The debate about concepts has always been shaped by a contrast between subjectivism, which treats them as phenomena in the mind or head of individuals, and objectivism, which insists that they exist independently of individual minds. The most prominent contemporary version of subjectivism is Fodor's RTM. The Fregean charge against subjectivism is that it cannot do justice to the fact that different individuals can share the same concepts. Proponents of RTM have accepted shareability as a ‘non-negotiable constraint’. At the same time they insist that by distinguishing between sign-types and – tokens the Fregean objection cannot just be circumvented but revealed to be fallacious. My paper rehabilitates the Fregean argument against subjectivism. The RTM response rests either on an equivocation of ‘concept’—between types which satisfy the non-negotiable constraint and tokens which are mental particulars in line with RTM doctrine—or on the untenable idea that one and the same entity can be both a shareable type and hence abstract and a concrete particular in the head. Furthermore, subjectivism cannot be rescued by adopting unorthodox metaphysical theories about the type/token and universal/particular contrasts. The final section argues that concepts are not representations or signs, but something represented by signs. Even if RTM is right to explain conceptual thinking by reference to the occurrence of mental representations, concepts themselves cannot be identical with such representations.