Can all the universities that claim to be "world-class" actually live up to the claim? If they could, would that be desirable public policy? It could be that there are so many different meanings of "world-class" that the term in practical effect is an oxymoron: the definition of "world" is determined locally when conceptually it should be defined internationally. This paper discusses different kinds of institutional quality, how quality is formed and how it can be measured, particularly by comparison. It also discusses the subtle but fundamental differences between quality and reputation. The paper concludes with the suggestion that world-class comparisons of research quality and productivity are possible, but that any broader application to the "world-class" quality of universities will be at best futile and at worst misleading.