Are the number words learnable? Bart Geurts University of Nijmegen Abstract It is widely held that children learn the concept of natural number by inductive inference from their knowledge of the first few numbers, helped by their ability to count. Rips et al. (2006) argue that this view is wrong, and I argue that their argument is wrong. What do number words mean? If a panel of linguists, psychologists, and philosophers was convened, it is more than likely that they would soon con- verge on an answer along the following lines: (1) The n -th number word denotes that property which a collection x has iff card(x) = n. (Here “iff” is short for “if and only if”, and “card(x)” is the number of individuals in x.) This answer is not unproblematic in every respect: in particular, the notion of “collection” raises some rather deep issues. But apart from that, (1) surely represents the majority view across disciplines. Natural though it may seem, this consensus shouldn’t be taken for granted, for there are perfectly reasonable alternatives. For example, one might view number words as being on a par with quantifiers like all, and for some time it was fashionable, in some circles at least, to construe two as “two or more”. But such dissident views are becoming increasingly marginal (Geurts 2006). Next question: How do children learn number words and the associated concepts? This question, too, has a standard answer, according to which the acquisition process involves three parts. First, children learn to recite the count words in sequence. Secondly, learning the meanings of the first January 23, 2007