Purity-F is false.

Yet another alternative is that detailed logical analysis of the Deductions reveals arguments sufficient to establish both that the one is and, importantly, that principles such as Purity-F and Uniqueness are false. As Rickless (2007, 136–137 and 211) argues, Purity-F is a background premise of both D1 and D4. Taken together, then, D1 and D2 are sufficient to establish that a contradiction follows from the hypothesis that the one is, on the assumption that Purity-F is true. That is, D1 and D2 to