 In addition to this taxonomical work, Fallis also argues for the philosophical thesis that gaps in proofs are not necessarily a bad thing. Building on (iii) above, he introduces the notion of a universally untraversed gap, in other words a gap that has not been bridged by any member of the mathematical community. Fallis claims that such gaps are not unusual and that at least some of the time proofs containing them are accepted by mathematicians in a justificatory context. This view is borne out in more recent work by Andersen (2018).