In The Principles of Mental Physics [Wells (2009), chapter 11], I explained that Comparation is the synthesis of mathematical equivalence relations. This mathematical definition is an abstract definition begging the question of equivalence. All objects are equivalent in some contexts and inequivalent in others. The definition of mathematical equivalence does not specify a context for the relation and, therefore, does not speak to the manner in which two comparands are to be regarded as being in equivalence. A father and son are "equivalent" in the context of belonging to the same family and "inequivalent" in the context of individuality. Thus we have both ⟨ father = son ⟩ and ⟨ father ≠ son ⟩ (likeness and non-likeness) depending on the context of comparison.
