The catenation and tensive structures as patterns for the semiotic square

Abstract

The aim of this article: to explore a suggestion of Zilberberg in an en passant speculation, when he proposes that “the categorical presupposes the progressive, that establishes the first one” and that “the categorical is reached by the suspension of the catenary terms and conservation of the extreme terms” (1981, p. 10). Catenary – from the Latin catena [chain] – is defined in dictionaries as a curve in which hangs, under the influence of their own weight, a thread suspended by the extremities. This geometric figure allows to “reflect” the tensive gradient – the figure of the letter L, with intensive vertical axis and extensive horizontal axis – coupled to its mirror (an inverted L), a second intensive and extensive axis. The first L would respond by the “tonicity” (in the intensive verticality) and its “degradation” (in the horizontal horizontality) of the first term (S1); the inverted L would respond by the tonicity and degradation of the second term (S2). In short, the tensive gradient is doubled to accommodate the two categorical terms of the semiotic square, which thus becomes tensive (or “tensivises”).