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1000 results for “Logical_Error”

  1. Steven Carneiro @[email protected] ·

    Qubit virtualization system for logical qubits:
    #quantumcomputing #logical #qubit #virtualization #microsoft #quantinuum #atomcomputing #technology #innovation
    ⚛️

    cio.com/article/3511493/micros

    #quantumcomputing #logical #qubit #virtualization #microsoft #quantinuum
  2. SilveringOfRose (In Short) @[email protected] ·

    **It's Just Logical**

    What if my ghost writer were
    Lines of code
    Housed on some machine
    What earnestness of verbiage
    Mingled with
    What #galore of processed words
    I might create
    But when innermost thoughts
    And creativity
    Are confined by the limits of logic
    Can we call it art
    And is it even
    Mine
    #vss365

    #TurnOfPhrase #RoomPrompt #poem #poetry #writing #vssPoem #PromptPoetry #280characters #SilverWrites

    #silverwrites #280characters #promptpoetry #vsspoem #writing #poetry
  3. SilveringOfRose (In Short) @[email protected] ·

    **It's Just Logical**

    What if my ghost writer were
    Lines of code
    Housed on some machine
    What earnestness of verbiage
    Mingled with
    What #galore of processed words
    I might create
    But when innermost thoughts
    And creativity
    Are confined by the limits of logic
    Can we call it art
    And is it even
    Mine
    #vss365

    #TurnOfPhrase #RoomPrompt #poem #poetry #writing #vssPoem #PromptPoetry #280characters #SilverWrites

    #galore #vss365 #turnofphrase #roomprompt #poem #poetry
  4. Vlad Masslove @[email protected] ·

    This letter seems very logical from #majorlabels point of view. Every corporation needs to grow at YTD sales and profit rate each year. And as soon as something starts to change then the #MusicBusiness model requires a change again...for the sake of competition. via publme.space/reactions/v/15969 musicbusinessworldwide.com/sir

    #majorlabels #musicbusiness
  5. Music Blocks programming @[email protected] ·

    If you want something logical yet unpredictable to listen to, try this Music Blocks projects that plays with ratios and prime factors: musicblocks.sugarlabs.org/inde

    It's hypnotic. ☮️ ☮️ ☮️

    #microtonal #MusicPlusCode #MusicPlusMath

    #microtonal #musicpluscode #musicplusmath
  6. Music Blocks programming @[email protected] ·

    If you want something logical yet unpredictable to listen to, try this Music Blocks projects that plays with ratios and prime factors: musicblocks.sugarlabs.org/inde

    It's hypnotic. ☮️ ☮️ ☮️

    #microtonal #MusicPlusCode #MusicPlusMath

    #musicplusmath #musicpluscode #microtonal
  7. Thiemo Fetzer 🇪🇺🇺🇦 - same @[email protected] ·

    Beautiful illustration of logical inconsistency in British Election Study.

    Or, well an indirect way to identify #Brexit #Protestvoters. At least if my understanding of what is going on is correct -- and I think most of my reading on Brexit turned out spot on so far.

    In the tabulation the population is BES respondents that said they would vote to Rejoin the EU. I cross tabulate this against self-reported EU referendum vote and self-reported regret of how they voted.

    See the issue?

    #brexit #protestvoters
  8. Agent Carter ✍️ @[email protected] ·

    @MrSpock

    Highly logical indeed! I was planning on making another donation to Joe anyway, but this event is added incentive! 🖖 :joebiden:
    #VoteBlueForABetterFuture

    #voteblueforabetterfuture
  9. Jon Awbrey @[email protected] ·

    Transformations of Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/05

    Re: Laws of Form
    • groups.io/g/lawsofform/topic/t

    Mauro Bertani
    • groups.io/g/lawsofform/message

    Dear Mauro,

    The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    Additional Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2024/03

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2024/01

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  10. Jon Awbrey @[email protected] ·

    Transformations of Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/05

    Re: Laws of Form
    • groups.io/g/lawsofform/topic/t

    Mauro Bertani
    • groups.io/g/lawsofform/message

    Dear Mauro,

    The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    Additional Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2024/03

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2024/01

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  11. Jon Awbrey @[email protected] ·

    Transformations of Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/05

    Re: Laws of Form
    • groups.io/g/lawsofform/topic/t

    Mauro Bertani
    • groups.io/g/lawsofform/message

    Dear Mauro,

    The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    Additional Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2024/03

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2024/01

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #peirce #logic #logicalgraphs #entitativegraphs #existentialgraphs #spencerbrown
  12. Jon Awbrey @[email protected] ·

    Transformations of Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/05

    Re: Laws of Form
    • groups.io/g/lawsofform/topic/t

    Mauro Bertani
    • groups.io/g/lawsofform/message

    Dear Mauro,

    The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    Additional Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Survey of Animated Logical Graphs
    • inquiryintoinquiry.com/2024/03

    Survey of Semiotics, Semiosis, Sign Relations
    • inquiryintoinquiry.com/2024/01

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  13. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • Discussion 2.2
    • inquiryintoinquiry.com/2024/05

    What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  14. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • Discussion 2.2
    • inquiryintoinquiry.com/2024/05

    What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  15. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • Discussion 2.2
    • inquiryintoinquiry.com/2024/05

    What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #peirce #logic #logicalgraphs #entitativegraphs #existentialgraphs #spencerbrown
  16. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • Discussion 2.2
    • inquiryintoinquiry.com/2024/05

    What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Logical Graphs • First Impressions
    • inquiryintoinquiry.com/2023/08

    Logical Graphs • Formal Development
    • inquiryintoinquiry.com/2023/09

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  17. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/05

    It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.

    Resources —

    Duality Indicating Unity
    • inquiryintoinquiry.com/2013/01

    C.S. Peirce • Logic of Number
    • inquiryintoinquiry.com/2012/09

    C.S. Peirce • Syllabus • Selection 1
    • inquiryintoinquiry.com/2014/08

    References —

    • Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.

    • Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  18. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/05

    It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.

    Resources —

    Duality Indicating Unity
    • inquiryintoinquiry.com/2013/01

    C.S. Peirce • Logic of Number
    • inquiryintoinquiry.com/2012/09

    C.S. Peirce • Syllabus • Selection 1
    • inquiryintoinquiry.com/2014/08

    References —

    • Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.

    • Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  19. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/05

    It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.

    Resources —

    Duality Indicating Unity
    • inquiryintoinquiry.com/2013/01

    C.S. Peirce • Logic of Number
    • inquiryintoinquiry.com/2012/09

    C.S. Peirce • Syllabus • Selection 1
    • inquiryintoinquiry.com/2014/08

    References —

    • Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.

    • Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #peirce #logic #logicalgraphs #entitativegraphs #existentialgraphs #spencerbrown
  20. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/05

    It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.

    Resources —

    Duality Indicating Unity
    • inquiryintoinquiry.com/2013/01

    C.S. Peirce • Logic of Number
    • inquiryintoinquiry.com/2012/09

    C.S. Peirce • Syllabus • Selection 1
    • inquiryintoinquiry.com/2014/08

    References —

    • Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.

    • Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  21. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.1
    • inquiryintoinquiry.com/2024/05

    “All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”

    — C.S. Peirce • “Logic of Number”

    “A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”

    — G. Spencer Brown • “Laws of Form”

    The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.

    A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.

    Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  22. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.1
    • inquiryintoinquiry.com/2024/05

    “All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”

    — C.S. Peirce • “Logic of Number”

    “A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”

    — G. Spencer Brown • “Laws of Form”

    The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.

    A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.

    Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  23. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.1
    • inquiryintoinquiry.com/2024/05

    “All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”

    — C.S. Peirce • “Logic of Number”

    “A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”

    — G. Spencer Brown • “Laws of Form”

    The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.

    A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.

    Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #peirce #logic #logicalgraphs #entitativegraphs #existentialgraphs #spencerbrown
  24. Jon Awbrey @[email protected] ·

    Mathematical Duality in Logical Graphs • 1.1
    • inquiryintoinquiry.com/2024/05

    “All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”

    — C.S. Peirce • “Logic of Number”

    “A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”

    — G. Spencer Brown • “Laws of Form”

    The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.

    A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.

    Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #MathematicalDuality #Form

    #form #mathematicalduality #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions
  25. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/04

    Re: Operator Variables in Logical Graphs • 1
    • inquiryintoinquiry.com/2024/04

    Re: Academia.edu • Stephen Duplantier
    • academia.edu/community/Lxn1Ww?

    SD:
    ❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞

    Stephen,

    “Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …

    As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Semeiotic
    • oeis.org/wiki/Semeiotic

    Sign Relations
    • oeis.org/wiki/Sign_relation

    Triadic Relations
    • oeis.org/wiki/Triadic_relation

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #logicaloperatorvariables #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions #lawsofform
  26. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/04

    Re: Operator Variables in Logical Graphs • 1
    • inquiryintoinquiry.com/2024/04

    Re: Academia.edu • Stephen Duplantier
    • academia.edu/community/Lxn1Ww?

    SD:
    ❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞

    Stephen,

    “Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …

    As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Semeiotic
    • oeis.org/wiki/Semeiotic

    Sign Relations
    • oeis.org/wiki/Sign_relation

    Triadic Relations
    • oeis.org/wiki/Triadic_relation

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #logicaloperatorvariables #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions #lawsofform
  27. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/04

    Re: Operator Variables in Logical Graphs • 1
    • inquiryintoinquiry.com/2024/04

    Re: Academia.edu • Stephen Duplantier
    • academia.edu/community/Lxn1Ww?

    SD:
    ❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞

    Stephen,

    “Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …

    As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Semeiotic
    • oeis.org/wiki/Semeiotic

    Sign Relations
    • oeis.org/wiki/Sign_relation

    Triadic Relations
    • oeis.org/wiki/Triadic_relation

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #peirce #logic #logicalgraphs #entitativegraphs #existentialgraphs #spencerbrown
  28. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • Discussion 1
    • inquiryintoinquiry.com/2024/04

    Re: Operator Variables in Logical Graphs • 1
    • inquiryintoinquiry.com/2024/04

    Re: Academia.edu • Stephen Duplantier
    • academia.edu/community/Lxn1Ww?

    SD:
    ❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞

    Stephen,

    “Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …

    As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.

    Resources —

    Logic Syllabus
    • inquiryintoinquiry.com/logic-s

    Semeiotic
    • oeis.org/wiki/Semeiotic

    Sign Relations
    • oeis.org/wiki/Sign_relation

    Triadic Relations
    • oeis.org/wiki/Triadic_relation

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #logicaloperatorvariables #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions #lawsofform
  29. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/04

    Consider De Morgan's rules:

    • ¬(A ∧ B) = ¬A ∨ ¬B

    • ¬(A ∨ B) = ¬A ∧ ¬B

    The common form exhibited by the two rules could be captured in a single formula by taking “o₁” and “o₂” as variable names ranging over a family of logical operators, then asking what substitutions for o₁ and o₂ would satisfy the following equation.

    • ¬(A o₁ B) = ¬A o₂ ¬B

    We already know two solutions to this “operator equation”, namely, (o₁, o₂) = (∧, ∨) and (o₁, o₂) = (∨, ∧). Wouldn't it be just like Peirce to ask if there are others?

    Having broached the subject of “logical operator variables”, I will leave it for now in the same way Peirce himself did:

    ❝I shall not further enlarge upon this matter at this point, although the conception mentioned opens a wide field; because it cannot be set in its proper light without overstepping the limits of dichotomic mathematics.❞ (Peirce, CP 4.306).

    Further exploration of operator variables and operator invariants treads on grounds traditionally known as second intentional logic and “opens a wide field”, as Peirce says. For now, however, I will tend to that corner of the field where our garden variety logical graphs grow, observing the ways in which operative variations and operative themes naturally develop on those grounds.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #logicaloperatorvariables #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions #lawsofform
  30. Jon Awbrey @[email protected] ·

    Operator Variables in Logical Graphs • 1.2
    • inquiryintoinquiry.com/2024/04

    Consider De Morgan's rules:

    • ¬(A ∧ B) = ¬A ∨ ¬B

    • ¬(A ∨ B) = ¬A ∧ ¬B

    The common form exhibited by the two rules could be captured in a single formula by taking “o₁” and “o₂” as variable names ranging over a family of logical operators, then asking what substitutions for o₁ and o₂ would satisfy the following equation.

    • ¬(A o₁ B) = ¬A o₂ ¬B

    We already know two solutions to this “operator equation”, namely, (o₁, o₂) = (∧, ∨) and (o₁, o₂) = (∨, ∧). Wouldn't it be just like Peirce to ask if there are others?

    Having broached the subject of “logical operator variables”, I will leave it for now in the same way Peirce himself did:

    ❝I shall not further enlarge upon this matter at this point, although the conception mentioned opens a wide field; because it cannot be set in its proper light without overstepping the limits of dichotomic mathematics.❞ (Peirce, CP 4.306).

    Further exploration of operator variables and operator invariants treads on grounds traditionally known as second intentional logic and “opens a wide field”, as Peirce says. For now, however, I will tend to that corner of the field where our garden variety logical graphs grow, observing the ways in which operative variations and operative themes naturally develop on those grounds.

    #Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
    #SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
    #CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables

    #logicaloperatorvariables #minimalnegationoperators #cactussyntax #propositionalcalculus #booleanfunctions #lawsofform
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