Many schools of modern linguistics generally adopt a rigid approach to categorisation by not allowing degrees of form class membership, degrees of resemblance to a prototype or overlaps between categories. This all-or-none conception of categorisation (Bolinger 1961) goes back to Aristotle, and has been pervasive and influential, especially in formal linguistics. The alternative view, prevalent amongst descriptive and cognitive linguists, is to posit grammars which pervasively display categorial vagueness, more usually called gradience. In this article I will begin by briefly tracing some of the ideas on gradience in linguistics and philosophy. I will then argue, firstly, that gradience should have a role to play in language studies (both descriptive and theoretical). Secondly, I will show that two types of category fluidity should be distinguished. One type I will call Subsective Gradience (SG). It is intra-categorial in nature, and allows for members of a class to display the properties of that class to varying degrees. The other type is called Intersective Gradience (IG). This is an inter-categorial phenomenon which is characterised by two form classes ‘converging’ on each other. Thirdly, I will argue that while the two types of gradience are grammatically real, IG is not as widespread as is often claimed. Finally, in this article I will attempt to be more precise about the vague phenomenon of gradience. To this end I will devise a formalisation of SG and IG, using a number of case studies mainly from English. The formalism makes use of morphosyntactic tests to establish whether an item belongs to a particular class or to a ‘bordering’ one by weighing up the form class features that apply to the item in question. This article can be seen to argue for a midway position between the Aristotelian and the cognitivist conceptions of categorisation in that I will defend a position that allows for gradience, but nevertheless maintains sharp boundaries between categories. The ideas put forward in this article have wider implications for the study of language, in that they address the problem posed by the existence of a tension between generally rigidly conceived linguistic concepts and the continuous phenomena they describe.