Sign Relations

[Jon Awbrey]

Greetings All,
I've been upgrading the formats and graphics of the more
often resorted to resources I've put on the web over the
years and I'll be hammering away at that into the future.

The various MediaWiki sites where I put copies of this work
are apparently going through some kind of transition as far
their math formatting goes, all of them in different stages
of change. As things stand, it looks like the Wikiversity
formatting is slightly improved over the others … for now.

Regards,
JonL

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

[Jon Awbrey]

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

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

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/

Regards,

Jon

cc: https://www.academia.edu/community/Vj32R6
cc: https://www.researchgate.net/post/Sign_Relations_First_Elements
cc: https://stream.syscoi.com/2025/12/15/sign-relations-definition/