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Peirce’s categories

Our first steps on the way to the solution of the enigma of the 66 classes of signs, still in the entrance of the labyrinth of semeiotic, must cross phenomenology or, using the term invented by Peirce, phaneroscopy. He defines it as:

that study which, supported by the direct observation of phanerons and generalizing its observations, signalizes several very broad classes of phanerons; describes the features of each; shows that although they are so inextricably mixed together that no one can be isolated, yet it is manifest that their characters are quite disparate; then proves, beyond question, that a certain very short list comprises all of these broadest categories of phanerons there are; and finally proceeds to the laborious and difficult task of enumerating the principal subdivisions of those categories (CP 1.286)

Peirce starts this task taking into account the two most influential lists of categories in the history of philosophy: Aristotle’s, with its table of ten predicates, and Kant’s, which enumerated twelve basic categories. Peirce noticed that these two lists shared a similar internal pattern: they always suggested triadic ramifications among their elements. This insight was enough for him to develop his fundamental list of three categories, which in the “New List” are called quality, relation and representation.

In the following figure, we present Peirce’s first list of categories in a triangular scheme, which allows us to visualize the relations among them.

Peirce's Triangular Scheme

Peirce tried other words to summarize his categories, but remained unsatisfied because none seemed to be able to capture the deepness of their meaning. On the contrary, the choice of terms from common language or extracted from classic Greek or Latin vocabulary only worsened the confusion because they sometimes carried along meanings that had little to do with those he wished to express. In order to prevent contamination of his three categories with the rancidity accumulated by the philosophical terms of the past, Peirce resorted to mathematics. He finally decided to call them firstness, secondness and thirdness and made a great effort to prove that they were universal, complete and irreducible (CP 8.328; 6.342-343).

The categories and their degenerations

Peirce’s first formulation of the categories was born under the aegis of his juvenile nominalism. When he started his way towards realism, he felt the necessity of revising them. That happened in 1885, when in the article “One, Two, Three: Fundamental Categories of Thought and of Nature” Peirce presented his categories no longer using the traditional logic of subject and predicate, but from the point of view of the logic of relations (Murphey, 1993, p.303).

The result of his continuing research on the essence of the categories debuted, in 1903, on the third conference he gave in Harvard in April 1903, “The Categories Continued”, when Peirce introduced the concept of degeneration of the relations. He was then convinced that the more complex categories (secondness and thirdness) could suffer what he called degeneration: a reduction of their ontological state. Thus, while firstness cannot suffer degeneration, secondness can degenerate towards firstness; thirdness, in its turn, can suffer two degrees of degeneration, becoming initially secondness and, in a subsequent degeneration, firstness. When not degenerated, the categories are called genuine (CP 5.66).

The resulting six divisions are:

Firstness

Firstness of secondness

Firstness of thirdness

Secondness

Secondness of thirdness

Thirdness

During the fourth of his conferences in Harvard, “The Seven Systems of Metaphysics, Peirce presented the diagram below, showing the possible ways of combining the categories and their degenerations and how each combination originates a different philosophic system. In this figure drawn by Peirce, each category is represented by a correspondent number of traces (cf. EP:180):

Categories and Degenerations

From the Categories to the Predicaments

In another version of Peirce’s original diagram, a little modified, it is possible to notice more clearly how the categories and their degenerations relate to one another. We have created a specific notation to facilitate its visualization: we will use an apostrophe (’) to indicate one degree of degeneration and two apostrophes (”) to indicate two degrees of degeneration. The three fundamental categories occupy the central hexagon of the figure, but their expansion (through degenerations) intersperses their own degenerated stages among themselves, as it can be seen in the figure below:

Categories

The more intermal part of the figure corresponds to the three cenopitagoric categories as they really appear in the phaneron. By maintaining the term categories for the elements of the internal part, we will use predicaments for the more external ones, which include the categories and their degenerations. The predicaments can be thought of as rhemes or predicates that represent the fundamental categories for an interpretant mind. By mind we mean not only human minds nor minds of living beings, but the Peircean notion of mind as a property of the whole universe.

Universal predicaments

We claim that the categories and their degenerations can be arranged in a table of fundamental ontological properties, as we do below. Our choice of colors was inspired by Goethe’s theory of colors, which we found surprisingly close to Peirce’s ideas.

The categorical degenerations suggested by Peirce are neither marginal phenomena nor extravagant refinements of his metaphysics. On the contrary, they reveal what we will call “universal predicaments” that can be organized in a triangle as below:

Universal Predicaments

The arrows that go from 1 to 2, and then from 2 to 3, mean material implication or illation. This is the implicative movement that produces the most fundamental rule of logic, the guiding-principle that medieval logicians called nota notae, from the latim nota notae est nota rei ipsius or “the predicate of a predicate is also the predicate of the subject of the predicate” (Lizska, 1996, p.58). Peirce used several symbols to express this logical relation, but the one that seemed most appropriate to him was “-<” , certainly because it expresses an inequality useful to the numerical treatment he was applying to his categories.

The arrow that goes from 1 to 2, taken separately, means involvement, in such a way that we can say, applying the nota notae principle, that:

1) quality is involved in spontaneity
2) spontaneity is involved in individuality
3) quality is involved in individuality

The inversion in the direction of this arrow produces what we will call dissolution.

The arrow that goes from 2 to 3, taken separately, means abstraction, in such a way that we can say, applying once again the nota notae principle, that:

1) particularity is an abstraction from individuality
2) generality is an abstraction from particularity
3) generality is an abstraction from individuality

The inversion of the direction of this arrow produces instantiation.

The movement from 1 to 3 described by the arrows causes semeiosis to develop, in such a way that a state in which there is little variety of properties of few things develops continuously into a state of many properties involved in many things, generating increase of information. In fact, in 1893 Peirce affirmed that:

Analogous to increase of information in us, there is a phenomenon of nature–development–by which a multitude of things come to have a multitude of characters, which have been involved in few characters in few things (CP 2.419).

Uncertainty in the predicaments

The analysis of the diagram of the relations among the universal predicaments reveals that, apart from a clear general tendency towards the increase of information, there is a principle of uncertainty between conjugated pairs of predicaments, here algebraically expressed by the sign of multiplication. According to this principle, in any state of information there will always be an entanglement between opposed pairs of predicaments, in such a way that we will never be able to distill them into their pure forms. The correlation happens as the table below expresses:

CorrelationsThe relations above can be better represented in the following figure:

Correlates Relations

Let us explore a little more the meaning of this principle:

a) Quality x particularity

Quality is pure intensity and originality, but these characteristics will fade when appearing replicated. On the other hand, a Particular is a replication of a model, and qualitative variations disturb its aimed fidelity to the norm expressed by the model. An artist, for instance, a painter, uses a qualitative strategy, while the graphic technician responsible for reproducing the painting on a printed poster uses the replicative strategy. For the first one, the loss of originality decreases the value of his work whereas, for the second, the occurrence of originality in the copies is considered a mistake to be eliminated. In fact, since Benjamin (1980), much has been said about the relations between quality and particularity in the work of art submitted to processes of replication, which tend to consume, to a certain degree, its qualitative or original “aura”.

b) Chaos X order

Chaos and order are closely related (Prigogine, 1996), as well as their derivations in the form of spontaneity x necessity, irritation x habit. Although there is a teleological movement conducting the reality to the strengthening of law and to the crystallization of habit, the principle of uncertainty affirms that, in any given state of information, chaos and order appear in varied tinges, without ever allowing one to eliminate completely the other. There are neither laws so rigid that cannot suffer exceptions, nor such absolute chaos that does not contain in its interior a seed of order.

c) Individuality X holicity

An individual only exists as a fracture in the continuum, whereas the continuum only exists as the suppression of individuality. For this reason, one depends on the other. Actually, they co-exist so that every individual has idealized limits and every continuum can be thought of as an individual (cf. CP 4.172). The principle of uncertainty of Heisenberg and its derivations in the form of oppositions like particle x wave type, locality x non-locality, discrete universe x holographic universe seem to be born from this correlation.