In this paper I present a dialogical formulation of free logic which allows a straightforward combination of paraconsistent and intuitionistic logic-I call this combination Frege's Nightmare. The ideas behind this combination can be expressed in few words: in an argumentation, it sometimes makes sense to restrict the use and introduction of singular terms in the context of quantification to a formal use of those terms. That is, the Proponent is allowed to use a constant for a defence (of an existential quantifier) or an attack (on a universal quantifier) iff this constant has been explicitly conceded by the Opponent. When the Opponent concedes any constant occurring in an atomic formula he concedes tertium non-datur (for this formula) to. This yield a free-logic which combines classical (for propositions with singular terms for realities) with intuitionistic logic (for propositions with singular terms for fictions). This extended free-logic can be also combined with paraconsistent logic in such a way that contradictory objects can be included in the domain of fictions. The idea is here to combine the concept of formal use of constants in free logics and that of the formal use of elementary negations in paraconsistent logics.