 These two questions arise because of a limitation in the logical form of these Fregean biconditional principles such as Hume’s Principle and Basic Law V. These contextual definitions combine two jobs which modern logicians now typically accomplish with separate principles. A properly reformulated theory of ‘logical’ objects should have separate principles: (1) one or more principles which assert the existence of logical objects, and (2) a separate identity principle which asserts the conditions under which logical objects are identical. The latter should specify identity conditions for logical objects in terms of their most salient characteristic, one which distinguishes them from other objects. Such an identity principle would then be more specific than the global identity principle for all objects (Leibniz’s Law) which asserts that if objects \(x\) and \(y\) fall under the same concepts, they are identical.