Abstract: The natural properties, according to Peter Gardenfors and Graham Oddie, are the convex subsets of a metric space in which the distances are degrees of dissimilarity. In this paper, I argue that this definition is incompatible with definitions of degree of dissimilarity as number or proportion of properties not in common, since in combination with them it entails that every property is a natural property, which is absurd. I suggest it follows that we should think of the definition of natural properties as convex subsets of metric space in which the distances are degrees of dissimilarity as a variety of resemblance nominalism.