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1000 results for “Logical_Error”
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Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/“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 -
Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/“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 -
Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/“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 -
Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/“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 -
Mathematical Duality in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/“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 -
There's honestly no logical or rational reason not to like this.
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Operator Variables in Logical Graphs • Discussion 2
• https://inquiryintoinquiry.com/2024/04/09/operator-variables-in-logical-graphs-discussion-2/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Cybernetics List • Lou Kauffman
• https://groups.google.com/g/cybcom/c/XKT76QI_OnI/m/3u9P2Ir5AgAJLK:
❝I am writing to comment that there are some quite interesting situations that generalize the DeMorgan Duality.❝One well-known one is this. Let R* denote the real numbers with a formal symbol @, denoting infinity, adjoined so that:
• @ + @ = @
• @ + 0 = @
• @ + x = @ when x is an ordinary real number
• 1 ÷ @ = 0❝(Of course you cannot do anything with @ or the system collapses. One can easily give the constraints.)
❝Define ¬x = 1/x.
• x + y = usual sum otherwise.
❝Define x ∗ y = xy/(x + y) = 1/((1/x) + (1/y)).
❝Then we have x ∗ y = ¬(¬x + ¬y), so that the system (R*, ¬, +, ∗) satisfies DeMorgan duality and it is a Boolean algebra when restricted to {0, @}.
❝Note also that ¬ fixes 1 and -1. This algebraic system occurs of course in electrical calculations and also in the properties of tangles in knot theory, as you can read in the last part of my included paper “Knot Logic”. I expect there is quite a bit more about this kind of duality in various (categorical) places.❞
Thanks, Lou, there's a lot to think about here, so I'll need to study it a while. Just off hand, the embedding into reals brings up a vague memory of the very curious way Peirce defines negation in his 1870 “Logic of Relatives”. I seem to recall it involving a power series, but it's been a while so I'll have to look it up again.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus -
Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1RxySD:
❝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
• https://inquiryintoinquiry.com/logic-syllabus/Semeiotic
• https://oeis.org/wiki/SemeioticSign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relation#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1RxySD:
❝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
• https://inquiryintoinquiry.com/logic-syllabus/Semeiotic
• https://oeis.org/wiki/SemeioticSign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relation#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1RxySD:
❝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
• https://inquiryintoinquiry.com/logic-syllabus/Semeiotic
• https://oeis.org/wiki/SemeioticSign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relation#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1RxySD:
❝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
• https://inquiryintoinquiry.com/logic-syllabus/Semeiotic
• https://oeis.org/wiki/SemeioticSign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relation#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • Discussion 1
• https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/Re: Operator Variables in Logical Graphs • 1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/Re: Academia.edu • Stephen Duplantier
• https://www.academia.edu/community/Lxn1Ww?c=yq1RxySD:
❝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
• https://inquiryintoinquiry.com/logic-syllabus/Semeiotic
• https://oeis.org/wiki/SemeioticSign Relations
• https://oeis.org/wiki/Sign_relationTriadic Relations
• https://oeis.org/wiki/Triadic_relation#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/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 -
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/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 -
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/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 -
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/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 -
Operator Variables in Logical Graphs • 1.2
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/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 -
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
Operator Variables in Logical Graphs • 1.1
• https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.
I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.
#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperators #LogicalOperatorVariables -
The meaning of “The Logical Song” according to Roger Hodgson
https://rockandrollgarage.com/the-meaning-of-the-logical-song-according-to-roger-hodgson/
#supertramp #rogerhodgson #prog #progrock #progressiverock #music #song #lyrics
-
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_SyllabusLogical Graphs
• https://oeis.org/wiki/Logical_GraphsMinimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operatorPropositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_SystemsExamples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_lawPraeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theoremaProof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_AnimationsExcursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_OverviewFutures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_GraphsApplications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_ProblemsExploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_DataDifferential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_OverviewSurvey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata -
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_SyllabusLogical Graphs
• https://oeis.org/wiki/Logical_GraphsMinimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operatorPropositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_SystemsExamples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_lawPraeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theoremaProof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_AnimationsExcursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_OverviewFutures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_GraphsApplications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_ProblemsExploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_DataDifferential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_OverviewSurvey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata -
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_SyllabusLogical Graphs
• https://oeis.org/wiki/Logical_GraphsMinimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operatorPropositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_SystemsExamples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_lawPraeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theoremaProof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_AnimationsExcursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_OverviewFutures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_GraphsApplications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_ProblemsExploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_DataDifferential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_OverviewSurvey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata -
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_SyllabusLogical Graphs
• https://oeis.org/wiki/Logical_GraphsMinimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operatorPropositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_SystemsExamples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_lawPraeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theoremaProof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_AnimationsExcursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_OverviewFutures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_GraphsApplications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_ProblemsExploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_DataDifferential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_OverviewSurvey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata -
Survey of Animated Logical Graphs • 7
• https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.
Please follow the above link for the full set of resources.
Articles and blog series on the core ideas are linked below.Beginnings —
Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/Elements —
Logic Syllabus
• https://oeis.org/wiki/Logic_SyllabusLogical Graphs
• https://oeis.org/wiki/Logical_GraphsMinimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operatorPropositional Equation Reasoning Systems
• https://oeis.org/wiki/Propositional_Equation_Reasoning_SystemsExamples —
Peirce's Law
• https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/
• https://oeis.org/wiki/Peirce%27s_lawPraeclarum Theorema
• https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/
• https://oeis.org/wiki/Logical_Graphs#Praeclarum_theoremaProof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_AnimationsExcursions —
Cactus Language
• https://oeis.org/wiki/Cactus_Language_%E2%80%A2_OverviewFutures Of Logical Graphs
• https://oeis.org/wiki/Futures_Of_Logical_GraphsApplications —
Applications of a Propositional Calculator • Constraint Satisfaction Problems
• https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_ProblemsExploratory Qualitative Analysis of Sequential Observation Data
• https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_DataDifferential Analytic Turing Automata
• https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_OverviewSurvey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#SpencerBrown #LawsOfForm #BooleanFunctions #PropositionalCalculus
#CactusSyntax #MinimalNegationOperator #PeircesLaw #TuringAutomata -
The next logical step in my evolution was to add vocals, and Blood and Blackouts would prove to be my most accessible release with its highly distorted riffs and vocals. I regret the industrial nature of the growls but it was as far as I was willing to go given my trepidation of being trans and singing at the time under my name.
Listeners have often referred to B&B as “essential.”
Highlights:
“Mania”
“Blood and Blackouts”
“Divine Right”
“Narcissus”
