiotics #signs #linguistics #languagemodels #saussure #peirce #derrida

    #llm #ai #semiotics #signs #linguistics #languagemodels
  3. Eric's Edge @[email protected] ·

    Development Blog - Three Ways of Knowing
    Building a Murder Mystery Game on Peircean Semiotics

    #Peirce
    #Game
    #Design
    #Semiotics
    ko-fi.com/post/Development-Blo

    #semiotics #design #game #peirce
  4. Eric's Edge @[email protected] ·

    Development Blog - Three Ways of Knowing
    Building a Murder Mystery Game on Peircean Semiotics

    #Peirce
    #Game
    #Design
    #Semiotics
    ko-fi.com/post/Development-Blo

    #semiotics #design #game #peirce
  5. Eric’s Edge @[email protected] ·

    Development Blog - Three Ways of Knowing
    Building a Murder Mystery Game on Peircean Semiotics

    #Peirce
    #Game
    #Design
    #Semiotics

    ko-fi.com/post/Develop...

    #peirce #game #design #semiotics
  6. Philosophics @[email protected] ·

    This article is less about what philosophy is about and more about why we can't particularly know some things, and why not.

    👉 open.substack.com/pub/brywilli

    #blog #substack #philosophy #language #ontology #semantics #semiotics #epistemology #etymology #communication #Heidegger #Derrida #Foucault #Wittgenstein #Nietzsche #Gadamer #Peirce #Gallie #McGilchrist #languageinsufficiency

    #blog #substack #philosophy #language #ontology #semantics
  7. Philosophics @[email protected] ·

    This article is less about what philosophy is about and more about why we can't particularly know some things, and why not.

    👉 open.substack.com/pub/brywilli

    #blog #substack #philosophy #language #ontology #semantics #semiotics #epistemology #etymology #communication #Heidegger #Derrida #Foucault #Wittgenstein #Nietzsche #Gadamer #Peirce #Gallie #McGilchrist #languageinsufficiency

    #blog #substack #philosophy #language #ontology #semantics
  8. Philosophics @[email protected] ·

    This article is less about what philosophy is about and more about why we can't particularly know some things, and why not.

    👉 open.substack.com/pub/brywilli

    #blog #substack #philosophy #language #ontology #semantics #semiotics #epistemology #etymology #communication #Heidegger #Derrida #Foucault #Wittgenstein #Nietzsche #Gadamer #Peirce #Gallie #McGilchrist #languageinsufficiency

    #blog #substack #philosophy #language #ontology #semantics
  9. Philosophics @[email protected] ·

    This article is less about what philosophy is about and more about why we can't particularly know some things, and why not.

    👉 open.substack.com/pub/brywilli

    #blog #substack #philosophy #language #ontology #semantics #semiotics #epistemology #etymology #communication #Heidegger #Derrida #Foucault #Wittgenstein #Nietzsche #Gadamer #Peirce #Gallie #McGilchrist #languageinsufficiency

    #blog #substack #philosophy #language #ontology #semantics
  10. Philosophics @[email protected] ·

    This article is less about what philosophy is about and more about why we can't particularly know some things, and why not.

    👉 open.substack.com/pub/brywilli

    #blog #substack #philosophy #language #ontology #semantics #semiotics #epistemology #etymology #communication #Heidegger #Derrida #Foucault #Wittgenstein #Nietzsche #Gadamer #Peirce #Gallie #McGilchrist #languageinsufficiency

    #languageinsufficiency #mcgilchrist #gallie #peirce #gadamer #nietzsche
  11. Jon Awbrey @[email protected] ·

    Icon, Likeness, Likely Story, Likelihood, Probability • 2
    • inquiryintoinquiry.com/2026/05

    Re: Peirce List • Phyllis Chiasson
    • web.archive.org/web/2013121115
    • web.archive.org/web/2013121103

    I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

    ❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

    Reference —

    Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource —

    Theme One Program • User Guide • Appendix A
    • academia.edu/5211369/Theme_One

    #Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
    #Logic #Mathematics #Probability #ProbableReasoning #Induction
    #Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

    #morphism #likeness #likelystory #likelihood #analogy #inquiry
  12. Jon Awbrey @[email protected] ·

    Icon, Likeness, Likely Story, Likelihood, Probability • 2
    • inquiryintoinquiry.com/2026/05

    Re: Peirce List • Phyllis Chiasson
    • web.archive.org/web/2013121115
    • web.archive.org/web/2013121103

    I'm still a bit fuzzy on how Aristotle's account relates to Peirce's usage, though I'm pretty sure Peirce must have taken Aristotle's usage into account, but it does seem that Aristotle drew some sort of distinction here, using a term “tekmerion” which gets translated as “index” to make the following remark later on in that chapter.

    ❝We must either classify signs in this way, and regard their middle term as an index [τεκµηριον] (for the name ‘index’ is given to that which causes us to know, and the middle term is especially of this nature), or describe the arguments drawn from the extremes as ‘signs’, and that which is drawn from the middle as an ‘index’. For the conclusion which is reached through the first figure is most generally accepted and most true.❞ (Aristotle, Prior Analytics, 2.27.70b1–6).

    Reference —

    Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource —

    Theme One Program • User Guide • Appendix A
    • academia.edu/5211369/Theme_One

    #Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
    #Logic #Mathematics #Probability #ProbableReasoning #Induction
    #Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

    #morphism #likeness #likelystory #likelihood #analogy #inquiry
  13. Jon Awbrey @[email protected] ·

    Icon, Likeness, Likely Story, Likelihood, Probability • 1
    • inquiryintoinquiry.com/2026/05

    Here's a likely locus classicus for “icon” in its logical sense —

    ❝A probability (εικος) is not the same as a sign (σηµειον). The former is a generally accepted premiss; for that which people know to happen or not to happen, or to be or not to be, usually in a particular way, is a probability:

    ❝For example, that the envious are malevolent or that those who are loved are affectionate.

    ❝A sign, however, means a demonstrative premiss which is necessary or generally accepted. That which coexists with something else, or before or after whose happening something else has happened, is a sign of that something’s having happened or being.❞ (Aristotle, Prior Analytics, 2.27.70a3–10).

    Reference —

    Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.

    Resource —

    Theme One Program • User Guide • Appendix A
    • academia.edu/5211369/Theme_One

    #Aristotle #Peirce #IconIndexSymbol #Semiotics #SignRelations
    #Logic #Mathematics #Probability #ProbableReasoning #Induction
    #Inquiry #Analogy #Likelihood #LikelyStory #Likeness #Morphism

    #morphism #likeness #likelystory #likelihood #analogy #inquiry
  14. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 2
    • inquiryintoinquiry.com/2015/01

    It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

    I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

    So I'll try to keep focused on that.

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  15. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 2
    • inquiryintoinquiry.com/2015/01

    It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

    I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

    So I'll try to keep focused on that.

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  16. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 2
    • inquiryintoinquiry.com/2015/01

    It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

    I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

    So I'll try to keep focused on that.

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  17. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 2
    • inquiryintoinquiry.com/2015/01

    It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

    I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

    So I'll try to keep focused on that.

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  18. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 2
    • inquiryintoinquiry.com/2015/01

    It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

    I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

    So I'll try to keep focused on that.

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #peirce #logic #mathematics #semiotics #logicalgraphs #graphtheory
  19. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    Double Negation
    • inquiryintoinquiry.com/wp-cont

    Peirce's Law
    • inquiryintoinquiry.com/wp-cont

    Praeclarum Theorema
    • inquiryintoinquiry.com/wp-cont

    Two‑Thirds Majority Function
    • inquiryintoinquiry.com/wp-cont

    A full discussion of logical graphs can be found in the following article.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/ldzadj
    cc: mathstodon.xyz/@Inquiry/116494
    cc: researchgate.net/post/Animated
    cc: stream.syscoi.com/2026/04/30/a
    cc: groups.io/g/lawsofform/topic/a

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  20. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    Double Negation
    • inquiryintoinquiry.com/wp-cont

    Peirce's Law
    • inquiryintoinquiry.com/wp-cont

    Praeclarum Theorema
    • inquiryintoinquiry.com/wp-cont

    Two‑Thirds Majority Function
    • inquiryintoinquiry.com/wp-cont

    A full discussion of logical graphs can be found in the following article.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/ldzadj
    cc: mathstodon.xyz/@Inquiry/116494
    cc: researchgate.net/post/Animated
    cc: stream.syscoi.com/2026/04/30/a
    cc: groups.io/g/lawsofform/topic/a

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  21. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    Double Negation
    • inquiryintoinquiry.com/wp-cont

    Peirce's Law
    • inquiryintoinquiry.com/wp-cont

    Praeclarum Theorema
    • inquiryintoinquiry.com/wp-cont

    Two‑Thirds Majority Function
    • inquiryintoinquiry.com/wp-cont

    A full discussion of logical graphs can be found in the following article.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/ldzadj
    cc: mathstodon.xyz/@Inquiry/116494
    cc: researchgate.net/post/Animated
    cc: stream.syscoi.com/2026/04/30/a
    cc: groups.io/g/lawsofform/topic/a

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  22. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    Double Negation
    • inquiryintoinquiry.com/wp-cont

    Peirce's Law
    • inquiryintoinquiry.com/wp-cont

    Praeclarum Theorema
    • inquiryintoinquiry.com/wp-cont

    Two‑Thirds Majority Function
    • inquiryintoinquiry.com/wp-cont

    A full discussion of logical graphs can be found in the following article.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/ldzadj
    cc: mathstodon.xyz/@Inquiry/116494
    cc: researchgate.net/post/Animated
    cc: stream.syscoi.com/2026/04/30/a
    cc: groups.io/g/lawsofform/topic/a

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  23. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    Double Negation
    • inquiryintoinquiry.com/wp-cont

    Peirce's Law
    • inquiryintoinquiry.com/wp-cont

    Praeclarum Theorema
    • inquiryintoinquiry.com/wp-cont

    Two‑Thirds Majority Function
    • inquiryintoinquiry.com/wp-cont

    A full discussion of logical graphs can be found in the following article.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2025/05

    cc: academia.edu/community/ldzadj
    cc: mathstodon.xyz/@Inquiry/116494
    cc: researchgate.net/post/Animated
    cc: stream.syscoi.com/2026/04/30/a
    cc: groups.io/g/lawsofform/topic/a

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #peirce #logic #mathematics #semiotics #logicalgraphs #graphtheory
  24. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    See the following article for a full discussion of this type of logical graph.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Additional Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  25. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    See the following article for a full discussion of this type of logical graph.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Additional Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  26. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    See the following article for a full discussion of this type of logical graph.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Additional Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  27. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    See the following article for a full discussion of this type of logical graph.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Additional Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #proofanimations #propositionalcalculus #lawsofform #spencerbrown #graphtheory #logicalgraphs
  28. Jon Awbrey @[email protected] ·

    Animated Logical Graphs • 1
    • inquiryintoinquiry.com/2015/01

    For Your Musement …

    Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

    Proof Animations
    • oeis.org/wiki/User:Jon_Awbrey/

    See the following article for a full discussion of this type of logical graph.

    Logical Graphs
    • oeis.org/wiki/Logical_Graphs

    Additional Resources —

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2024/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2024/09

    #Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
    #SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

    #peirce #logic #mathematics #semiotics #logicalgraphs #graphtheory
  29. Jon Awbrey @[email protected] ·

    Reflection On Recursion • Discussion 1
    • inquiryintoinquiry.com/2026/04

    Re: Reflection On Recursion • 1
    • inquiryintoinquiry.com/2026/04
    Re: Laws of Form • John Mingers
    • groups.io/g/lawsofform/message

    JM:
    ❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

    ❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

    Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

    I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

    After a while, it simply becomes time to change the paradigm …

    Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

    And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

    Et sic deinceps …

    #Peirce #Logic #Mathematics
    #Recursion #Reflection #Semiotics
    #SignRelations #TriadicRelations

    #triadicrelations #semiotics #reflection #recursion #mathematics #logic
  30. Jon Awbrey @[email protected] ·

    Reflection On Recursion • Discussion 1
    • inquiryintoinquiry.com/2026/04

    Re: Reflection On Recursion • 1
    • inquiryintoinquiry.com/2026/04
    Re: Laws of Form • John Mingers
    • groups.io/g/lawsofform/message

    JM:
    ❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

    ❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

    Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

    I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

    After a while, it simply becomes time to change the paradigm …

    Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

    And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

    Et sic deinceps …

    #Peirce #Logic #Mathematics
    #Recursion #Reflection #Semiotics
    #SignRelations #TriadicRelations

    #triadicrelations #semiotics #reflection #recursion #mathematics #logic
  31. Jon Awbrey @[email protected] ·

    Reflection On Recursion • Discussion 1
    • inquiryintoinquiry.com/2026/04

    Re: Reflection On Recursion • 1
    • inquiryintoinquiry.com/2026/04
    Re: Laws of Form • John Mingers
    • groups.io/g/lawsofform/message

    JM:
    ❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

    ❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

    Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

    I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

    After a while, it simply becomes time to change the paradigm …

    Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

    And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

    Et sic deinceps …

    #Peirce #Logic #Mathematics
    #Recursion #Reflection #Semiotics
    #SignRelations #TriadicRelations

    #triadicrelations #semiotics #reflection #recursion #mathematics #logic
  32. Jon Awbrey @[email protected] ·

    Reflection On Recursion • Discussion 1
    • inquiryintoinquiry.com/2026/04

    Re: Reflection On Recursion • 1
    • inquiryintoinquiry.com/2026/04
    Re: Laws of Form • John Mingers
    • groups.io/g/lawsofform/message

    JM:
    ❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

    ❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

    Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

    I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

    After a while, it simply becomes time to change the paradigm …

    Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

    And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

    Et sic deinceps …

    #Peirce #Logic #Mathematics
    #Recursion #Reflection #Semiotics
    #SignRelations #TriadicRelations

    #signrelations #peirce #logic #mathematics #recursion #reflection
  33. Jon Awbrey @[email protected] ·

    Reflection On Recursion • Discussion 1
    • inquiryintoinquiry.com/2026/04

    Re: Reflection On Recursion • 1
    • inquiryintoinquiry.com/2026/04
    Re: Laws of Form • John Mingers
    • groups.io/g/lawsofform/message

    JM:
    ❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

    ❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

    Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

    I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

    After a while, it simply becomes time to change the paradigm …

    Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

    And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

    Et sic deinceps …

    #Peirce #Logic #Mathematics
    #Recursion #Reflection #Semiotics
    #SignRelations #TriadicRelations

    #triadicrelations #semiotics #reflection #recursion #mathematics #logic
  34. 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
  35. 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
  36. 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
  37. 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

    #peirce #higherordersignrelations #inquiry #inquiryintoinquiry #logic #mathematics
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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

    #peirce #higherordersignrelations #inquiry #inquiryintoinquiry #logic #mathematics
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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

    #peirce #higherordersignrelations #inquiry #inquiryintoinquiry #logic #mathematics
  48. 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
  49. 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
  50. 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