Talk:Class

There are a couple problems with my understanding Copi’s definition of a “class”. First, Copi distinguishes between a class C and the mathematical object 1 contained within C. I can’t think of any examples of classes in which 1 is different from C.  Also, if 1 = C, then C must contain itself as a member. This is not actually a contradiction as there is nothing preventing a class from containing itself as a member.

Second, sets are typically considered to be “small classes”. However, the axiom 0 ≠ 1 specifically rules out singleton sets as a Copi class. Again, this is not actually a contradiction as there is no requirement that all sets be classes. However, sets are generally regarded as classes. One way to resolve this problem is to refer to Copi classes as “non-trivial classes” and refer to singleton sets and “the” empty set as trivial classes. A class could then be formally defined as a mathematical object which is either a trivial class or a non-trivial class. Unfortunately, Copi did not elect to use this terminology. --173.206.237.178 23:16, 19 June 2011 (UTC)