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Feb 18, 2024, 10:54:14 AMFeb 18

to Conceptual Graphs, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Sign Relations, Triadic Relations, Relation Theory • 1

• http://inquiryintoinquiry.com/2024/02/18/sign-relations-triadic-relations-relation-theory-1-a/

All,

To understand how signs work in Peirce's theory of triadic sign relations,

or “semiotics”, we have to understand, in order of increasing generality,

sign relations, triadic relations, and relations in general, each as

conceived in Peirce's logic of relative terms and the corresponding

mathematics of relations.

Toward that understanding, here are the current versions of articles

I long ago contributed to Wikipedia and Wikiversity and continue to

develop at a number of other places.

Sign Relations

• https://oeis.org/wiki/Sign_relation

Triadic Relations

• https://oeis.org/wiki/Triadic_relation

Relation Theory

• https://oeis.org/wiki/Relation_theory

Regards,

Jon

cc: https://www.academia.edu/community/VqqE7g

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

• http://inquiryintoinquiry.com/2024/02/18/sign-relations-triadic-relations-relation-theory-1-a/

All,

To understand how signs work in Peirce's theory of triadic sign relations,

or “semiotics”, we have to understand, in order of increasing generality,

sign relations, triadic relations, and relations in general, each as

conceived in Peirce's logic of relative terms and the corresponding

mathematics of relations.

Toward that understanding, here are the current versions of articles

I long ago contributed to Wikipedia and Wikiversity and continue to

develop at a number of other places.

Sign Relations

• https://oeis.org/wiki/Sign_relation

Triadic Relations

• https://oeis.org/wiki/Triadic_relation

Relation Theory

• https://oeis.org/wiki/Relation_theory

Regards,

Jon

cc: https://www.academia.edu/community/VqqE7g

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

Feb 19, 2024, 2:40:22 PMFeb 19

to Conceptual Graphs, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Sign Relations, Triadic Relations, Relation Theory • 2

• https://inquiryintoinquiry.com/2024/02/19/sign-relations-triadic-relations-relation-theory-2/

All,

I always have trouble deciding whether to start with the genus

and drive down to the species or begin with concrete examples

and accompany Sisyphus up Mt. Abstraction.

To start at the wide end of the funnel, the following article takes up

relations in general, focusing on the discrete mathematical varieties

we find most useful in applications, for example, as background for

empirical data sets and relational data bases.

Relation Theory

• OEIS Wiki ( https://oeis.org/wiki/Relation_theory )

• Wikiversity ( https://en.wikiversity.org/wiki/Relation_theory )

Regards,

Jon

cc: https://www.academia.edu/community/l7je8O

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

• https://inquiryintoinquiry.com/2024/02/19/sign-relations-triadic-relations-relation-theory-2/

All,

I always have trouble deciding whether to start with the genus

and drive down to the species or begin with concrete examples

and accompany Sisyphus up Mt. Abstraction.

To start at the wide end of the funnel, the following article takes up

relations in general, focusing on the discrete mathematical varieties

we find most useful in applications, for example, as background for

empirical data sets and relational data bases.

Relation Theory

• OEIS Wiki ( https://oeis.org/wiki/Relation_theory )

• Wikiversity ( https://en.wikiversity.org/wiki/Relation_theory )

Regards,

Jon

cc: https://www.academia.edu/community/l7je8O

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

Feb 20, 2024, 5:32:11 PMFeb 20

to Conceptual Graphs, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Sign Relations, Triadic Relations, Relation Theory • 3

• https://inquiryintoinquiry.com/2024/02/20/sign-relations-triadic-relations-relation-theory-3/

All,

The middle ground between relations in general and the

class of sign relations we need for logic, inquiry, and

communication is occupied by triadic relations, also called

ternary or 3‑place relations.

Triadic relations are some of the most pervasive in mathematics,

over and above the importance of sign relations for logic.

For a primer on triadic relations, with examples from mathematics

and semiotics, see the article linked below.

Triadic Relations

• OEIS Wiki ( https://oeis.org/wiki/Triadic_relation )

• Wikiversity ( https://en.wikiversity.org/wiki/Triadic_relation )

Regards,

Jon

cc: https://www.academia.edu/community/lOaQqB

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

• https://inquiryintoinquiry.com/2024/02/20/sign-relations-triadic-relations-relation-theory-3/

All,

The middle ground between relations in general and the

class of sign relations we need for logic, inquiry, and

communication is occupied by triadic relations, also called

ternary or 3‑place relations.

Triadic relations are some of the most pervasive in mathematics,

over and above the importance of sign relations for logic.

For a primer on triadic relations, with examples from mathematics

and semiotics, see the article linked below.

Triadic Relations

• OEIS Wiki ( https://oeis.org/wiki/Triadic_relation )

• Wikiversity ( https://en.wikiversity.org/wiki/Triadic_relation )

Regards,

Jon

cc: https://www.academia.edu/community/lOaQqB

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

Feb 22, 2024, 2:15:36 PMFeb 22

to Conceptual Graphs, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Sign Relations, Triadic Relations, Relation Theory • 4

• https://inquiryintoinquiry.com/2024/02/22/sign-relations-triadic-relations-relation-theory-4/

All,

For ease of reference, here are two variants of Peirce's

1902 definition of a sign, which he gives in the process

of defining logic.

Selections from C.S. Peirce, “Carnegie Application” (1902)

❝No. 12. On the Definition of Logic❞

❝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.❞ (NEM 4, 20–21).

❝No. 12. On the Definition of Logic❞ [Earlier Draft]

❝Logic is formal semiotic. A sign is something, A, which brings

something, B, its interpretant sign, determined or created by it,

into the same sort of correspondence (or a lower implied sort) with

something, C, its object, as that in which itself stands to C.

❝This definition no more involves any reference to human thought than does

the definition of a line as the place within which a particle lies during

a lapse of time. It is from this definition that I deduce the principles

of logic by mathematical reasoning, and by mathematical reasoning that,

I aver, will support criticism of Weierstrassian severity, and that is

perfectly evident. The word “formal” in the definition is also defined.❞

(NEM 4, 54).

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 ( https://cspeirce.com/menu/library/bycsp/l75/l75.htm )

Regards,

Jon

cc: https://www.academia.edu/community/5wovoK

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

• https://inquiryintoinquiry.com/2024/02/22/sign-relations-triadic-relations-relation-theory-4/

All,

For ease of reference, here are two variants of Peirce's

1902 definition of a sign, which he gives in the process

of defining logic.

Selections from C.S. Peirce, “Carnegie Application” (1902)

❝No. 12. On the Definition of Logic❞

❝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.❞ (NEM 4, 20–21).

❝No. 12. On the Definition of Logic❞ [Earlier Draft]

❝Logic is formal semiotic. A sign is something, A, which brings

something, B, its interpretant sign, determined or created by it,

into the same sort of correspondence (or a lower implied sort) with

something, C, its object, as that in which itself stands to C.

❝This definition no more involves any reference to human thought than does

the definition of a line as the place within which a particle lies during

a lapse of time. It is from this definition that I deduce the principles

of logic by mathematical reasoning, and by mathematical reasoning that,

I aver, will support criticism of Weierstrassian severity, and that is

perfectly evident. The word “formal” in the definition is also defined.❞

(NEM 4, 54).

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 ( https://cspeirce.com/menu/library/bycsp/l75/l75.htm )

Regards,

Jon

cc: https://www.academia.edu/community/5wovoK

cc: https://mathstodon.xyz/@Inquiry/111953119107815922

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