The Logic of Vagueness and The Category of Synechism

In his article "Issues of Pragmaticism" published in 1905, in The Monist (vol. 15, pp. 481?99), Charles S. Peirce complains that "Logicians have been at fault in giving Vagueness the go-by, so far as not even to analyze it." That same year, occupying himself with the consequences of "Critical com monsensism," he affirmed, "I have worked out the logic of vagueness with something like completeness," a statement that causes the majority of the commentators on his work, including the editors of the Collected Papers1 to ask where this logic is to be found. The fever for finding Peirce's manuscripts is fed by the hope of some researchers of discovering the logic of vagueness, a hope that has grown since Carolyn Eisele's publication of his mathematical works. Others?and I count myself among them?believe that in reality this is a matter of something already known. That is, they interpret the affirma tion ending the paragraph of reproach addressed to logicians, "The present writer has done his best to work out the Stechiology (or Stoicheiology), Critic, and Methodeutik of the subject," (i.e., Vagueness) as a tripartite semiotic of the vague, still limited, according to Peirce's older works (1896, "Preface" to The Simplest Mathematics), to symbols, that is, to the signs of natural language examined from the perspective of logic. If Peirce could read how much is written today on the type of problems he had in mind when he used the term "vagueness," he would surely clarify himself. But at the same time, he would observe that in the place of a logic of the vague, more types of semantics of linguistic imprecision have developed that either ignore him as a possible predecessor?and not the least among the reasons for this would be, in addition to the unfortunate manner in which he was published, his vague mode of expression?or cite him inappropriately. In connection to all these problems, and especially in direct relation to this very theme, I intend the following: 1) to consider vagueness in connection to the general vision of Peirce's philosophy, examining the logic of vagueness a) in the context of the epoch and b) from the perspective of the present; 2) to explain vagueness in the context of the current semiotic tendency, that is, its epistemological and not gnoseological aspects, a problem of pragmatics and not semantics; 3) to attempt to establish the reciprocal relationship between the logic of vagueness and the category of the synechism (the principle of the continuum) and the way in which they lead to fuzzy types of logic.