The dominant model of curriculum design in the last century assumed that school education could be organized around aims, defined primarily in terms of students' behaviour. The credentials of this model were questioned by, among others, Lawrence Stenhouse, who pointed out that education serves purposes that cannot be stated in terms of behavioural objectives. In this article, I offer support for Stenhouse's conclusion and go beyond it, showing that if education aims at critical understanding of its own value, then it is even more radically open-ended than Stenhouse argued. My argument is based on two premises. One of them is that the reason why people disagree about what education involves is that they have less-than-perfect knowledge of what human characteristics are worth cultivating. This premise is supported by a theory of meaning advanced by Hilary Putnam. The other premise is that one of the aims of education is intellectual independence. From these premises, I conclude that a successful course of education serves purposes that cannot be completely stated in advance.