Abstract
In this paper one of the popular conceptions of rigidity of general names is presented and discussed. According to this view general terms\' rigidity consists in the fact that they have the same abstract designatum (namely a kind or a property) in all possible words. It is argued that the view which says that all general names are in fact abstract names is no good, because (i) in postulating the existence of abstract designatum, it \'multiplies entities beyond necessity\', (ii) it either trivialises the notion of rigidity or else entangles us in an unresolvable discussion as to the nature of universals, (iii) is ad hoc, and (iv) rigidity defined in this conception cannot play any of the roles that Kripke wanted the notion of rigidity for general terms to play