Full Idea
The fallacy of division is the claim that what is true of a set must therefore be true of its members.
Gist of Idea
What is true of a set is also true of its members
Source
PG (Db (ideas) [2031])
Book Reference
A Reaction
Clearly a fallacy, but if you only accept sets which are rational, then there is always a reason why a particular is a member of a set, and you can infer facts about particulars from the nature of the set