 However this issue unfolds, externalism about empty concepts faces a further challenge (Segal 2000, pp. 54–56). Consider: Either the externalist sees the unicorn-concept as necessarily empty or  not.[15]  If the former, then the view implies that unicorns are impossible objects, like round squares. And that is rather counterintuitive (yet see Kripke 1972 on unicorns). But taking the other horn (sorry), a contingently empty concept would have its content fixed by descriptors like “horse with a horn.” In this case, EXT seems false. For the constancy of the descriptors guarantees that the concept has the same content in every possible world, whether or not it contains unicorns (Segal 2000; see also Besson 2012). (But for replies, see Korman 2006 and Parent 2015a, 2017, ch. 4.)