Does everything resemble everything else to the same degree?

According to Satosi Watanabe's "theorem of the ugly duckling", the number of predicates satisfied by any two different particulars is a constant, which does not depend on the choice of the two particulars. If the number of predicates satisfied by two particulars is their number of properties in common, and the degree of resemblance between two particulars is a function of their number of properties in common, then it follows that the degree of resemblance between any two different particulars is also constant, which is absurd. Avoiding this absurd conclusion requires questioning assumptions about infinity in the proof or interpretation of the theorem, adopting a sparse conception of properties, or denying degree of resemblance is a function of number of properties in common. After arguing against both the first two options, this paper argues for a version of the third which analyses degree of resemblance as a function of properties in common, but weighted by their degree of naturalness or importance.