 One broad sort of objection, if it should be called that, is that rigidity does, in some respect, the work attributed to it; but rigidity is superfluous to the task of explaining that work because the work is the result of other, more fundamental phenomena (for different approaches along these lines, see Jylkkä 2008, pp. 69–72; Schwartz 2002; Soames 2002, e.g., pp. 310–11). For all this objection tells, rigidity might remain interesting as a special case of more fundamental phenomena.  More damaging for property rigidity would be its rejection in favor of competing mechanisms alleged to do comparable work (Haukioja 2012; Nimtz 2019).