Meaningful quantification of species diversity requires that both ‘species’ and ‘diversity’ are unambiguously defined. Rigorous rules of nomenclature exist to ensure that each species has a single unique name, but the naming of concepts is much more variable. As a consequence, ‘diversity’ has been defined in so many different ways that its ability to transfer accurate information has been compromised. This problem can be solved by defining ‘diversity’ as the effective number of species (or other types of interest), and using the term ‘true diversity’ to specify that this narrow concept is being used (analogously to using the term ‘true bugs’ when adhering to a narrow circumscription of ‘bugs’). Other measures related to diversity (such as entropies and probabilities) continue to be useful, but they represent different phenomena and should therefore be referred to by different names. Total species diversity in a dataset can be partitioned into two components in several different ways. The components of a specific multiplicative partitioning can be called true alpha diversity and true beta diversity. When the partitioning is done in some other way, the resulting components are different and should be called by other names. For example, the beta component of additive partitioning does not equal true beta diversity, but can logically be called species turnover. All the phenomena that have been called ‘beta diversity’ in the ecological literature have also been called by alternative unique names. Consequently, a consistent terminology is already available; only a general agreement to use it is lacking.