Full Idea
To be a universal, a resemblance must hold between many pairs of white things. We can't say there is a different resemblance between each pair, since the resemblances must resemble each other, so we are forced to admit that resemblance is a universal.
Gist of Idea
'Resemblance Nominalism' won't work, because the theory treats resemblance itself as a universal
Source
Bertrand Russell (Problems of Philosophy [1912], Ch. 9)
Book Reference
'A Companion to Metaphysics', ed/tr. Kim,Jaegwon/Sosa,Ernest [Blackwell 1995], p.55
A Reaction
Apparently this objection is much discussed and controversial. It looks like a threat to any theory of universals (involving 'sets', or 'concepts', or 'predicates'). We seem to need 'basic' and 'derivative' universals. Cf Idea 7956.
Related Ideas
Idea 7956 If all and only red things were round things, we would need to specify the 'respect' of the resemblance [Goodman, by Macdonald,C]
Idea 12661 The different types of resemblance don't resemble one another [Fodor]
Idea 19253 We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce]