The problem of the many: a view from the semantics of numerals and countability

This paper addresses both semantic issues of countability in linguistics, and philosophical issues arising from the problem of the many. I argue (i) that the problem of the many is orthogonal to vagueness and we should look to the semantics of count nouns and numerals for its solution; (ii) that the problem of the many is a challenge for contemporary mereological analyses of count nouns in semantics; but (iii) that the count criterion in these theories can be weakened to avoid the problem. Specifically, weak quantization is proposed as the criterion: a sum, x, counts as n Ps if and only if x has n disjoint parts, each of which is in the extension of P, but where the sum of no two of them is also in the extension of P. I show how importing this idea into the semantics of numerals provides a semantic means of dissolving the paradox.