Rossella Marrano (Scuola Normale Superiore Pisa) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Degrees of Truth Explained Away". Abstract: The notion of degrees of truth arising in infinite-valued logics has been the object of long-standing criticisms. In this paper I focus on the alleged intrinsic philosophical implausibility of degrees of truth, namely on objections concerning their very nature and their role, rather than on objections questioning the adequacy of degrees of truth as a model for vagueness. I suggest that interpretative problems encountered by the notion are due to a problem of formalisation. On the one hand, indeed, degrees of truth are artificial, to the extent that they are not present in the phenomenon they are meant to model, i.e. graded truth. On the other hand, however, they cannot be considered as artefacts of the standard model, contra what is sometimes argued in the literature. I thus propose an alternative formalisation for graded truth based on comparative judgements with respect to the truth. This model provides a philosophical underpinning for degrees of truth of structuralist flavour: they are possible numerical measures of a comparative notion of truth. As such, degrees of truth can be considered artefacts of the model, thus avoiding the aforementioned objections.