Let’s start as simply as possible. The following figure is typical of many I have used to illustrate sign relations from the time I first began studying Peirce’s theory of signs.
Figure 2. An Elementary Sign Relation
As the drafter of that drawing I can speak with authority about the artist’s intentions in drawing it and also about the conventions of interpretation that formed the matrix of its gestation and delivery.
Just by way of refreshing my own memory, here is how we set it up:
Figure 2 represents an “elementary sign relation”. It is a single transaction that takes place among three entities, the object o, the sign s, and the interpretant i, and it is usually represented by means of the ordered triple (o, s, i).
One of the interpretive conventions implied in that sort of setup is a very old one indeed. It goes back to the earliest styles of presentation in mathematics. Namely, one draws a figure that is intended as “representative” of many figures. Being drawn as it must be, the figure is imperfect, individual, peculiar, special, but it is intended to be taken as a representative of its class: generic, ideal, typical. That is the main convention of interpretation that goes into giving diagrams and figures their significant power.