This paper is a study of Brentano’s ontology, and more specifically of his theory of substance and accident as put forward toward the end of his life in the materials collected together as the Kategorienlehre or Theory of Categories. Here Brentano presents an auditious (re-)interpretation of Aristotle’s theory of substance and accidence. We show that on the view Brentano initially defends, it is space which serves as the single substance upon which all other entities depend as accidents. In an appendix, (...) however, Brentano puts forward an even more radical suggestion, inspired by the physics of Kelvin. According to this final view, space itself is an accident of a deeper substance: the present time. (shrink)