Can we make sense of MacFarlane's relative truth?

John MacFarlane's truth relativism (2005, 2007, 2011, 2014) makes use of two notions of propositional truth: a monadic assessment sensitive one taken to be our ordinary truth notion, and a non-monadic one that is meant to account for the assessment sensitivity of the former notion. Some authors (Cappelen and Hawthorne, 2009, 2011; Montminy, 2009; Soames, 2011) contend that any theory introducing a technical non-monadic truth notion has to make sense of it (i.e. show that it is a truth notion) by defining or characterizing it in terms of ordinary monadic truth. First, I give some reasons why the relativist should not discard this approach to make sense of the notion of truth relative to a context of assessment. Second, I argue that an illuminating characterization of this notion must provide an answer to a dilemma Paul Boghossian (2011) poses to the relativist. Third, I single out the characterization that can answer this dilemma. Finally, I contend that the relativist still needs to show that this solution works for each case subject to a relativist treatment.