That self-same objects are like other self-same objects, is an assumption distinct from the Law of Identity, and any interpretation of it that excludes this assumption is to be repudiated. But does not the law of Identity as well as the law of the likeness of mutually exclusive identities presuppose that there are objects self-same, like others, and different from others? Certainly: this is one of the presuppositions of Logic.[6] We assume that the world of which we talk and reason is separated into such objects in our thoughts. We assume that such words as _Socrates_ represent individual objects with a self-same being or substance; that such words as _wisdom_, _humour_, _ugliness_, _running_, _sitting_, _here_, _there_, represent attributes, qualities, characters or predicates of individuals; that such words as _man_ represent groups or classes of individuals. Some logicians in expressing the Law of Identity have their eye specially upon the objects signified by general names or abstract names, _man_, _education_.[7] "A concept is identical with the sum of its characters," or, "Classes are identical with the sum of the individuals composing them". The assumptions thus expressed in technical language which will hereafter be explained are undoubtedly assumptions that Logic makes: but since they are statements of the internal constitution of some of the identities that words represent, to call them the Law of Identity is to depart confusingly from traditional usage.[8] That throughout any logical process a word must signify the same object, is one proposition: that the object signified by a general name is identical with the sum of the individuals to each of whom it is applicable, or with the sum of the characters that they bear in common, is another proposition. Logic assumes both: Aristotle assumed both: but it is the first that is historically the original of all expressions of the Law of Identity in modern text-books.