Sign Relations, Triadic Relations, Relation Theory

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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

[Jon Awbrey]

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

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