Sum Individuals and Proportion Problem

Abstract

This paper proposes that the so-called proportion problem, which was observed in Kadmon (1987, 1990) as a problem to the analyses of Kamp (1981) and Heim (1982), can be overcome by adopting the notion of 'sum individuals.' It will be suggested that given a donkey sentence with an asymmetric reading, a set of sum individuals of the 'dependent' variable is computed and this is introduced to the antecedent level as a variable of sum individuals. In this way, we can make the dependent variable accessible from the consequent level and avoid the proportion problem. In addition, it will be shown that the process of computing the sum individuals is necessary in order to explain the existence of weak and strong readings of quantified sentences.