One of the compelling aspects of Real Spaces is the way in which it invites us to interrogate the nature and use of concepts in art history. It does this through its construction of a schema of concepts, of varying levels of generality, all linked to the concept of space. Summers’ replacement of one set of concepts, grounded in the visual and the formal, with another, grounded in the spatial, retains ‘the breadth of the general concept, while denying art’s exclusive and reductive association with sight and vision’. This new schema refreshes the ‘analytic and interpretive tools’ that go beyond Eurocentric associations of formalism, allowing ‘many more kinds of art to be meaningfully approached’ and offering a ‘theoretical basis for a more intercultural art history’. Summers’ approach raises important questions for art history’s use of concepts in an ‘intercultural’ or world art history: questions including their character as generals, or universals, their relation to language, their role as categories, their ostensibly ‘Western’ or Eurocentric nature, and the assumptions we make in employing them. I will sketch some of the outlines of this problematic field and register a few points of critique. Rather than general concepts employed within a general theory, I propose that an intercultural art history requires an investment of concepts as ‘vectors’ of thought rather than abstractions. By ‘vector’ (a concept I borrow and repurpose from Gilles Deleuze and Felix Guattari) I mean an orientation with direction, which shapes both the direction of thought and the relation of thoughts to each other. Unlike Summers, I believe that insights from critical theory, in particular poststructuralist philosophies of difference, are important for such a project, as is an ongoing engagement with contemporary art.