One of the major problems confronting biologists is that of classifying organisms. This is usually done in a hierarchical manner. First, organisms are grouped together into classes (called 'taxa' by biologists) which are assumed to be incapable of significant subdivision; then, these classes are in turn grouped so that the members of a number of classes at the lowest level also form a class at the next higher level. This process is repeated until, at the highest level, all organisms are grouped into a very few large classes. The classes at what is usually the lowest level are called 'species', and it is primarily with these that we are concerned in this paper. Species give rise to two major problems. In the first place, one must decide on criteria for the inclusion (or exclusion) of a particular organism into a particular species. In the second place, one has to put such criteria of demarcation into practice. Obviously, the two problems are not entirely separate, since there would be little point in choosing criteria which were, for practical reasons, impossible to apply. However, here we shall ignore the second problem and discuss only the first. I believe that, in the course of the discussion, light will be shed not only upon the nature of the concepts used for biological classification, but upon scientific concepts in general.