If there are infinitely many forms of oneness, then there must be more than one form corresponding to the property of being one.

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