LANGUAGE I express the same thought as if on December I say ‘It is snowing today’ It was left to logicians of a later generation to try to incorporate such complications into formal systems The Pragmatists on Language and Truth Charles Sanders Peirce, who had developed quantificational theory independently of Frege, likewise expressed, in a different terminology, many of Frege’s insights into philosophy of language Both philosophers rejected the traditional way of distinguishing between subject and predicate, and analysed propositions into elements of two kinds, one a complete symbol (the arguments in Frege’s Begriffsschrift) and the other an incomplete, or unsaturated, symbol (the functions of Begriffsschrift) The proper names that Frege called ‘arguments’ Peirce called ‘indices’, and Frege’s concept expressions or functions were called by Peirce ‘icons’ For Peirce a particularly important class of icons was expressions for relations ‘In the statement of a relationship,’ he wrote, ‘the designations of the correlates ought to be considered as so many logical subjects and the relative itself as the predicate.’ In his treatment of sentences concerning two-place relationships such as ‘John loves Mary’ Peirce differed little from Frege However, he extended the notion of relationship in two directions, by considering what he called the ‘valency’ (i.e the number of arguments) of different relations He was interested in particular in three-place relationships (such as ‘John gave Fido to Mary’); and in addition to ‘polyadic’ relationships with two or more subjects, he introduced the term ‘monadic relationship’ for ordinary one-place predicates such as ‘ is wise’ He was even willing to call a complete proposition a ‘medadic relation’—that is, a relative proposition with zero (in Greek meden) unsaturated places Peirce’s logic and theory of language was embedded in a general theory of signs, which he called ‘semiotics’, and to which he attached great importance A sign stands for an object by being understood or interpreted by an intelligent being; the interpretation is itself a further sign Peirce calls the external sign a ‘representamen’ and the sign as understood ‘the interpretant’ The semiotic function of signs is a triadic relation between representamen, object, and interpretant 126