ASSERTIONS ARE A SYMBOLIC FORM that exists only within species-specifically human language. Language, of course, allows for many other conventions of symbolic expression: greetings, exclamations, commands, exhortations, imprecations, interrogatives, and so forth. But assertions are unique in possessing, of themselves, a truth-value--that is to say, in being adjudicable as true or false. All other varieties of discourse are adjudicable as true or false by reason of assertions they presuppose, contain, or imply. But the assertion as such is what is directly so adjudicable.
A. Choosing Terminology: New Bottles for Old Wine. An assertion, in traditional logic, is commonly called a "proposition." The status of the proposition as such, as distinct from its particular linguistic expression, has led to many debates over the centuries. Among recent philosophers who call themselves "linguistic," some have preferred to speak rather of "statements" or "sentences" ("sentences in the indicative mood," "declarative sentences with tenseless verbs," and so forth(1)) than propositions, in order to evade debate over the objective status of propositions. But this preference amounts to little more than a verbal dodge. The irreducible fact is that, whatever it be called, there is a unit of discourse which of itself is adjudicable as true or false; and this unit, whatever it be called, is the focal point of logical concern--both as to what are the linguistic factors necessary to constitute it, and as to what are the further linguistic constructs that can be made from it in the line of truth and falsity--when we say of a position that it is incomplete, inconsistent, "full of holes," well-reasoned, and so on.
It is important to note that although some linguistic units of discourse are adjudicable as true or false, these linguistic units are far from the only elements of our experience that exhibit that quality. While debates among logicians, particularly within the framework of so-called linguistic philosophy, have been cast in a decidedly glottocentric mold over the past fifty years, introduction of the semiotic point of view into the debate immediately indicates ways of breaking this mold and giving new life to the concerns of logic, which was originally conceived as providing an interpretive instrument useful across the range of human concerns, at least insofar as these concerns involve or are brought to expression in the peculiar symbolic form of linguistic discourse.
As in so many other areas of semiotic inquiry, the principal clues in this area of "logical language," so to say, have been provided by the seminal work of Charles Sanders Peirce, the first, and so far the only, logician who attempted to rethink the concerns of logical tradition from the perspective of the sign. It is true that a long line of Latin philosophers, in the Iberian world of Renaissance times particularly, from Domingo de Soto(2) to John Poinsot(3) and Comas del Brugar,(4) explicitly recognized well before Peirce that the doctrine of signs provides the foundation for any inquiry, including inquiry within logic. Before Peirce, however, no one attempted to rebuild the whole logical edifice, so to speak, with an eye to demonstrating at each step the reliance on semiotic foundations.
New ways of thinking require, inevitably, new ways of speaking. Thus, among Peirce's first moves toward reconstituting logic as semiotic was the attempt to settle upon a suitable vocabulary. Having already in play the basic trichotomy of sign as icon, index, and symbol, with species-specifically human language located as a principally symbolic function, Peirce soon proposed a trichotomic subdivision of symbols specifically applicable to the concerns of logic. The centerpiece in this subdivision was what Peirce called the "dicisign," that is, a sign which "says something" (from the Latin dicere, to speak or to say), which makes an assertion, and by so doing conveys information in the manner adjudicable as true or false. …