In his famous work on vagueness, Russell named 'fallacy of verbalism' the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories - the non-adjunctive and relevant approaches, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of their underlying semantics. The meaning of 'intuitive reading' is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsis-tentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense - therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of para-consistencv - and this could be a welcome result for a dialetheist.