Expecting moral philosophers to be reliable

Are philosophers’ intuitions more reliable than philosophical novices’? Are we entitled to assume the superiority of philosophers’ intuitions just as we assume that experts in other domains have more reliable intuitions than novices? Ryberg raises some doubts and his arguments promise to undermine the expertise defence of intuition-use in philosophy once and for all. In this paper, I raise a number of objections to these arguments. I argue that philosophers receive sufficient feedback about the quality of their intuitions and that philosophers’ experience in philosophy plausibly affects their intuitions. Consequently, the type of argument Ryberg offers fails to undermine the expertise defence of intuition-use in philosophy.

Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.