  Roughly, Vaihinger reconstructs the argument as follows: (1) Some differences in the spatial properties of objects cannot be known through the pure understanding; (2) All differences between things in themselves can be known through the pure understanding; (C) Space is not a thing in itself. Premise (2), however, violates Kant’s noumenal ignorance doctrine, according to which things in themselves cannot be known through the understanding’s categories. Thus, Vaihinger concludes, “this assumption [that things in themselves are knowable through the pure understanding] is obviously anathema to Kantian criticism, and an archaic reversion to dogmatism” (1881–92, 2:528). More specifically, his claim is that the premise is residue from Kant’s view in the 1770 Dissertation, according to which things in themselves are objects as the pure understanding knows them (1881–92, 2:354, 453, 522).