Full Idea
A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought.
Gist of Idea
A set is a collection into a whole of distinct objects of our intuition or thought
Source
George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2
Book Reference
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.22
A Reaction
This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects.