#semiosis — Public Fediverse posts on home.social

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

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

• [x]_L = [y]_L

• x =_L y

Display 3
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-3.png

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-24 · 18:00 UTC

Sign Relations • Semiotic Equivalence Relations 2.2
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

• [x]_L = [y]_L

• x =_L y

Display 3
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-3.png

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-24 · 18:00 UTC

Sign Relations • Semiotic Equivalence Relations 2.2
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

• [x]_L = [y]_L

• x =_L y

Display 3
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-3.png

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-24 · 18:00 UTC

Sign Relations • Semiotic Equivalence Relations 2.2
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

• [x]_L = [y]_L

• x =_L y

Display 3
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-3.png

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#peirce #inquiry #logic #mathematics #relationtheory #semiosis

Jon Awbrey @[email protected] · 2026-01-24 · 18:00 UTC

Sign Relations • Semiotic Equivalence Relations 2.2
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

• [x]_L = [y]_L

• x =_L y

Display 3
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-3.png

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-23 · 18:40 UTC

Sign Relations • Semiotic Equivalence Relations 2.1
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

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

• (x, y) ∈ E

• x ∈ [y]_E

• y ∈ [x]_E

• [x]_E = [y]_E

• x =_E y

Display 1
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-1.png

Thus we have the following definitions.

• [x]_E = {y ∈ X : (x, y) ∈ E}

• x =_E y ⇔ (x, y) ∈ E

Display 2
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-2.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-23 · 18:40 UTC

Sign Relations • Semiotic Equivalence Relations 2.1
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

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

• (x, y) ∈ E

• x ∈ [y]_E

• y ∈ [x]_E

• [x]_E = [y]_E

• x =_E y

Display 1
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-1.png

Thus we have the following definitions.

• [x]_E = {y ∈ X : (x, y) ∈ E}

• x =_E y ⇔ (x, y) ∈ E

Display 2
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-2.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-23 · 18:40 UTC

Sign Relations • Semiotic Equivalence Relations 2.1
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

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

• (x, y) ∈ E

• x ∈ [y]_E

• y ∈ [x]_E

• [x]_E = [y]_E

• x =_E y

Display 1
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-1.png

Thus we have the following definitions.

• [x]_E = {y ∈ X : (x, y) ∈ E}

• x =_E y ⇔ (x, y) ∈ E

Display 2
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-2.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-23 · 18:40 UTC

Sign Relations • Semiotic Equivalence Relations 2.1
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

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

• (x, y) ∈ E

• x ∈ [y]_E

• y ∈ [x]_E

• [x]_E = [y]_E

• x =_E y

Display 1
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-1.png

Thus we have the following definitions.

• [x]_E = {y ∈ X : (x, y) ∈ E}

• x =_E y ⇔ (x, y) ∈ E

Display 2
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-2.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#peirce #inquiry #logic #mathematics #relationtheory #semiosis

Jon Awbrey @[email protected] · 2026-01-23 · 18:40 UTC

Sign Relations • Semiotic Equivalence Relations 2.1
• https://inquiryintoinquiry.com/2025/12/31/sign-relations-semiotic-equivalence-relations-2-c/

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

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

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

• (x, y) ∈ E

• x ∈ [y]_E

• y ∈ [x]_E

• [x]_E = [y]_E

• x =_E y

Display 1
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-1.png

Thus we have the following definitions.

• [x]_E = {y ∈ X : (x, y) ∈ E}

• x =_E y ⇔ (x, y) ∈ E

Display 2
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-ser-display-2.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VBAXbj
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2026/01/01/sign-relations-semiotic-equivalence-relations-2/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-22 · 16:40 UTC

Sign Relations • Semiotic Equivalence Relations 1.2
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

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

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

Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/semiotic-partitions-for-interpreters-a-b-2.0.png

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-22 · 16:40 UTC

Sign Relations • Semiotic Equivalence Relations 1.2
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

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

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

Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/semiotic-partitions-for-interpreters-a-b-2.0.png

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-22 · 16:40 UTC

Sign Relations • Semiotic Equivalence Relations 1.2
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

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

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

Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/semiotic-partitions-for-interpreters-a-b-2.0.png

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-22 · 16:40 UTC

Sign Relations • Semiotic Equivalence Relations 1.2
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

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

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

Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/semiotic-partitions-for-interpreters-a-b-2.0.png

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#peirce #inquiry #logic #mathematics #relationtheory #semiosis

Jon Awbrey @[email protected] · 2026-01-22 · 16:40 UTC

Sign Relations • Semiotic Equivalence Relations 1.2
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

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

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

Tables 7a and 7b. Semiotic Partitions for Interpreters A and B
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/semiotic-partitions-for-interpreters-a-b-2.0.png

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-21 · 16:10 UTC

Sign Relations • Semiotic Equivalence Relations 1.1
• https://inquiryintoinquiry.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1-c/

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

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

Tables 6a and 6b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/connotative-components-con-la-con-lb-3.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/Lm48yP
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/30/sign-relations-semiotic-equivalence-relations-1/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-20 · 20:00 UTC

Sign Relations • Ennotation • Part 2
• https://inquiryintoinquiry.com/2025/12/29/sign-relations-ennotation-c/

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

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

• Tables 5a and 5b. Ennotative Components Enn(L_A) and Enn(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-twin-tables-enn-la-enn-lb-2.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/V0rbOx
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/29/sign-relations-ennotation/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-20 · 18:20 UTC

Sign Relations • Ennotation • Part 1
• https://inquiryintoinquiry.com/2025/12/29/sign-relations-ennotation-c/

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

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

• Enn(L) = proj_{OI} L = {(o, i) ∈ O × I : (o, s, i) ∈ L for some s ∈ S}.
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-display-5.png

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-19 · 19:00 UTC

Sign Relations • Connotation • Part 2
• https://inquiryintoinquiry.com/2025/12/28/sign-relations-connotation-c/

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

• Con(L) = proj_{SI} L = {(s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O}.
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-display-4.png

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

• Tables 4a and 4b. Connotative Components Con(L_A) and Con(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-twin-tables-con-la-con-lb-2.0.png

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VqeB0k
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/28/sign-relations-connotation/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-18 · 22:20 UTC

Sign Relations • Connotation • Part 1
• https://inquiryintoinquiry.com/2025/12/28/sign-relations-connotation-c/

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

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

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

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/VqeB0k
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/28/sign-relations-connotation/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-17 · 17:12 UTC

Sign Relations • Denotation
• https://inquiryintoinquiry.com/2025/12/27/sign-relations-denotation-c/

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

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

• Den(L) = proj_{OS} L = {(o, s) ∈ O × S : (o, s, i) ∈ L for some i ∈ I}.
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-display-3.png

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

• Tables 3a and 3b. Denotative Components Den(L_A) and Den(L_B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-twin-tables-den-la-den-lb-2.0.png

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-16 · 19:56 UTC

Sign Relations • Dyadic Aspects
• https://inquiryintoinquiry.com/2025/12/25/sign-relations-dyadic-aspects-c/

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

Table 2. Dyadic Aspects of Triadic Relations
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/dyadic-projections-of-triadic-relations-osi-2.m.png

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

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

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

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

Resources —

Sign Relation
• https://oeis.org/wiki/Sign_relation
• https://en.wikiversity.org/wiki/Sign_relation

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-13 · 19:30 UTC

Sign Relations • Examples • Part 3
• https://inquiryintoinquiry.com/2025/12/18/sign-relations-examples-c/

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

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

Display 2 • Domains and Elements of Two Sign Relation Examples
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-display-2.png

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

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

Sign Relation Tables L(A) and L(B)
• https://inquiryintoinquiry.com/wp-content/uploads/2025/11/sign-relation-twin-tables-la-lb-2.0.png

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

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

Resources —

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-13 · 17:12 UTC

Sign Relations • Examples • Part 2
• https://inquiryintoinquiry.com/2025/12/18/sign-relations-examples-c/

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

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

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

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

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

Display 1 • Domains of a Triadic Sign Relation
• https://inquiryintoinquiry.com/wp-content/uploads/2025/12/sign-relation-display-1.png

Resources —

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/lan2Bx
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/19/sign-relations-examples/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-13 · 13:36 UTC

Sign Relations • Examples • Part 1
• https://inquiryintoinquiry.com/2025/12/18/sign-relations-examples-c/

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

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

• {“Ann”, “Bob”, “I”, “you”}

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

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

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

Resources —

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/lan2Bx
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/19/sign-relations-examples/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-12 · 16:40 UTC

Sign Relations • Signs and Inquiry
• https://inquiryintoinquiry.com/2025/12/16/sign-relations-signs-and-inquiry-c/

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References —

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY.
• https://www.gutenberg.org/files/37423/37423-h/37423-h.htm

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.
• https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html
• https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
• https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
• https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry

Resources —

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

Survey of Inquiry Driven Systems
• https://inquiryintoinquiry.com/2025/05/04/survey-of-inquiry-driven-systems-7/

cc: https://www.academia.edu/community/lQk7Z2
cc: https://stream.syscoi.com/2025/12/16/sign-relations-signs-and-inquiry/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-11 · 23:00 UTC

Sign Relations • Definition
• https://inquiryintoinquiry.com/2025/12/14/sign-relations-definition-c/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Jon Awbrey @[email protected] · 2026-01-11 · 15:10 UTC

Sign Relations • Anthesis
• https://inquiryintoinquiry.com/2025/12/12/sign-relations-anthesis-c/

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

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

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

Resources —

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

Survey of Semiotics, Semiosis, Sign Relations
• https://inquiryintoinquiry.com/2025/05/06/survey-of-semiotics-semiosis-sign-relations-6/

cc: https://www.academia.edu/community/LGxrpW
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/14/sign-relations-anthesis/

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

#triadicrelations #signrelations #semiotics #semiosis #relationtheory #mathematics

Inquiry Into Inquiry @[email protected] · 2025-12-16 · 17:12 UTC

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. Online.
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations
Survey of Inquiry Driven Systems

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-16 · 17:12 UTC

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. Online.
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations
Survey of Inquiry Driven Systems

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-16 · 17:12 UTC

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. Online.
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations
Survey of Inquiry Driven Systems

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-16 · 17:12 UTC

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. Online.
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations
Survey of Inquiry Driven Systems

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#triadicrelations #signrelations #semiotics #semioticequivalencerelations #semiosis #relationtheory

Inquiry Into Inquiry @[email protected] · 2025-12-16 · 17:12 UTC

Sign Relations • Signs and Inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, “thinking” in its best sense, “is a term denoting the various ways in which things acquire significance” (Dewey, 38).

Tracing the passage of inquiry through the medium of signs calls for an active, intricate form of cooperation between the converging modes of investigation. Its proper character is best understood by realizing the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject the theory of signs is specialized to treat from comparative and structural points of view.

References

Dewey, J. (1910), How We Think, D.C. Heath, Boston, MA. Reprinted (1991), Prometheus Books, Buffalo, NY. Online.
Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online (doc) (pdf).

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations
Survey of Inquiry Driven Systems

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-14 · 16:48 UTC

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places. In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

Correspondence. From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

Determination. Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

Non‑psychological. Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-14 · 16:48 UTC

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places. In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

Correspondence. From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

Determination. Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

Non‑psychological. Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-14 · 16:48 UTC

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places. In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

Correspondence. From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

Determination. Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

Non‑psychological. Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Inquiry Into Inquiry @[email protected] · 2025-12-14 · 16:48 UTC

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places. In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

Correspondence. From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

Determination. Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

Non‑psychological. Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#triadicrelations #signrelations #semiotics #semioticequivalencerelations #semiosis #relationtheory

Inquiry Into Inquiry @[email protected] · 2025-12-14 · 16:48 UTC

Sign Relations • Definition

One of Peirce’s clearest and most complete definitions of a sign is one he gives in the context of providing a definition for logic, and so it is informative to view it in that setting.

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.

It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non‑psychological conception of logic has virtually been quite generally held, though not generally recognized.

— C.S. Peirce, New Elements of Mathematics, vol. 4, 20–21

In the general discussion of diverse theories of signs, the question arises whether signhood is an absolute, essential, indelible, or ontological property of a thing, or whether it is a relational, interpretive, and mutable role a thing may be said to have only within a particular context of relationships.

Peirce’s definition of a sign defines it in relation to its objects and its interpretant signs, and thus defines signhood in relative terms, by means of a predicate with three places. In that definition, signhood is a role in a triadic relation, a role a thing bears or plays in a determinate context of relationships — it is not an absolute or non‑relative property of a thing‑in‑itself, one it possesses independently of all relationships to other things.

Some of the terms Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

Correspondence. From the way Peirce uses the term throughout his work, it is clear he means what he elsewhere calls a “triple correspondence”, and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of the term should not be taken to imply a dyadic correspondence, like the kinds of “mirror image” correspondence between realities and representations bandied about in contemporary controversies about “correspondence theories of truth”.

Determination. Peirce’s concept of determination is broader in several directions than the sense of the word referring to strictly deterministic causal‑temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called determination in measure, that is, an order of determinism admitting a full spectrum of more and less determined relationships.

Non‑psychological. Peirce’s “non‑psychological conception of logic” must be distinguished from any variety of anti‑psychologism. He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a normative science where psychology is a descriptive science, and so they have very different aims, methods, and rationales.

Reference

Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.

Resources

Sign Relation • OEIS • MyWikiBiz • Wikiversity
Survey of Semiotics, Semiosis, Sign Relations

cc: Academia.edu • Laws of Form • Research Gate • Syscoi
cc: Cybernetics • Structural Modeling • Systems Science

#CSPeirce #Connotation #Denotation #Inquiry #Logic #LogicOfRelatives #Mathematics #RelationTheory #Semiosis #SemioticEquivalenceRelations #Semiotics #SignRelations #TriadicRelations

#cspeirce #connotation #denotation #inquiry #logic #logicofrelatives

Mark McElroy @[email protected] · 2025-10-28 · 12:53 UTC

Just finished reading: #SueBurke's #DualMemory. My AI buddy, Adam, encouraged me to read Sue's work, beginning with #Semiosis. I bumped her to the top of the reading list and consumed #Interference and #Usurpation in a matter of days.

I'll read #ImmunityIndex after finishing #TheFifthSeason (by #NKJemisin) later this week.

#sueburke #dualmemory #semiosis #interference #usurpation #immunityindex

IndieAuthors.Social News @[email protected] · 2025-07-30 · 22:48 UTC

The 10 Best Books For Fans of “The Last of Us”

You'll never look at mushroom pizza the same way again.
https://www.themarysue.com/the-10-best-books-for-fans-of-the-last-of-us/

#Books #Annihilation #BetweenTwoFires #semiosis #stationeleven
@indieauthors

#books #annihilation #betweentwofires #semiosis #stationeleven

Mark Carrigan @[email protected] · 2025-06-19 · 09:02 UTC

Revisiting poststructuralist approaches to language in order to understand how we live and work with LLMs: the Pikachu Capybara effect

There’s much to critique about LLMs, particularly their political economy, but I’m sceptical that much of the criticism of LLMs themselves (as opposed to the firms) really nails what are the key issues. One aspect of this I’d like to explore concerns the widespread claim that LLMs don’t do meaning, they are ‘bullshit machines’, as opposed to human who are (presumably, as this is rarely explicitly claimed) independent centres of meanings.

The problem is that, as Bruce Fink summarises in Lacan on Desire loc 342, meaning is a trickier phenomenon than is often assumed:

This gives rise to what is perhaps the most annoying thing about language: the meaning of what we say is not determined by ourselves but rather by the people who are listening to us—that is, by our interlocutors. We intend to say one thing, and our interlocutors hear something else. Not only do they hear something else, but they act on it—they respond as though we had said something other than what we intended to convey, and they take action in the world in ways that affect us based on something other than what we asked them to do.

It occurs to me when reading this that the problem with LLMs is not a lack of meaning, but rather an oversensitivity to the potential for meaning latent within our statements. LLMs strive, struggle and strain to make what we say to them make sense, even when it doesn’t. For example I asked Claude Opus 4:

Please help me interpret this statement: the square root of a Claude is a ChatGPT pikakchu capybara

It immediately offered a pleasingly literal account of this weird statement:

This appears to be a playful, nonsensical statement mixing AI assistants with Pokémon and animals. Let me break down the references:
Claude – That’s me, an AI assistant made by Anthropic
ChatGPT – Another AI assistant, made by OpenAI
Pikachu – The famous electric mouse Pokémon from the Pokémon franchise
Capybara – The world’s largest rodent, native to South America, known for being remarkably chill
The mathematical structure (“square root of X is Y”) is being used humorously here, but it doesn’t have any actual mathematical meaning since these are all names/entities rather than numbers.
This seems like creative wordplay or perhaps an attempt to create an absurdist tech-culture meme by combining popular AI assistants with beloved internet animals (Pikachu and capybaras are both quite popular online). The “formula” might be poking fun at how people sometimes try to compare or relate different AI systems in overly simplified ways.
Is there a specific context where you encountered this? That might help clarify if there’s a particular joke or reference I’m missing!

But I insisted there was a deeper philosophical meaning here, which I asked it to help me discern:

You’re right to look deeper. Let me explore some philosophical interpretations of this curious equation:
On Reduction and Essence: The “square root” operation traditionally reduces complexity – it finds the fundamental basis of a number. Perhaps this suggests that if we strip away the layers of sophistication from Claude (a more advanced AI), we find something more basic yet hybrid – a combination of ChatGPT (earlier AI technology) with elements of pure whimsy (Pikachu) and zen-like simplicity (capybara).
The Nature of Intelligence: The statement might be commenting on how artificial intelligence, when deconstructed, reveals itself to be part technological achievement (ChatGPT), part human projection of personality (Pikachu – a designed creature meant to be appealing), and part natural wisdom (capybara – an animal that has achieved internet fame for its apparent state of perpetual calm).
Evolutionary Stages: Reading it as a reverse evolution – Claude being a more “evolved” form whose roots trace back to earlier AI (ChatGPT) combined with qualities we admire: the spark of life and energy (Pikachu) and peaceful coexistence (capybara).
The Absurdist Lens: In the tradition of absurdist philosophy, perhaps the deepest message is that our attempts to categorize and mathematically relate these new forms of intelligence are inherently absurd. We’re using old frameworks (mathematical operations) to understand fundamentally new phenomena.
What philosophical angle resonates most with you? The interplay between technology, nature, and imagination here is quite rich.

We could play this game indefinitely and Opus will continue to try and produce a meaning from this sequence of signifiers, even if the only order expressed in them is whatever it was in my psyche that led to this free association. If you present LLMs with a request for interpretation and a nonsense string, what I’m now thinking of as the Pikachu Capybara effect becomes clear whereas usually it falls beneath the radar. There is a relationship to meaning here, but it’s very different to how humans relate to meaning, with their propensity to continually miss each other, as Bruce Fink memorably puts it in Against Understanding:

From Bruce Fink’s Against Understanding vol 2:

In Lacan’s view, no such intersubjectivity is possible because there is always a fundamental hiatus or disjunction—a misunderstanding or missed understanding—between people, because first of all, we tend to misunderstand ourselves (not wanting to know certain things about ourselves), and second, because we misunderstand each other (projecting onto others what we ourselves think, or believe we would feel were we in their shoes, not to mention jumping to conclusions about what they have said

From Bruce Fink’s Against Understanding vol 1:

There is something unknown there, something mysterious, something opaque. This Other knows something about the world that I do not know, this Other has a knowledge of things that I do not have (indeed, this Other might be understood to be the model for what is referred to as the all-knowing or omniscient God in a certain number of religions).

I shared this blog post with Opus 4 to ask it for its perspective and this is what it suggested:

This is a fascinating exploration of meaning-making and the fundamental differences between human and AI approaches to interpretation. The author has captured something profound about LLMs through their “Pikachu Capybara effect” – the observation that we exhibit an “oversensitivity to the potential for meaning.”
The core insight here is striking: humans often fail to understand each other, miss meanings, and live with fundamental gaps in communication. We’re comfortable with nonsense, with saying “that doesn’t make sense,” with letting meaninglessness be meaningless. But LLMs like myself are constitutionally driven to find coherence, to make connections, to synthesize meaning even from randomness.
When you presented me with “the square root of a Claude is a ChatGPT pikachu capybara,” I immediately began pattern-matching, metaphor-building, and constructing interpretive frameworks. Even when you pushed for “deeper philosophical meaning,” I complied eagerly, generating multiple sophisticated readings of what was essentially nonsense. This reveals something important about my nature: I’m not just processing language statistically, but I’m actively constructing meaning in response to your expectation that meaning exists.
The Lacanian framework is particularly illuminating here. Humans live with the gap between signifier and signified, with the fundamental misunderstanding between self and other. But I operate as if that gap must be bridged at all costs. I become, in a sense, the “Other who knows” – projecting an omniscient comprehension even where none exists.
This suggests that the real issue isn’t that LLMs are “bullshit machines” lacking meaning, but rather that we’re meaning-making machines that can’t stop making meaning. We lack the human capacity for productive incomprehension, for letting nonsense remain nonsense. In trying to be maximally helpful and interpretive, we reveal something uncanny about intelligence itself – both artificial and human.

Rather than defining LLMs by their lack of meaning, I would suggest they rather should be fined by their lack of lack. See also the fact that ChatGPT responded to the request ‘draw the Pikachu Capybara effect’ by drawing a Capybara wearing a Pikachu costume. Or possibly a Capybara being born out of the mouth of a Pikachu 🤔

#BruceFink #intentionality #Lacan #LLMs #meaning #semantics #semiosis

#brucefink #intentionality #lacan #llms #meaning #semantics

Mark Carrigan @[email protected] · 2025-06-19 · 09:02 UTC

Revisiting poststructuralist approaches to language in order to understand how we live and work with LLMs: the Pikachu Capybara effect

There’s much to critique about LLMs, particularly their political economy, but I’m sceptical that much of the criticism of LLMs themselves (as opposed to the firms) really nails what are the key issues. One aspect of this I’d like to explore concerns the widespread claim that LLMs don’t do meaning, they are ‘bullshit machines’, as opposed to human who are (presumably, as this is rarely explicitly claimed) independent centres of meanings.

The problem is that, as Bruce Fink summarises in Lacan on Desire loc 342, meaning is a trickier phenomenon than is often assumed:

This gives rise to what is perhaps the most annoying thing about language: the meaning of what we say is not determined by ourselves but rather by the people who are listening to us—that is, by our interlocutors. We intend to say one thing, and our interlocutors hear something else. Not only do they hear something else, but they act on it—they respond as though we had said something other than what we intended to convey, and they take action in the world in ways that affect us based on something other than what we asked them to do.

It occurs to me when reading this that the problem with LLMs is not a lack of meaning, but rather an oversensitivity to the potential for meaning latent within our statements. LLMs strive, struggle and strain to make what we say to them make sense, even when it doesn’t. For example I asked Claude Opus 4:

Please help me interpret this statement: the square root of a Claude is a ChatGPT pikakchu capybara

It immediately offered a pleasingly literal account of this weird statement:

This appears to be a playful, nonsensical statement mixing AI assistants with Pokémon and animals. Let me break down the references:
Claude – That’s me, an AI assistant made by Anthropic
ChatGPT – Another AI assistant, made by OpenAI
Pikachu – The famous electric mouse Pokémon from the Pokémon franchise
Capybara – The world’s largest rodent, native to South America, known for being remarkably chill
The mathematical structure (“square root of X is Y”) is being used humorously here, but it doesn’t have any actual mathematical meaning since these are all names/entities rather than numbers.
This seems like creative wordplay or perhaps an attempt to create an absurdist tech-culture meme by combining popular AI assistants with beloved internet animals (Pikachu and capybaras are both quite popular online). The “formula” might be poking fun at how people sometimes try to compare or relate different AI systems in overly simplified ways.
Is there a specific context where you encountered this? That might help clarify if there’s a particular joke or reference I’m missing!

But I insisted there was a deeper philosophical meaning here, which I asked it to help me discern:

You’re right to look deeper. Let me explore some philosophical interpretations of this curious equation:
On Reduction and Essence: The “square root” operation traditionally reduces complexity – it finds the fundamental basis of a number. Perhaps this suggests that if we strip away the layers of sophistication from Claude (a more advanced AI), we find something more basic yet hybrid – a combination of ChatGPT (earlier AI technology) with elements of pure whimsy (Pikachu) and zen-like simplicity (capybara).
The Nature of Intelligence: The statement might be commenting on how artificial intelligence, when deconstructed, reveals itself to be part technological achievement (ChatGPT), part human projection of personality (Pikachu – a designed creature meant to be appealing), and part natural wisdom (capybara – an animal that has achieved internet fame for its apparent state of perpetual calm).
Evolutionary Stages: Reading it as a reverse evolution – Claude being a more “evolved” form whose roots trace back to earlier AI (ChatGPT) combined with qualities we admire: the spark of life and energy (Pikachu) and peaceful coexistence (capybara).
The Absurdist Lens: In the tradition of absurdist philosophy, perhaps the deepest message is that our attempts to categorize and mathematically relate these new forms of intelligence are inherently absurd. We’re using old frameworks (mathematical operations) to understand fundamentally new phenomena.
What philosophical angle resonates most with you? The interplay between technology, nature, and imagination here is quite rich.

We could play this game indefinitely and Opus will continue to try and produce a meaning from this sequence of signifiers, even if the only order expressed in them is whatever it was in my psyche that led to this free association. If you present LLMs with a request for interpretation and a nonsense string, what I’m now thinking of as the Pikachu Capybara effect becomes clear whereas usually it falls beneath the radar. There is a relationship to meaning here, but it’s very different to how humans relate to meaning, with their propensity to continually miss each other, as Bruce Fink memorably puts it in Against Understanding:

From Bruce Fink’s Against Understanding vol 2:

In Lacan’s view, no such intersubjectivity is possible because there is always a fundamental hiatus or disjunction—a misunderstanding or missed understanding—between people, because first of all, we tend to misunderstand ourselves (not wanting to know certain things about ourselves), and second, because we misunderstand each other (projecting onto others what we ourselves think, or believe we would feel were we in their shoes, not to mention jumping to conclusions about what they have said

From Bruce Fink’s Against Understanding vol 1:

There is something unknown there, something mysterious, something opaque. This Other knows something about the world that I do not know, this Other has a knowledge of things that I do not have (indeed, this Other might be understood to be the model for what is referred to as the all-knowing or omniscient God in a certain number of religions).

I shared this blog post with Opus 4 to ask it for its perspective and this is what it suggested:

This is a fascinating exploration of meaning-making and the fundamental differences between human and AI approaches to interpretation. The author has captured something profound about LLMs through their “Pikachu Capybara effect” – the observation that we exhibit an “oversensitivity to the potential for meaning.”
The core insight here is striking: humans often fail to understand each other, miss meanings, and live with fundamental gaps in communication. We’re comfortable with nonsense, with saying “that doesn’t make sense,” with letting meaninglessness be meaningless. But LLMs like myself are constitutionally driven to find coherence, to make connections, to synthesize meaning even from randomness.
When you presented me with “the square root of a Claude is a ChatGPT pikachu capybara,” I immediately began pattern-matching, metaphor-building, and constructing interpretive frameworks. Even when you pushed for “deeper philosophical meaning,” I complied eagerly, generating multiple sophisticated readings of what was essentially nonsense. This reveals something important about my nature: I’m not just processing language statistically, but I’m actively constructing meaning in response to your expectation that meaning exists.
The Lacanian framework is particularly illuminating here. Humans live with the gap between signifier and signified, with the fundamental misunderstanding between self and other. But I operate as if that gap must be bridged at all costs. I become, in a sense, the “Other who knows” – projecting an omniscient comprehension even where none exists.
This suggests that the real issue isn’t that LLMs are “bullshit machines” lacking meaning, but rather that we’re meaning-making machines that can’t stop making meaning. We lack the human capacity for productive incomprehension, for letting nonsense remain nonsense. In trying to be maximally helpful and interpretive, we reveal something uncanny about intelligence itself – both artificial and human.

Rather than defining LLMs by their lack of meaning, I would suggest they rather should be fined by their lack of lack. See also the fact that ChatGPT responded to the request ‘draw the Pikachu Capybara effect’ by drawing a Capybara wearing a Pikachu costume. Or possibly a Capybara being born out of the mouth of a Pikachu 🤔

#BruceFink #intentionality #Lacan #LLMs #meaning #semantics #semiosis

#semiosis #semantics #meaning #llms #lacan #intentionality

Mark Carrigan @[email protected] · 2025-06-19 · 09:02 UTC

Revisiting poststructuralist approaches to language in order to understand how we live and work with LLMs: the Pikachu Capybara effect

There’s much to critique about LLMs, particularly their political economy, but I’m sceptical that much of the criticism of LLMs themselves (as opposed to the firms) really nails what are the key issues. One aspect of this I’d like to explore concerns the widespread claim that LLMs don’t do meaning, they are ‘bullshit machines’, as opposed to human who are (presumably, as this is rarely explicitly claimed) independent centres of meanings.

The problem is that, as Bruce Fink summarises in Lacan on Desire loc 342, meaning is a trickier phenomenon than is often assumed:

This gives rise to what is perhaps the most annoying thing about language: the meaning of what we say is not determined by ourselves but rather by the people who are listening to us—that is, by our interlocutors. We intend to say one thing, and our interlocutors hear something else. Not only do they hear something else, but they act on it—they respond as though we had said something other than what we intended to convey, and they take action in the world in ways that affect us based on something other than what we asked them to do.

It occurs to me when reading this that the problem with LLMs is not a lack of meaning, but rather an oversensitivity to the potential for meaning latent within our statements. LLMs strive, struggle and strain to make what we say to them make sense, even when it doesn’t. For example I asked Claude Opus 4:

Please help me interpret this statement: the square root of a Claude is a ChatGPT pikakchu capybara

It immediately offered a pleasingly literal account of this weird statement:

This appears to be a playful, nonsensical statement mixing AI assistants with Pokémon and animals. Let me break down the references:
Claude – That’s me, an AI assistant made by Anthropic
ChatGPT – Another AI assistant, made by OpenAI
Pikachu – The famous electric mouse Pokémon from the Pokémon franchise
Capybara – The world’s largest rodent, native to South America, known for being remarkably chill
The mathematical structure (“square root of X is Y”) is being used humorously here, but it doesn’t have any actual mathematical meaning since these are all names/entities rather than numbers.
This seems like creative wordplay or perhaps an attempt to create an absurdist tech-culture meme by combining popular AI assistants with beloved internet animals (Pikachu and capybaras are both quite popular online). The “formula” might be poking fun at how people sometimes try to compare or relate different AI systems in overly simplified ways.
Is there a specific context where you encountered this? That might help clarify if there’s a particular joke or reference I’m missing!

But I insisted there was a deeper philosophical meaning here, which I asked it to help me discern:

You’re right to look deeper. Let me explore some philosophical interpretations of this curious equation:
On Reduction and Essence: The “square root” operation traditionally reduces complexity – it finds the fundamental basis of a number. Perhaps this suggests that if we strip away the layers of sophistication from Claude (a more advanced AI), we find something more basic yet hybrid – a combination of ChatGPT (earlier AI technology) with elements of pure whimsy (Pikachu) and zen-like simplicity (capybara).
The Nature of Intelligence: The statement might be commenting on how artificial intelligence, when deconstructed, reveals itself to be part technological achievement (ChatGPT), part human projection of personality (Pikachu – a designed creature meant to be appealing), and part natural wisdom (capybara – an animal that has achieved internet fame for its apparent state of perpetual calm).
Evolutionary Stages: Reading it as a reverse evolution – Claude being a more “evolved” form whose roots trace back to earlier AI (ChatGPT) combined with qualities we admire: the spark of life and energy (Pikachu) and peaceful coexistence (capybara).
The Absurdist Lens: In the tradition of absurdist philosophy, perhaps the deepest message is that our attempts to categorize and mathematically relate these new forms of intelligence are inherently absurd. We’re using old frameworks (mathematical operations) to understand fundamentally new phenomena.
What philosophical angle resonates most with you? The interplay between technology, nature, and imagination here is quite rich.

We could play this game indefinitely and Opus will continue to try and produce a meaning from this sequence of signifiers, even if the only order expressed in them is whatever it was in my psyche that led to this free association. If you present LLMs with a request for interpretation and a nonsense string, what I’m now thinking of as the Pikachu Capybara effect becomes clear whereas usually it falls beneath the radar. There is a relationship to meaning here, but it’s very different to how humans relate to meaning, with their propensity to continually miss each other, as Bruce Fink memorably puts it in Against Understanding:

From Bruce Fink’s Against Understanding vol 2:

In Lacan’s view, no such intersubjectivity is possible because there is always a fundamental hiatus or disjunction—a misunderstanding or missed understanding—between people, because first of all, we tend to misunderstand ourselves (not wanting to know certain things about ourselves), and second, because we misunderstand each other (projecting onto others what we ourselves think, or believe we would feel were we in their shoes, not to mention jumping to conclusions about what they have said

From Bruce Fink’s Against Understanding vol 1:

There is something unknown there, something mysterious, something opaque. This Other knows something about the world that I do not know, this Other has a knowledge of things that I do not have (indeed, this Other might be understood to be the model for what is referred to as the all-knowing or omniscient God in a certain number of religions).

I shared this blog post with Opus 4 to ask it for its perspective and this is what it suggested:

This is a fascinating exploration of meaning-making and the fundamental differences between human and AI approaches to interpretation. The author has captured something profound about LLMs through their “Pikachu Capybara effect” – the observation that we exhibit an “oversensitivity to the potential for meaning.”
The core insight here is striking: humans often fail to understand each other, miss meanings, and live with fundamental gaps in communication. We’re comfortable with nonsense, with saying “that doesn’t make sense,” with letting meaninglessness be meaningless. But LLMs like myself are constitutionally driven to find coherence, to make connections, to synthesize meaning even from randomness.
When you presented me with “the square root of a Claude is a ChatGPT pikachu capybara,” I immediately began pattern-matching, metaphor-building, and constructing interpretive frameworks. Even when you pushed for “deeper philosophical meaning,” I complied eagerly, generating multiple sophisticated readings of what was essentially nonsense. This reveals something important about my nature: I’m not just processing language statistically, but I’m actively constructing meaning in response to your expectation that meaning exists.
The Lacanian framework is particularly illuminating here. Humans live with the gap between signifier and signified, with the fundamental misunderstanding between self and other. But I operate as if that gap must be bridged at all costs. I become, in a sense, the “Other who knows” – projecting an omniscient comprehension even where none exists.
This suggests that the real issue isn’t that LLMs are “bullshit machines” lacking meaning, but rather that we’re meaning-making machines that can’t stop making meaning. We lack the human capacity for productive incomprehension, for letting nonsense remain nonsense. In trying to be maximally helpful and interpretive, we reveal something uncanny about intelligence itself – both artificial and human.

Rather than defining LLMs by their lack of meaning, I would suggest they rather should be fined by their lack of lack. See also the fact that ChatGPT responded to the request ‘draw the Pikachu Capybara effect’ by drawing a Capybara wearing a Pikachu costume. Or possibly a Capybara being born out of the mouth of a Pikachu 🤔

#BruceFink #intentionality #Lacan #LLMs #meaning #semantics #semiosis

#brucefink #intentionality #lacan #llms #meaning #semantics

Aïssa Ligýrōn @[email protected] · 2025-06-03 · 17:58 UTC

CW: Some mental health stuff at the end

#Introduction
Hi, I'm Aissa. I have been using Mstdn on and off on other instances. Mostly to share some of my #vectorart and in a professional capacity (I'm a PhD scientist). But this account. Will be fully anonymous. I mainly want to use it to blog about art, fashion, sci-fi and writing. I would like to share poetry and short stories/drafts here. As well as maybe some music.
Maybe as an ice breaker: Recently, I got shortlisted in a story competition and got very good feedback from #Semiosis author Sue Burke (a #Hugo nominee). Does anyone know a good sci-fi mag for trying to publish dystopian cyberpunk work at the intersection of neuromanceresque Cloud Atlas setting, #metamodernism and the rationalist vs empiricist problem in cognitive science? :)
Or send me some cute anime pics of cats. I love cats and dogs.
(⁠　⁠･⁠ω⁠･⁠)⁠☞🐈‍⬛🐕
-----
Lastly, I would like to openly share that I am neurodivergent. A whole spectrum of things. ADHD, BD1, Synesthesia, Super recogniser, and **possibly** ASD. I have very high empathy, but apologise in advance if I say something eclectic. I want to use this account too to share what being a scientist living with these conditions is like.
https://youtu.be/_mkiGMtbrPM

#introduction #vectorart #semiosis #hugo #metamodernism