Once we accept the idea that forced expansions are an important manifestation of human rationality, we need a theory of concepts, reference, and thought to accommodate them. In this chapter I present a picture of this sort for the notions of concepts and reference, trying to make it as close as possible to Frege's realism and extensionalism for concepts. In chapter 8 I shall examine its implication for the notion of thought. Let me state at the outset that I do not pretend that the picture I shall propose in the following chapter is the best that could be formulated, but I do claim that it is a better idealization than Frege's. Later I will discuss the implications of forced expansions for definitions, focusing on Wittgenstein's thesis that definitions are not always feasible because of the ever-present possibility of expansion. I shall argue that the view he offers in connection with his notion of family resemblance cannot be derived from the expansion of concepts. Afterwards I will briefly examine two pictures of concepts that give an important place to non-arbitrary expansions but which are not faithful to Frege's realism.

STAGES OF CONCEPTS

If the development of concepts is not to be described merely as the replacement of one concept by another, must we accept the strange idea that the same concept can have different extensions?