 Suppose that \(x\) is a cube and \(y\) is also a cube. It follows that \(x\) is the same shape as \(y.\) So the relation that \(x\) bears to \(y\) when \(x\) is the same shape as \(y\) is internal in Armstrong’s sense. By contrast, spatio-temporal relations are external (in his sense) because the intrinsic characteristics of \(x\) and \(y\) don’t necessitate how close or far apart \(x\) and \(y\) are. Lewis intends his distinction to classify the same way. If \(x\) is the same shape as \(y\), but \(w\) is not the same shape as z, then there must be some difference in intrinsic nature either between \(x\) and \(w\) or else between \(y\) and \(z\). So the relation that \(x\) bears to \(y\) when \(x\) is the same shape as \(y\) is internal in Lewis’s sense. Lewis also claims that the distance between \(x\) and \(y\) is an external relation because the following conditions are met: (1) \(x\) may be closer to \(y\) than \(w\) is to \(z\) even though \(x\) is an intrinsic duplicate of \(w\), i.e., shares all and only the same intrinsic characteristics, and \(y\) an intrinsic duplicate of \(z\); (2) the distance between \(x\) and \(y\) does supervene upon the nature of the composite \(x+y\). (We’ll return in  section 3  to the question whether, as Lewis claims, distance relation supervene upon the nature of composites.) But the relation that \(x\) bears to \(y\) when \(x\) is the same shape as \(y\) isn’t internal in Moore’s sense because, let us suppose, \(x\) might have been spherical whilst \(y\) remained a cube; so it doesn’t follow from the mere fact that \(x\) exists that \(x\) is the same shape as \(y\).