Neural plasticity has been invoked as a powerful argument against nativism. However, there is a line of argument, which is well exemplified by Pinker (The blank slate: the modern denial of human nature, Penguin, New York, 2002) and more recently by Laurence and Margolis (in: Laurence and Margolis (eds) The conceptual mind: new directions in the study of concepts, MIT, Cambridge, 2015) with respect to concept nativism, according to which even extreme cases of plasticity show important innate constraints, so that one should rather speak of "constrained plasticity". According to this view, cortical areas are not really equipotential, they perform instead different kinds of computation, follow essentially different learning rules, or have a fixed internal structure acting as a filter for specific categories of inputs. We intend to analyze this argument, in the light of a review of current neuroscientific literature on plasticity. Our conclusion is that Laurence and Margolis are right in their appeal to innate constraints on connectivity-a thesis that is nowadays welcome to both nativists (Mahon and Caramazza in Trends Cogn Sci 15:97-103, 2011) and non-nativists (Pulvermüller et al. in Biol Cybern 108:573-593, 2014)-but there is little support for their claim of further innate differentiation between and within cortical areas. As we will show, there is instead strong evidence that the cortex is characterized by the indefinite repetition of substantially identical computational units, giving rise in any of its portions to Hebbian, input-dependent plasticity. Although this is entirely compatible with the existence of innate constraints on the brain's connectivity, the cerebral cortex archi-B Alessio Plebe 123 Synthese tecture based on a multiplicity of maps correlating with one another has important computational consequences, a point that has been underestimated by traditional connectionist approaches.