The Principle of the Identity of Indiscernibles (hereafter, PII) holds that, if any objects share all the same properties, these objects are identical. To avoid triviality, PII is typically interpreted with the domain of properties restricted to what are usually taken to be qualitative properties. (On PII, see Rodriguez-Pererya (2010), Hawley (2009) and Della Rocca (2005).)