 At this point some confusion is natural about what relevant logicians are attempting to do. The variable sharing principle is only a necessary condition that a logic must have to count as a relevance logic. It is not sufficient. Moreover, this principle does not give us a criterion that eliminates all of the paradoxes and fallacies. Some remain paradoxical or fallacious even though they satisfy variable sharing. As we shall see, however, relevant logic does provide us with a relevant notion of proof in terms of the real use of premises (see the section “Proof Theory” below), but it does not by itself tell us what counts as a true (and relevant) implication. It is only when the formal theory is put together with a philosophical interpretation that it can do this (see the section “Semantics for Relevant Implication” below).