In this unashamed polemic I argue that most extant plant species currently represented by a Linnean binomial exist only at the most basic level of a primary hypothesis that has not yet been subjected to the crucial test of circumscription. Rigorous circumscription requires sampling of numerous populations across the full range of a putative species and its supposed close relatives for several properties, including analytical morphology and genetics, preferably supported by gene exchange experiments and autecological observations. In the absence of genuine, demonstrable discontinuities in at least one biologically meaningful property, perceived species boundaries remain entirely arbitrary, thereby hindering rather than assisting every kind of biological investigation. The term 'cryptic species' has many implied definitions, but in my opinion it simply boils down to the many situations where limited morphological and molecular differentiation leave the analyst unsure whether credible species boundaries exist among the representative individuals analysed. The lack of obvious discontinuities typically reflects ongoing gene-flow and/or low levels of extinction of intermediate lineages. At present, the status of a putative species is rarely subjected to critical appraisal through the lens of any specified species concept or evolutionary mechanism, despite the widely accepted primacy of species in systematic biology.