CiteWeb id: 20160000056

CiteWeb score: 661

DOI: 10.1016/B978-0-12-545850-4.50014-5

of ordinary English." Taking as building bricks basic linguistic items of the categories proper name (prn), formula (fml), one-place verb (lvb), two-place verb (2vb), common noun (cmn), adformula (adf), adverb (adv) and adjective (adj)2, he gives rules for concatenation of these into non-basic items of the same categories and, in parallel, the recursive definition of denotations of non-basic items in terms of those of the basic ones. Let 'Dprn(a)' mean 'the denotation of a, taken as a proper name', and similarly 'Dfml(a)', 'Dlvb(a)' and so on. (This multiplicity of denotation-functions is necessary because a word may be meaningful in more than one category; for example 'orange' may be either a colour-adjective or a common noun denoting a fruit.) The denotation Dprn(a) of a proper name a is an individual; and the denotation Dfml(a) of a formula a is a proposition, in turn identified (as commonly in logic) with a set of possible universes. The denotations of items of other categories are functions; thus: the denotation Dlvb(a) of a one-place verb a is a function that maps individuals on to propositions. (The idea is that the denota tion of the one-place verb 'walks' is the function that maps the individual Mary on to the proposition that Mary walks, the in dividual Rover on to the proposition that Rover walks, and so on.) the denotation D2Vb(a) of a two-place (that is, transitive) verb a is a function that maps pairs of individuals on to propositions. (The two-place verb 'walks' maps the pair consisting of Mary and Rover on to the proposition that Mary walks Rover.)