Rom Harré thinks that the Emergence–Reduction debate, conceived as a vertical problem, is partly ill posed. Even if he doesn’t wholly reject the traditional definition of an emergent property as a property of a collection but not of its components, his point is that this definition doesn’t exhaust all the dimensions of emergence. According to Harré there is another kind (or dimension) of emergence, which we may call—somewhat paradoxically—“horizontal emergence”: two properties of a substance are horizontally emergent relative to each other if they cannot be displayed in the same conditions. Contrary to vertical emergence, horizontal emergence is a symmetrical relation. Harré endorses horizontal emergentism. I argue that this position faces a principled difficulty: it makes it impossible to bind different horizontally emergent discourses in an interesting way. Physics and biology for example become “island” discourses, each speaking of a distinct kind of entities. The only way to ensure that two different discourses can relate to the same entity is to reintroduce verticality into the picture.