Free logics reject the classical assumption that every term of a given first-order language refers to an individual in the domain of quantification. According to the Quinean interpretation of the quantifiers, this move amounts to the rejection of the idea that every term must always denote an existent object. On the other hand, paraconsistent and paracomplete logics differ from classical logic by rejecting the validity of the principles ofexplosion and excluded middle, respectively. Although paraconsistent and paracomplete logics are usually characterized as subsystems of classical logic, some paraconsistent logics (that may also be paracomplete), the so-calledLFIs (LFIUs), are sufficiently expressive to allow recovering every classical inferences in certain circumstances. In this talk, I present free versions of some LFIs and indicate some of its potential philosophical applications. Specifically, we shall discuss how the existence predicate E, that is often used in the formulation of free logics, may be combined with the LFIs’ consistency (classicality) operator to allow specifying the scope of classical logic in terms of the kinds of object one is reasoning about. As we shall see, in the systems to be presented, although every classical inference turns out to be valid with respect to objects that satisfy E(i.e., objects that really exist), violations of certain classical principles may still occur whenever objects that fail to do so are concerned.