Art's relationship with education is often characterised by paradox. Yet art is often reified within an education system that refuses to see the pedagogical strengths of paradox. This article approaches art education from three positions. The first is that art is a construct that is neither natural nor necessary. The second is that there are no aesthetic or pedagogical imperatives, but that art education is the recognition of groundlessness where paradox facilitates learning. The third approach is to reposition art with regards to its relationship with learning, education and schooling. Here it is argued that art's only choice is to deschool learning. The latter is moved by an underlying dilemma as to whether art, considered as an autonomous human act, could ever engage with systems of learning without being turned into a tool or a thing. Unless art education is deschooled, the teaching and learning of art remains trapped between the assumptions of process and product. So the idea of art and education as shared practices within schooling remains somewhat dubious unless art's practices are recognised in parts perceived as wholes and where conclusions are marked by open-endedness. No possibilities for art or learning could ever emerge unless a radically different set of conditions give way to a state of affairs where knowledge is a matter to be discovered but never determined, and where a fixed ground is transformed into a wide horizon.