 At first blush this response seems somewhat desperate. Haven’t the respective conditions been defined in such a way that they are simple equivalents by fiat? That would, of course, be the case if \(m\) and \(a\) had been introduced as defined terms into \(h\)-\(r\)-\(w\). But if that were the intention then the likeness theorist could retort that the calculation of distances should proceed in terms of the primitives, not the introduced terms. However, that is not the only way the argument can be read. We are asked to contemplate two partially overlapping sequences of conditions, and two spaces of possibilities generated by those two sequences. We can thus think of each possibility as a point in a simple three dimensional space. These points are ordered triples of 0s and 1s, the \(n\)th entry being 0 if the \(n\)th condition is satisfied and 1 if it isn’t. Thinking of possibilities in this way, we already have rudimentary geometrical features generated simply by the selection of generating conditions. Points are adjacent if they differ on only one dimension. A path is a sequence of adjacent points. A point \(q\) is between two points \(p\) and \(r\) if \(q\) lies on a shortest path from \(p\) to \(r\). A region of possibility space is convex if it is closed under the betweenness relation – anything between two points in the region is also in the region (Oddie 1987, Goldstick and O’Neill 1988).