In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals (...) of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided. (shrink)

To what extent are countability distinctions subject to systematic semantic variation? Could there be a language with no countability distinctions—in particular, one where all nouns are count? I argue that the answer is no: even in a language where all NPs have the core morphosyntactic properties of English count NPs, such as combining with numerals directly and showing singular/plural contrasts, countability distinctions still emerge on close inspection. I divide these distinctions into those related to sums and those related to parts. (...) In the Sahaptian language Nez Perce, evidence can be found for both types of distinction, in spite of the absence of anything like a traditional mass–count division in noun morphosyntax. I propose an extension of the Nez Perce analysis to Yudja, analyzed by Lima as lacking any countability distinctions. More generally, I suggest that at least one countability distinction may be universal and that languages without any countability distinctions may be unlearnable. (shrink)

English mass noun phrases & count noun phrases differ only minimally grammatically. The basis for the difference is ascribed to a difference in the features +/-CT. These features serve the morphosyntactic function of determining the available options for the assigment of grammatical number, itself determined by the features +/-PL: +CT places no restriction on the available options, while -CT, in the unmarked case, restricts the available options to -PL. They also serve the semantic function of determining the sort of denotation (...) associated with demonstrative & quantified noun phrases. The feature -CT requires that the associated denotation be the set whose sole member is the greatest aggregate of which the noun phrase or noun is true; the feature +CT requires that the associated denotation be the set whose members are all & only those minimal aggregates of which the noun phrase or noun is true. At the same time, neither mass NPs nor count NPs that are arguments of a predicate have their predicate evaluated with respect to their denotations. Rather, the predicate is evaluated with respect to an aggregation, a set of aggregates constructed from the denotation of the noun phrase that is an argument of the predicate. 3 Tables, 4 Figures, 74 References. AA. (shrink)