Triadomania

Many of us new to the details of C.S. Peirce’s sign categories find them difficult to define, identify, remember, recall and use. As Miss Brodie said of the use of the quarter hour, I refuse to be intimidated by Peirce’s fine semiological distinctions.

I’m assuming Peirce’s system constitutes a kind of brain trainer, the understanding of which improves the mind and constitutes a bit of “theory” for writers, artists and designers — something to give weight to practices that we undertake anyway without recourse to theory. Indeed, Peirce’s system appears as something to be taught and learned even for its own sake. Peirce implies as much:

“It is a  nice problem to say to what class a given sign belongs; since all the circumstances of the case have to be considered. But it is seldom requisite to be very accurate; for if one does not locate the sign precisely, one will easily come near enough to its character for any ordinary purpose of logic” (297).

Wrestling with Peirce’s sign categories reminds me of the journey of the ethics scholar or liberal theologian. It’s the process you go though to reconcile difficult categories, contradictions and incommensurables (e.g. the holy trinity) that provides the benefit.

Ten classes of sign

Especially in its extended form Peirce’s system looks something like the Periodic Table in chemistry. It has interesting internal symmetries, but provides nothing like the utility of the Periodic Table in predicting the behaviour of its elements.

The geometry of Peirce’s ten classes of sign diagram rewards further examination. As I said in my previous post, you don’t even have to know what these terms mean to grasp the cunning symmetry of this geometry. I have redrawn his ten sign diagram here to amplify three points he asserts about its internal relationships.

• The numbered squares are displayed here such that those joined by a thick grey line are alike in two respects, i.e. they share two terms. Those squares joined by a thin black line are alike in only one respect.
• The three apexes of the triangle (top left, top right and the bottom) have no terms in common with the squares on the opposite side of the triangle. They are diametrically opposed categories.
• In his original version of the diagram, there are terms in the squares that are in a lighter font. I’ve reproduced that distinction in the diagram below. Peirce says these lighter terms are superfluous and can be discarded as you don’t need them to discriminate between the squares. So it is sufficient to label the bottom square a Dicent Sinsign, as there is no other square with those two terms. On the other hand, the central square needs to retain its three terms (Rhematic Indexical Legisign) as there are other sign categories around it that share two of its terms.

The central sign category (number 6) acts as a kind of pivot. In fact, a rhematic indexical legisign is a sign as generally understood independently of Peirce’s schema. The word “that,” known as an indexical or a demonstrative pronoun in grammar, provides a good example, as does any other means of deliberately pointing something out — with a finger for example.

The “legisign” term in the category description reminds us that there is some convention to the method of pointing. Like terms in language, it has to be learned. There is nothing in the word “that” hinting at what we are referring to. I don’t think Peirce brings this out, but the other categories seem to orbit around that basic linguistic sign category.

Unpacking the sign class list

Here is a further explanation of the sign categories, numbered in the order Peirce discusses them, and derived from his account and that of commentators.

1. Qualisign: simply a quality, … too heavy, hot, disgusting, red, bright red, too red, not red enough. A paint colour swatch is an obvious example of a sign. It indicates what you will find if you buy a particular tin of paint. As Atkin (p.143) points out, it is not the shape of the swatch, or the kind of paper it is printed on that makes the swatch act as a sign, but the colour, as a quality. So a qualisign is that aspect of a particular sign that delivers the information irrespective of the medium in which it appears.
2. Iconic Sinsign: A good example of this is a diagram, drawing or painting. The sign resembles in some way the object to which it draws attention. This type of sign is a one-off. The floor plan I have just drawn is of a particular building. A map of Edinburgh functions as a sign of that particular place.
3. Rhematic Indexical Sinsign: a raw, spontaneous cry that does not belong to any particular language convention, such as the cry of a baby, a shriek of pain, a laugh.
4. Dicent Sinsign: though the term “index” is omitted from this category, it refers to Peirce’s original description of an index. It is a sign that emanates from its object, as smoke does from fire, and is therefore a sign of fire. We may also say that the dicent sinsign is caused by its object, as smoke is caused by fire. In this we would also say that the sign does not resemble its object. Smoke does not look or feel like fire. In a previous post I also placed an explosion within this category.
5. Iconic Legisign: this is a generalised diagram that does not belong to any particular instance. So Peirce’s ten classes of sign diagram is an iconic legisign, as is a generic typological floor plan diagram of the kind found in Durand’s neo-classical catalogues of floor plans that don’t belong to any building in particular.
6. Rhematic Indexical Legisign: this is a demonstrative pronoun as described above (this, that, these, etc).
7. Dicent Indexical Legisign: this is simple statement that delivers information about the object it references. So a cry from someone selling goods at a market or from a street vendor is this kind of sign.
8. Rhematic Symbol: a common noun (house, car, tree) would be such a sign. It’s an arbitrary reference to its object decided by convention in language.
9. Dicent Symbol: this is an assertion that claims some ground in being true, i.e. something that exists, or at least can be tested: the sky is blue, it sometimes snows in December, lithium atoms have 3 electrons.
10. Argument: This is a rule of inference: if there are no clouds then the sky will be blue; all dogs are mammals; when the swallows fly high the weather will be dry; do not park on a double yellow line or you will be fined. Unfortunately an argument is also a term in an equation or predicate in formal logic. Peirce means “argument” in the sense of what gets passed around in spirited conversation: e.g. what is your argument? To avoid (or contribute to) this confusion Peirce also described this sign category as a delome (not in the OED).

Triophilia

Peirce’s complicated categorisation system is sandwiched between two propositions. One is his desire to show how wrong Rene Descartes was in asserting that reason can proceed in our minds independently of the world around us. For Peirce, thought involves signs, and signs are everywhere in the world. The second is to set the stage for his innovative discussion of logic.

As with any iconic legisign (generic diagram) it is tempting for someone whose sense of logic has been contaminated by the philosophy of deconstruction to look for the interstices in such a schema, the bits left out, and the priorities it conceals.

Unfortunately Derrida said little about Peirce’s philosophy, which does contain assertions about the relationship between speech and writing. It also comes under the charge of being overtly metaphysical — a grounded theory of everything. On the other hand, Peirce refers to how every sign seems to trace back to another sign, and other signs follow, ad infinitum.

From a design point of view I’m drawn to the seductive and obsessive nature of Peirce’s diagram (iconic legisign) and its triangulated (triadic) construction. For a discussion of triadomania and triadomany see the book by C.W. Spinks — which requires closer investigation.

References

• Atkin, A. (2016), Peirce, Abingdon, Oxon: Routledge.
• Spinks, C. W. (1991), Peirce and Triadomania: A Walk in the Semiotic Wilderness, Berlin: Walter de Gruyter.
• Peirce, C. S. (1992), ‘Nomenclature and Divisions of Triadic Relations, as Far as They Are Determined’, The Essential Peirce, Selected Philosophical Writings Volume 2 (1893-1913): 289-99, Bloomington, IN: Indiana University Press.