Although modal logicians have traditionally been interested in counterfactuals, only recently has the application of possible world semantics to the problem of counterfactuals begun to yield formal semantics which appear to capture the truth conditions of ordinary English counterfactuals.1 The advance has been brought about by defining similarity structures on sets of possible worlds. This use of similarity among possible worlds in the analysis of counterfactuals has been the subject of considerable theoretical development. Through the work of Lewis, Stalnaker, van Fraassen, Thomason, et. al. , the basic idea has been modified and generalized in the direction of higher order quantification (over modalities), various indexings for selection functions, impossible worlds as limits of sequences of possible worlds, counternecessaries, countercomparatives, counterfactual probabilities, and so on, all accompanied by elegant model-theoretic notions and axiomatics. Our natural tendency to preserve the products of great labor is, in this case, reinforced by the power and elegance of the theories themselves. But however elegant and powerful the similarity approach is in its full theoretical development, there are difficulties at its foundations-difficulties which cast doubt on the use of the notion of comparative similarity of possible worlds in the analysis of counterfactuals. This paper, then, is concerned to point out some of these difficulties, which surround the basic assumptions of the similarity approach in its application to the problem of counterfactuals. I shall not be arguing that the similarity approach does not capture the logic of counterfactual inference. In fact it