Full Idea
The example which presents the most serious challenge to nominalism is 'there are shapes which are never exemplified'.
Gist of Idea
'There are shapes which are never exemplified' is the toughest example for nominalists
Source
J Hoffman/G Rosenkrantz (Platonistic Theories of Universals [2003], 3)
Book Reference
'The Oxford Handbook of Metaphysics', ed/tr. Loux,M /Zimmerman,D [OUP 2005], p.62
A Reaction
To 'exemplify' a shape must it be a physical object, or a drawing of such an object, or a description? If none of those have ever existed, I'm not sure what 'are' is supposed to mean. They seem to be possibilia (with all the associated problems).