  The right sides of (O) and (O′) are conjunctions. The intuitive content of (O) is simple in spite of its formal complexity. It establishes that the sentence “A is a” is equivalent to the following conditions (a) A is not an empty term; (b) there is only one A; (c) whatever is A, is also a. Thus, “A is a” is a singular sentence which is true if and only if (a)-(c) hold. In particular, such a sentence is false if A is a general or an empty term. On the other hand, (O) (or O′) is valid for all terms, even general or empty ones. Thus, LO is valid in all domains, including the empty one and can be regarded as the first system of free logic. In LO we can define two important concepts, namely that of existence and that of being an object. This is done by (I use non-symbolic forms): (1) for any A, A exists = for some x, x is A; (2) for any A, A is an object = for some x, A is x. LO performs functions usually provided by predicate logic. The meaning of the constant ε is sufficiently general to define identity and the inclusion of classes. Since these concepts are definable in elementary ontology, it is stronger than first-order logic.