 Armstrong (Armstrong, Martin &amp; Place 1996, chapter 3) puts forward one argument for the identity of dispositions with their causal bases that basically goes as follows: since dispositions are by definition properties that play certain causal roles, and since in fact their causal bases are what play those roles, it follows that dispositions are in fact identical with their causal bases. Armstrong claims that his identification of dispositions with their causal bases is a ‘contingent identification’ (Armstrong et al. 1996, p. 39): As a matter of fact the property that plays the brittleness role is such-and-such, but it might have been a different property that played that role; if so, brittleness would have been identical with that different property. This feature of Armstrong’s view exposes it to Prior et al.’s (1982) argument from rigid designation. Following Kripke, Prior et al. take names of properties to be ‘rigid designators’, referring to the same property in every possible world (in which that property exists). As Kripke (1972) demonstrates, if \(a\) and \(b\) are rigid designators then the identity statement \(a = b\) is necessarily true if it is true at all. So on the assumption that, for example, ‘brittleness’ and ‘microstructural property so-and-so’ are rigid designators, the possibility that the causal basis for brittleness might have been something other than microstructural property so-and-so shows that brittleness is not identical with microstructural property so-and-so. (See McKitrick 2003b for a reply to this argument. For additional arguments against Armstrong’s view, see Prior et al. 1982 and Prior 1985; for discussions on them, see Mumford 1998, chapter 5 and McKitrick 2003b.)