Full Idea
Most sets are uninteresting because they are utterly heterogeneous, that is, the members have nothing in common. For most sets there is no common property F, such that the set is the set of all the Fs.
Gist of Idea
In most sets there is no property common to all the members
Source
David M. Armstrong (Properties [1992], §1)
Book Reference
'Properties', ed/tr. Mellor,D.H. /Oliver,A [OUP 1997], p.161
A Reaction
One might link the interesting sets together by resemblance, without invoking the actual existence of an item F which all the members carry (like freemasons' briefcases). Personally I am only really interested in 'natural' sets.