Full Idea
The usual objection to taking properties as sets is that different properties may happen to be coextensive. Creatures with hearts are creatures with kidneys. Talking donkeys are flying pigs (since there are none). Yet the properties differ.
Gist of Idea
Properties don't seem to be sets, because different properties can have the same set
Source
David Lewis (On the Plurality of Worlds [1986], 1.5)
Book Reference
Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.51
A Reaction
This is the difficulty which Lewis proposes to solve by defining properties across possible situations as well as actual ones, so that the properties can come apart. Nice move.