The arrival of embodied, enactive and extended accounts of minds has sparked interest in how such new thinking about minds might influence and reshape our thinking about the production and appreciation of art. This paper clarifies why radically enactive approaches to aesthetics ought to be favoured. This is achieved in three stages. First, a properly enactive vision of aesthetics is distinguished from weaker, embodied and extended accounts of art. The latter are shown to be compatible with the strongest and most ambitious versions of internalism about artful minds (section "More than Embodied and Extended Artful Minds"). Second, the commitments of ambitious versions of neuroaesthetics – theories that attempt to understand artful minds as wholly internal and neurally based – are examined. It is revealed that ambitious neuroaesthetic theories, those that endorse the representational theory of mind and essentialism about art, are incompatible with a radically enactive aesthetics (section "Neuroaesthetics"). Third, an analysis is provided to show how commitment to representationalism of a Cartesian stripe is the true source of the internalist and disembodied vision of artful minds promoted by ambitious neuroaesthetic theories (section "Essentially Disembodied Minds"). Finally, readers are directed to general arguments – provided in other works – for favouring the anti-representationalist radical enactivism over the theories of mind assumed by ambitious neuroaesthetic theories (section "Radically Enactive Aesthetics").