Are concepts stable entities, unchanged from context to context? Or rather are they context-dependent structures, created on the fly? We argue that this does not constitute a genuine dilemma. Our main thesis is that the more a pattern of features is general and shared, the more it qualifies as a concept. Contextualists have not shown that conceptual structures lack a stable, general core, acting as an attractor on idiosyncratic information. What they have done instead is to give a contribution to the comprehension of how conceptual structure organized around such a stable core can produce contextually appropriate representations on demand.