Abstract: Contemporary semantic analyses of number words, such as ‘four’, can be divided into two kinds. On the first (substantivalism), the lexical meaning of ‘four’ is that of a numeral naming a number as a primitive semantic entity, and all other meanings of ‘four’ are derivable from that numeral via type-shifting. On the second kind (adjectivalism), the lexical meaning of ‘four’ is that of a predicative adjective true of pluralities having exactly four countable parts, and all other meanings of ‘four’ are derivable from that adjective via type-shifting. Although both kinds of analyses provide significant empirical coverage, both also suffer from crippling theoretical difficulties. Specifically, substantivalism requires a non-uniform analysis of adjectival nominalization, while adjectivalism not only threatens an infinite regress, it also appears to make numerous false semantic predictions. In this talk, I sketch a novel version of adjectivalism which avoids these problems. I conclude by suggesting that the semantics also has surprising, important consequences for the philosophy of mathematics and developmental psychology.