 There are some problems for the set-theoretic paraphrase. Suppose one truly says “the melted sugar here is the same sugar that was in the packet.” If ‘sugar’ in this context referred to the various lumps and grains of sugar in a packet, then, if there are no more lumps or grains after the melting, then the set-equality, and hence the identity-claim, comes out false. As Pelletier points out, when we identify some stuff, there are many different individuating standards available (e.g., ‘packets of ___’, ‘bottles of ___’, ‘granules of ___’), and different divisions will yield different sets (1974, p. 94). This ends up either under-determining which identities hold, or, absurdly, entailing that some stuff is distinct from itself.