The Semeiotic of Three Correlates
The categories and their degenerations, once applied to logic, enabled Peirce to build his first classificatory system upon three correlates, delivered to the audience of the lectures that he gave at the Lowell Institute, in 1903, and printed in the Syllabus.
Between 1902 and 1903, in the same period Peirce intensified his studies about perception, he understood that a complete description of the sign should take into account not only its representative and interpretative phases, but also the material or presentative ones too. Something is a sign only if it is interpreted as such by something or someone. This is the presentative dimension that, added to the other two, will form the three correlates of the 1903 3-trichotomic classification (based on three trichotomies):
The relations among the three correlates can be represented by Peirce’s symbol of illation enchaining the three of them: 1C -< 2C -< 3C.
The Table of the Ten Classes of Signs
The crossing of the three ontological categories (firstness, secondness and thirdness), with three correlates of the sign (1C, 2C and 3C), produces the following table of signs (the terminology is the same used by Peirce in 1903):
|Categories||First Correlate (S)||Second Correlate (S-DO)||Third Correlate (S-DO-I)|
Having this list of nine genuine types of signs (that is, signs without any degeneration) in hand, we can relate the three correlates using the same rule of material implication we already discussed when we saw the universal predicaments.
By the principle of the nota notae, the third correlate can be a quality in any situation, for this predicament is always present in all three correlates, whether in its pure form or involved in existence or law. The third correlate can be an existent only if the two others are at least existents too. And it can be a law only if the two others are necessarily laws. Similar restrictions occur between the first and second correlates.
When we apply this rule to explore the possible combinations among the genuine types of signs distributed in the three correlates, we have the formation of ten genuine classes of signs:
The ten genuine classes of signs can be arranged triangularly to form the famous figure Peirce made of them in the Syllabus.
The arrows that go from 1 to 2 and from 2 to 3 fulfill the same functions we saw in the discussion about the predicaments: involvement and abstraction when the movement is crescent; and instantiation and dissolution when the movement is the inverse.
The degeneration of the types of signs
As we did when deriving six universal predicaments from the three categories, we now apply the notation of an apostrophe (’) to indicate one degree of degeneration, and two apostrophes (”) to indicate double degeneration. A genuine secondness can degenerate in firstness of secondness (1’) and a genuine thirdness can degenerate either in a secondness of thirdness (2’) or in a firstness of thirdness (1”).
In the table below, I present the genuine signs and their possible ontological degenerations the way I conceive them:
|First Correlate||Second Correlate||Third Correlate|
|Firstness of the secondness (1’)||altersign||eidoseme||syntax|
|Firstness of thirdness (1”)||holosign||metaphor||abduction|
|Secondness of thirdness (2’)||replica||metonymy||induction|
Some of the terms above, as syntax, metaphor and eidoseme were created or discussed by Peirce in his articles and manuscripts. In this case, my concern was to try to respect the meaning intended by Peirce, although using it in favor of the theoretical board that I am assembling. Metonymy has an already established meaning in semeiotic and theory of language, pairing with metaphor—which is what I find interesting and promising for the research on the relations between semeiotic and cognitive sciences in general. Altersign and holosign are my introductions. They were made, however, trying to respect the rule of composition adopted by Peirce when inventing qualisign, sinsign and legisign, in which the prefix denotes the main property of each type of sign.
The Periodic Table of 66 Classes of Signs
If we apply the principle of material implication among the correlates (1C-<2C-<3C), taking into account the types of genuine and degenerated signs that we have described before, we get as a result the arrangement of 66 classes of signs.
In our Semeiotic Wheel, we cross Goethe’s theory of colors and Peirce’s theory of categories to build a moving disk where the sixty-six classes of signs follow naturally from the logic described above.
These sixty-six classes of signs can be arranged into a triangular figure that preserves the same relations of involvement and generalization of the ten classes of genuine signs. Actually, the triangle is clearly an expansion from the triangle presented by Peirce in the Syllabus and discussed at the beginning of this page. In fact, the genuine signs appear distributed throughout the triangle of the sixty-six classes maintaining the same logical relations of implication and involvement they have in the 10-class triangle.
The twelve voids, represented by black holes, appear by a mathematical necessity linked to the number of possible degenerations in each of the three vertexes: the pole of thirdness may degenerate twice, the one of secondness just once and the one of firstness does not suffer any degeneration.
A similar feature can be seen in Cartesian geometry. World map charters face it when they struggle to represent the surface of the Earth (a three-dimensional object) on a bi-dimensional sheet of paper: they must choose between distorting the representation of the territories closer to the poles or, otherwise, leaving empty spaces, as we did.