The Periodic Table
The Periodic Table of Classes of Signs
The sixty-six classes of signs can be arranged in a triangular chart having the categories (firstness, secondness and thirdness) as vertexes. The black windows or “holes” correspond to the classes eliminated by the rule of the razor of causality.
The arrows correspond to the logical relation of illation or material implication. The arrows that go from 1 to 2 correspond to the four periods of semeiosis: grounding, presentation, representation and communication. As a corollary, presentation involves grounding, representation involves the first two and communication involves all the other three.
The arrows going from 2 to 3, which we know indicate generalization, here also correspond to the four phases or stages of inquiry: perceptive, inquisitive, deliberative and scientific. This means that all knowledge begins with perception, that deliberation demands both perception and inquisition and the scientific method is a generalization of the previous ones.
A handful of vagueness
Peirce’s categoriology, with its predicaments and relations of uncertainty, forms the continuous substratum that allows the action of sign. Therefore, semeiosis should also be considered as a continuous phenomenon subject to the same relations of uncertainty, although also describable through general classes capable of grouping the signs according to their most remarkable features. As Mihai Nadin affirms (1983, p.163):
The typology of the sign classes (the ten, the 28, the 66), as confirmed by the mathematical theory of categories should be understood as a network of fundamental reference points in the generalized semeiotic field. Whenever this typology is transformed into an end in itself, it leads only to formalistic semeiotics. To give a name to a sign (to identify it) does not solve the problem of the way it functions in the semeiotic field. The sign can be conceived and interpreted only within the framework of the logic of vagueness and with the participation of the doctrine of the continuum. Fuzzy categories, the extension of the mathematical concept of category, fulfill this desideratum and perfect Peirce’s table of fundamental signs by realizing the image of the continuum, hence also the dynamics of sign processes.