As we saw in the Introduction, Frege summarily dismissed any notion of conceptual expansions. Since his theory is the simplest and the strongest, it will be useful to begin with it. There is another reason for beginning with Frege's position. Even though Frege started out by questioning the nature of numbers and attempting to understand deduction, he was the first to do so on the basis of a broader view of language, thought, and reference. In this respect no logician prior to Frege was better able to provide a philosophical dimension to the issue of expansions, which can be useful for the philosophy of language. Thus, examining Frege's opposition to expansions should be a natural way of getting into the philosophical discussions of expansions, some of which were mentioned in the previous chapter.

Frege presents three arguments to demonstrate that the idea of the expansion of concepts is incoherent. These arguments can be separated from Frege's inner motivations for abolishing the idea, and therefore deserve careful study. I present them in order of importance, beginning with the least important.

THE ARGUMENT FROM REALISM

Frege's realism about concepts and their place in the world of reference leads naturally to the notion that concepts cannot change, and thus cannot be expanded. Once concepts are detached from the thinking subject, they do not undergo the developments that subjects do.