 Problems arise even with continua of properties where there is no independent reason to posit different degrees of naturalness. Consider mass. If we assign all mass-interval properties like having a mass between 100 and 105 kg positive naturalness scores, we will get the disastrous result that any two objects that differ in mass are dissimilar to the same, infinite, degree. But if we assign them all a score of zero, it seems impossible to recover the intuitive judgment that objects whose masses differed by only 1% could resemble more closely than any objects whose mass differed by 10% possibly could. We might hope to thread the needle by saying that most mass-interval properties score zero but a few (countably many) are natural enough to get positive scores. But this seems to require invidiously privileging some units for mass over others, and will still make for counterintuitive discontinuities in the similarity measure as discussed under  (c).[15] 