 There is plenty of room for variation, for MFD fails to specify truth conditions for atomic formulas (including identities) when they contain empty descriptions, and there are many ways to do it. Making all atomic formulas containing empty descriptions false yields a negative free description theory axiomatizable by adding (LL) to NFL (Burge 1974, Lambert 2001h). The result is essentially Bertrand Russell’s theory of definite descriptions, but with the description operator taken as primitive rather than contextually defined.