The more profound and important laws of nature are often expressible in the form of simple identities; in addition to some instances which have already been given, I may suggest, Crystals of cubical system = Crystals not possessing the power of double refraction. All definitions are necessarily of this form, whether the objects defined be many, few, or singular. Thus we may say, Common salt = Sodium chloride. Chlorophyl = Green colouring matter of leaves. Square = Equal-sided rectangle. It is an extraordinary fact that propositions of this elementary form, all-important and very numerous as they are, had no recognised place in Aristotle’s system of Logic. Accordingly their importance was overlooked until very recent times, and logic was the most deformed of sciences. But it is impossible that Aristotle or any other person should avoid constantly using them; not a term could be defined without their use. In one place at least Aristotle actually notices a proposition of the kind. He observes: “We sometimes say that that white thing is Socrates, or that the object approaching is Callias.”[51] Here we certainly have simple identity of terms; but he considered such propositions purely accidental, and came to the unfortunate conclusion, that “Singulars cannot be predicated of other terms.” [51] *Prior Analytics*, i. cap. xxvii. 3. Propositions may also express the identity of extensive groups of objects taken collectively or in one connected whole; as when we say, The Queen, Lords, and Commons = The Legislature of the United Kingdom. When Blackstone asserts that “The only true and natural foundation of society are the wants and fears of individuals,” we must interpret him as meaning that the whole of the wants and fears of individuals in the aggregate form the foundation of society. But many propositions which might seem to be collective are but groups of singular propositions or identities. When we say “Potassium and sodium are the metallic bases of potash and soda,” we obviously mean, Potassium = Metallic base of potash; Sodium = Metallic base of soda. It is the work of grammatical analysis to separate the various propositions often combined into a single sentence. Logic cannot be properly required to interpret the forms and devices of language, but only to treat the meaning when clearly exhibited. *Partial Identities.*