Collective signs and generality in the trichotomy of the dynamic object in Charles S. Peirce’s semiotics

Abstract

According to Peirce, generality has a distributive character, that is, the character of a law that can be applied to anything that may exist in a class, without asserting whether there is anything or what that thing is, but providing a description of how the individuals of that class should be selected (EP 2:284, 1903). Rodrigues (2017) asserts that Peirce does not regard the generality expressed in universal quantifiers as having a collective character, in the sense of signifying a particular singular group, a given collection. In 1905, Peirce (EP 2:352-353) stated that “a collective term is singular, since it denotes a given group and a given collection”. In 1908, however, Peirce used the term “collective” to describe the class of signs that have a dynamic object of thirdness, which is the category of generality. But he also employs the term “distributive” to describe the class of signs that have an immediate object of thirdness. Thus, in his descriptions of the ten trichotomies, the terms “collective” and “distributive” are used when Peirce wants to describe the mode of being of thirdness, i.e., that of generality. Although Peirce denied that generality has a collective character in the case of logical quantifiers, he considered using the term “collective” to describe the generality of dynamic objects. Consequently, it is necessary to discuss the meaning of the term “collective” when applied to thirdness in the trichotomy of the dynamic object. This is precisely the purpose of this article, which begins by presenting the problem of using this terminology in semiotics and the notions of collective and distributive in semantics and philosophy. Then, it shows how the terms appear in the texts in which Peirce conceives the ten trichotomies and focuses on the use of the term “collective” in two letters, one to William James, from 1909, and the other to the English logician P. E. B. Jourdain, from 1908. Starting from those two letters, we present the relationship between the term “collective” and the notion of continuity that culminates in the distinction between finite and enumerable collections and infinite and innumerable collections, suggesting that the notion of collective in the dynamic object has the meaning of an infinite and innumerable collection, associating the notion of dynamic object with the notion of continuum.