Full Idea
Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory.
Gist of Idea
Predicativism makes theories of huge cardinals impossible
Source
David Bostock (Philosophy of Mathematics [2009], 8.3)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.251
A Reaction
I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible?