## Sign Relations, Triadic Relations, Relation Theory • Discussion 10

Continuing a discussion on the generative power of symbols (1) (2) (3).

If it’s true what I say about symbols being the genus of all signs then it must be possible to say what differentia are added to the genus in order to generate every subtended species, beginning with icons and indices.

Turning first to icons, we have the following from Peirce.

In the first place there are likenesses or copies — such as statues, pictures, emblems, hieroglyphics, and the like.  Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters.  The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less;  for they stand for whatever they resemble and they resemble everything more or less.  (Peirce 1866, Lecture 7, 467).

Let’s say we look inside a triadic sign relation $L \subseteq O \times S \times I$ and we notice a triple $(o, s, i)$ where $o$ and $s$ have a character $\chi$ in common.  We may quite naturally be tempted to make a further leap and suppose the sign $s$ receives the interpretant sign $i$ precisely by virtue of the character $\chi$ shared by $o$ and $s.$  I know that looks like a lot of supposing but the fact is we do the like all the time without hardly giving it a second thought.  But critical reflection demands we bat an $i$ and give it second and third thoughts.

The catch is tucked away in Peirce’s last sentence.  “The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less;  for they stand for whatever they resemble and they resemble everything more or less.”

There may be a lot of characters shared by $o$ and $s$ in a given environment or universe of discourse, any selection of which may account for the linking of $o$ and $s$ to $i.$  As long as we remain content to operate in a theoretical vacuum devoid of empirical grounding, who’s to say any number of them do not qualify?

But a question arises when we use a sign relation $L$ to model an empirical system of interpretive practice, whether its agent is a single individual or a whole community of interpretation.  The question is — Do the characters we mark as effective in our model actually do the job for the agent?

An icon denotes its objects by virtue of qualities it shares with its objects.  But icons are icons solely because they are interpreted as icons, by dint of particular qualities chosen from many by the very process of interpretation in view.  This gives us a glimmer of the interpretive character of sign typing, that sign typologies are not absolute but relative to the sign relation at hand.  To paraphrase William James — The trail of the hermeneutic serpent is over all.

### Reference

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, in Writings of Charles S. Peirce : A Chronological Edition, Volume 1 (1857–1866), Peirce Edition Project, Indiana University Press, Bloomington and Indianapolis, IN, 1982.  Lowell Lectures of 1866, 357–504.

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