 One way of bringing system into the discussion of criteria of identity is to make use of the distinction between one-level and two-level criteria of identity (Williamson 1990, Lowe 2012). The Fregean criteria of identity for directions and numbers are two-level. The objects for which the criterion is given are distinct from, and can be pictured as at a higher level than, the entities between which the relation specified holds. A two-level criterion for the Fs takes the form (restricting ourselves to examples in which the criterial relation holds between objects):